809 commands extracted from the HP 50g Advanced User's Reference Manual. 408 are implemented in this RPL app. Sections are reproduced verbatim from the PDF.
Command
Returns a solution in polynomials u and v of au+bv =c where a and b are polynomials in the current CAS independent variable, and c is a value.
Level 3/Argument 1: The polynomial corresponding to a. Level 2/Argument 2: The polynomial corresponding to b. Level 1/Argument 3: The value corresponding to c.
Level 2/Item 1: The solution corresponding to u. Level 1/Item 2: The solution corresponding to v.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Find a solution in polynomials u and v for the following equation:
2 2
( x + x + 1 )u + ( x + 4 ) V = 13
| Command | ABCUV(X^2+X+1,X^2+4,13) |
|---|---|
| Result | {-(X+3),X+4} |
IABCUV, EGCD
Function
Absolute Value Function: Returns the absolute value of its argument. ABS has a derivative (SIGN) but not an inverse. In the case of an array, ABS returns the Frobenius (Euclidean) norm of the array, defined as the square root of the sum of the squares of the absolute values of all n elements. That is:
n 2
∑ zi i=1
Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | |x| |
| (x,y) | → | 2 |
| x +y 2 | ||
| x_unit | → | |x|_unit |
| [array] | → | ||array|| |
| `symb` | → | `ABS(symb)` |
NEG, SIGN
Command
Acknowledge Alarm Command: Acknowledges the oldest past-due alarm. ACK clears the alert annunciator if there are both no other past-due alarms and no other active alert sources (such as a low battery condition).
ACK has no effect on control alarms. Control alarms that come due are automatically acknowledged and saved in the system alarm list.
Repeat Alarms Not Rescheduled (–43), Acknowledged Alarms Saved (–44)
None
ACKALL
Command
Acknowledge All Alarms Command: Acknowledges all past-due alarms. ACKALL clears the alert annunciator if there are no other active alert sources (such as a low battery condition). ACKALL has no effect on control alarms. Control alarms that come due are automatically acknowledged and saved in the system alarm list.
Repeat Alarms Not Rescheduled (–43), Acknowledged Alarms Saved (–44)
None
ACK
Analytic Function
Arc Cosine Analytic Function: Returns the value of the angle having the given cosine. For a real argument x in the domain –1 ≤x ≤ 1, the result ranges from 0 to 180 degrees (0 to π radians; 0 to 200 grads). A real argument outside of this domain is converted to a complex argument, z = x + 0i, and the result is complex. The inverse of COS is a relation, not a function, since COS sends more than one argument to the same result. The inverse relation for COS is expressed by ISOL as the general solution s1*ACOS(Z)+2*π*n1 The function ACOS is the inverse of a part of COS, a part defined by restricting the domain of COS such that:
View these graphs with domain and range reversed to see how the domain of COS is restricted to make an inverse function possible. Consider the vertical band in the lower graph as the restricted domain Z = (x, y). COS sends this domain onto the whole complex plane in the range W = (u, v) = COS(x, y) in the upper graph.
Principal Solution (–1), Numerical Results (–3), Angle Mode (–17, –18)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| z | → | acos z |
| `symb` | → | `ACOS(symb)` |
ASIN, ATAN, COS, ISOL
Command
Transforms an expression by replacing acos(x) in subexpressions with π/2–asin(x).
The expression to transform.
The transformed expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Simplify the following expression:
arc cos -- ---- + arc cos ( x ) 2 3
| Command | ACOS2S(ACOS(2/3)+ACOS(X)) |
|---|---|
| Result | π/2-ASIN(2/3)+π/2-ASIN(X) |
ASIN2C, ASIN2T, ATAN2S
Analytic Function
Inverse Hyperbolic Cosine Analytic Function: Returns the inverse hyperbolic cosine of the argument. For real arguments x < 1, ACOSH returns the complex result obtained for the argument (x, 0). The inverse of ACOSH is a relation, not a function, since COSH sends more than one argument to the same result. The inverse relation for COSH is expressed by ISOL as the general solution: s1*ACOSH(Z)+2*π*i*n1 The function ACOSH is the inverse of a part of COSH, a part defined by restricting the domain of COSH such that:
Principal Solution (–1), Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| z | → | acosh z |
| `symb` | → | `ACOSH(symb)` |
ASINH, ATANH, COSH, ISOL
Command
Add List Command: Adds corresponding elements of two lists or adds a number to each of the elements of a list. ADD executes the + command once for each of the elements in the list. If two lists are the arguments, they must have the same number of elements as ADD will execute the + command once for each corresponding pair of elements. If one argument is a non-list object, ADD will attempt to execute the + command using the non-list object and each element of the list argument, returning the result to the corresponding position in the result. (See the + command entry to see the object combinations that are defined.) If an undefined addition is encountered, a Bad Argument Type error results.
Binary Integer Wordsize (–5 through –10)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| { list1 } | { list2 } | → | { listresult } |
| { list } | objnon-list | → | { listresult } |
| objnon-list | { list } | → | { listresult } |
+, ΔLIST, ΠLIST, ΣLIST
Function
Adds two expressions or values, modulo the current modulus.
Level 2/Argument 1: The first expression. Level 1/Argument 2: The second expression.
The sum of the two expressions, modulo the current modulus.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Express the result of the following addition in modulo 7. (x2+3x+6)+(9x+3) Note: Before trying this example, use the CAS modes input form to set the modulo to 7.
| Command | ADDTMOD(X^2+3*X+6,9*X+3) |
|---|---|
| Result | X^2-2*X+2 |
Command
Adds specified global names to the reserved variable REALASSUME. This is a list of the global variables that will be treated by some CAS operations as real numbers when Complex mode is set. If a variable is already in the REALASSSUME list, this command removes any additional assumptions made on it by ASSUME.
Level 1/Item 1: The name of the global variable to be added to the REALASSUME list, or a list of names.
No output in RPN mode, NOVAL in Algebraic mode.
If the “all variables are real” flag is set (flag –128 set), ADDTOREAL will not add anything to the REALASSUME list, as all variables are assumed real anyway. In this case it will only remove further assumptions made by ASSUME.
ASSUME, DEF, STORE, UNASSUME, UNBIND
Command
Displays a menu or list of CAS algebraic operations.
If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered list. If the flag is set, displays the operations as a menu of function keys.
ARIT, CONSTANTS, DIFF, EXP&LN, INTEGER, MAIN, MATHS, MATR, MODULAR, POLYNOMIAL, REWRITE, TESTS, TRIGO
Analytic Function
Common Antilogarithm Analytic Function: Returns the common antilogarithm; that is, 10 raised to the given power. For complex arguments: 10(x,y) = ecx cos cy + i ecx sin cy where c = ln 10.
Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| z | → | 10z |
| `symb` | → | `ALOG(symb)` |
EXP, LN, LOG
Command
Amortize Command: Amortizes a loan or investment based upon the current amortization settings. Values must be stored in the TVM variables (I%YR, PV, PMT, and PYR). The number of payments n is taken from the input together with flag –14.
Financial Payment Mode (–14)
| Level 1/Argument 1 | Level 3/Item 1 | Level 2/Item 2 | Level 1/Item 3 | |
|---|---|---|---|---|
| n | → | principal | interest | balance |
TVM, TVMBEG, TVMEND, TVMROOT
Function
And Function: Returns the logical AND of two arguments. When the arguments are binary integers or strings, AND does a bit-by-bit (base 2) logical comparison.
| bit1 | bit2 | bit1 AND bit2 |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Numerical Results (–3), Binary Integer Wordsize (–5 through –10)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| #n1 | #n2 | → | #n3 |
| “string1” | “string2” | → | “string3” |
| T/F1 | T/F2 | → | 0/1 |
| T/F | `symb` | → | `T/F AND symb` |
| `symb` | T/F | → | `symb AND T/F`` |
| `symb1` | `symb2` | → | `symb1 AND symb2` |
NOT, OR, XOR
Command
Animate Command: Displays graphic objects in sequence. ANIMATE displays a series of graphics objects (or variables containing them) one after the other. You can use a list to specify the area of the screen you want to animate (pixel coordinates #X and #Y), the number of seconds before the next grob is displayed (delay), and the number of times the sequence is run (rep). If rep is set to 0, the sequence is played approximately one million times (1,048,575 cycles), or until you press − (the $ key). If you use a list on level 1, all parameters must be present. If the list specifier is not used, the delay between each grob will default to 0.1 second. The animation displays PICT while displaying the grobs. The grobs and the animate parameters are left on the stack.
| Ln+1.../A1 | L1/An+1 | L1/I1 | |
|---|---|---|---|
| grobn...grob1 | ngrobs | → | same stack |
| grobn...grob1 | { n {#X#Y } delay rep } | → | same stack |
| L = Level, A = Argument, I = item | |||
The following program draws half a cylinder and rotates it: « PARSURFACE { `COS(X)` `SIN(X)` Y } STEQ « I 180 I + XXRNG ERASE DRAW PICT RCL » I 0 359 8 SEQ OBJ ANIMATE DROPN » This program also illustrates the use of SEQ and PARSURFACE. You can adjust the increment value used with SEQ (8 is used here) to change the number of images drawn by the program, or to use less memory.
BLANK, →GROB
Command
Recalls the nth answer from history, where n is an integer, in algebraic mode only. When called directly from the keybard in RPN mode, it takes no input and performs the LASTARG command. When the command name is typed manually in RPN mode, it performs PICK, with the exception that any stack levels containing null-tagged expressions (surrounded by `
characters), as might have been left on the stack by entries when running in algebraic mode, will be ignored.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| n | → | objn |
LAST, LASTARG, PICK
Function
Apply to Arguments Function: Creates an expression from the specified function name and arguments. A user-defined function f that checks its arguments for special cases often can’t determine whether a symbolic argument x represents one of the special cases. The function f can use APPLY to create a new expression f(x). If the user now evaluates f(x), x is evaluated before f, so the argument to f will be the result obtained by evaluating x. When evaluated in an algebraic expression, APPLY evaluates the arguments (to resolve local names in user-defined functions) before creating the new object.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| { symb1 ... symbn } | `name` | → | `name(symb1 ... symbn)` |
The following user-defined function Asin is a variant of the built-in function ASIN. Asin checks for special numerical arguments. If the argument on the stack is symbolic (the second case in the case structure), Asin uses APPLY to return the expression `Asin(argument)`.
« → argument « CASE -3 FS? THEN argument ASIN END
{ 6 7 9 } argument TYPE POS THEN `APPLY(Asin,argument)` EVAL END `argument==1` THEN `π/2` END `argument==-1` THEN `-π/2` END argument ASIN END » » `OAsinK
QUOTE, |
Command
Draw Arc Command: Draws an arc in PICT counterclockwise from xθ1 to xθ2, with its center at the coordinate specified in argument 1 or level 4 and its radius specified in argument 2 or level 3. ARC always draws an arc of constant radius in pixels, even when the radius and center are specified in user-units, regardless of the relative scales in user-units of the x- and y-axes. With user-unit arguments, the arc starts at the pixel specified by (x, y) + (a, b), where (a, b) is the rectangular conversion of the polar coordinate (xradius, xθ1). The resultant distance in pixels from the starting point to the center pixel is used as the actual radius, r`. The arc stops at the pixel specified by (r`, xθ2). If xθ1 = xθ2, ARC plots one point. If |xθ1 – xθ2| >360 degrees, 2π radians, or 400 grads, ARC draws a complete circle.
Angle Mode (–17 and –18). The setting of flags –17 and –18 determine the interpretation of xθ1 and xθ2 (degrees, radians, or grads).
| Level 4/Argument 1 Level 3/Argument 2 Level 2/Argument 3 Level 1/Argument 4 | Level 1/Item 1 | |||
|---|---|---|---|---|
| (x, y) | xradius | x θ1 | x θ2 | → |
| { #n,#m } | #nradius | x θ1 | x θ2 | → |
Angle Mode (–17 and –18)
BOX, LINE, TLINE
Command
Archive HOME Command: Creates a backup copy of the HOME directory (that is, all variables), the user-key assignments, and the alarm catalog in the specified backup object (:nport:name) in RAM or flash ROM. The specified port number can be 0 through 3, where 3 is the SD card. (Port 3 only applies to the HP 50g and 49g+.) An error will result if there is not enough memory in the specified port to copy the HOME directory. If the backup object is “:IO:name”, then the copied directory is transmitted in binary via Kermit protocol through the current I/O port to the specified filename. To save flag settings, execute RCLF and store the resulting list in a variable.
I/O Device (–33), I/O Messages (–39), I/O Device for Wire (–78) if the argument is “:IO:name”.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| :nport :name | → | |
| :IO :name | → |
RESTORE
Function
Argument Function: Returns the (real) polar angle θ of a complex number (x, y). The polar angle θ is equal to:
Angle mode (–17, –18)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| (x, y) | → | θ |
| `symb` | → | `ARG(symb)` |
ATAN
Command
Displays a menu or list showing the three CAS submenus for arithmetical operations, INTEGER, MODULAR and POLYNOMIAL.
If the CHOOSE boxes flag is clear (flag –117 clear), displays the submenus as a numbered list. If the flag is set, displays the operations as a menu of function keys.
ALGB, CONSTANTS, DIFF, EXP&LN, INTEGER, MAIN, MATHS, MATR, MODULAR, POLYNOMIAL, REWRITE, TESTS, TRIGO
Command
Array to Stack Command: Takes an array and returns its elements as separate real or complex numbers. Also returns a list of the dimensions of the array. If the argument is an n-element vector, the first element is returned to level n + 1 (not level nm + 1), and the nth element to level 2.
| Level 1/Argument 1 | Lnm+1/A1 ... L2/Anm | Level1/Itemnm+1 | |
|---|---|---|---|
| [ vector ] | → | z1 ... zn | { nelement } |
| [[ matrix ]] | → | z11 ... znm | { nrow mcol } |
| L = Level; I = item | |||
→ARRY, DTAG, EQ→, LIST→, OBJ→, STR→
Command
Stack to Array Command: Returns a vector of n real or complex elements or a matrix of n × m real or complex elements. The elements of the result array should be entered in row order. If one or more of the elements is a complex number, the result array will be complex.
| Levelnm+1/Argument1 7 Level2/Argumentnm Level1/Argumentnm+1 | Level1/Item1 | ||
|---|---|---|---|
| z1 … zn | nelement | → | [ vector ] |
| z1 1 … zn m | { nrow, mcol } | → | [[ matrix ]] |
ARRY→, LIST→, →LIST, OBJ→, STR→, →TAG, →UNIT
Analytic Function
Arc Sine Analytic Function: Returns the value of the angle having the given sine. For a real argument x in the domain –1 ≤ x ≤ 1, the result ranges from –90 to +90 degrees (–π/2 to +π/2 radians; –100 to +100 grads). A real argument outside of this domain is converted to a complex argument z = x + 0i, and the result is complex.
The inverse of SIN is a relation, not a function, since SIN sends more than one argument to the same result. The inverse relation for SIN is expressed by ISOL as the general solution: ASIN(Z)*(-1)^n1+π*n1 The function ASIN is the inverse of a part of SIN, a part defined by restricting the domain of SIN such that:
Principal Solution (–1), Numerical Results (–3), Angle Mode (–17, –18)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| z | → | asin z |
| `symb` | → | `ASIN(symb)` |
ACOS, ATAN, ISOL, SIN
Command
Transforms an expression by replacing asin(x) subexpressions with π/2–acos(x) subexpressions.
An expression
The transformed expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
ACOS2S, ASIN2T, ATAN2S
Command
Transforms an expression by replacing asin(x) subexpressions with the following: - x - atan - ------------------ - 1 – x 2-
An expression.
The transformed expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
ASIN2C, ACOS2S, ATAN2S
Analytic Function
Arc Hyperbolic Sine Analytic Function: Returns the inverse hyperbolic sine of the argument. The inverse of SINH is a relation, not a function, since SINH sends more than one argument to the same result. The inverse relation for SINH is expressed by ISOL as the general solution: ASINH(Z)*(–1)^n1+π*i*n1 The function ASINH is the inverse of a part of SINH, a part defined by restricting the domain of SINH such that:
The principal branch used by the calculator for ASINH was chosen because it is analytic in the regions where the arguments of the real-valued function are defined. The branch cut for the complex-valued ASINH function occurs where the corresponding real-valued function is undefined. The principal branch also preserves most of the important symmetries. The graph for ASINH can be found from the graph for ASIN (see ASIN) and the relationship asinh z = –i asin iz.
Principal Solution (–1), Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| z | → | asinh z |
| `symb` | → | `ASINH(symb)` |
ACOSH, ATANH, ISOL, SINH
Command
Assign Command: Defines a single key on the user keyboard by assigning the given object to the key xkey, which is specified as rc.pf. The argument xkey is a real number rc.pf specifying the key by its row number r, column number c, shift plane p and shift-and-hold flag f. A value of f=0 represents a normal shifted key assignment (where the shift is released prior to pressing the key); whereby f=1 corresponds to a shift-and- hold key assignment indicated by “&” in the table below (where the shift is held while pressing the key). The legal values for p and f are as follows:
Value of Value
Shift Shift
.pf of .pf
.00 or .10 Unshifted [key]
.20 !(left-shifted) [key] .21 ! & [key]
.30 …(right-shifted) [key] .31 … & [key]
.40 ~(alpha-shifted) [key] .41 ~& [key]
.50 ~!(alpha left-shifted) [key] .51 ~!& [key]
.60 ~…(alpha right-shifted) [key] .61 ~…& [key]
Once ASN has been executed, pressing a given key in User or 1-User mode executes the user- assigned object. The user key assignment remains in effect until the assignment is altered by ASN, STOKEYS, or DELKEYS. Keys without user assignments maintain their standard definitions. If the argument obj is the name SKEY, then the specified key is restored to its standard key assignment on the user keyboard. This is meaningful only when all standard key assignments had been suppressed (for the user keyboard) by the command S DELKEYS (see DELKEYS). To make multiple key assignments simultaneously, use STOKEYS. To delete key assignments, use DELKEYS.
Be careful not to reassign or suppress the keys necessary to cancel User mode. If this happens, exit User mode by doing a system halt (“warm start”): press and hold ‡and C simultaneously, releasing Cfirst. This cancels User mode.
User-Mode Lock (–61) and User Mode (–62) affect the status of the user keyboard
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| obj | xkey | → | |
| `SKEY` | xkey | → |
Executing ASN with GETI in level 2 and 75.3 in level 1 assigns GETI to …Õon the user keyboard. (…Õ has a location of 75.3 because it is seven rows down, five columns across, and right-shifted.) When the calculator is in User mode, pressing …Õ now executes GETI (instead of executing Õ).
DELKEYS, RCLKEYS, STOKEYS
Command
Arithmetic Shift Right Command: Shifts a binary integer one bit to the right, except for the most significant bit, which is maintained. The most significant bit is preserved while the remaining (wordsize –1) bits are shifted right one bit. The second-most significant bit is replaced with a zero. The least significant bit is shifted out and lost. An arithmetic shift is useful for preserving the sign bit of a binary integer that will be shifted. Although the calculator makes no special provision for signed binary integers, you can still interpret a number as a signed quantity.
Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| #n1 | → | #n2 |
SL, SLB, SR, SRB
Function
Adds global names to the reserved variable REALASSUME, with specific assumptions. REALASSUME is a list of the global variables that will be considered by some CAS operations to represent real numbers when complex mode is set. ASSUME adds further assumptions, for example that a variable is greater than or equal to zero. Assumptions must be of the form v≤expression, or v≥expression, where v is the variable name. Several assumptions can be combined. These assumptions are used by the solve commands; for example if a variable is assumed to be greater than zero then the solvers will not look for solutions where that variable is negative. Some of the solvers will give complex solutions for variables even if they are in REALASSUME.
Level 1/Item 1: An expression giving the name of the global variable to be added to the REALASSUME list, and the assumption to be placed on it, or a list of such assumptions.
Level 1/Item 1: The input expression or list of expressions.
Add the CAS assumption that the global variable Z is real and positive. Note that ASSUME will replace Z>0 with Z≥0, which does not guarantee that Z is positive, so Z≥MINR is used instead, which guarantees that Z is greater than or equal to the smallest positive number the calculator recognizes.
| Command | ASSUME(Z≥MINR) |
|---|---|
| Result | Z≥MINR |
ADDTOREAL, UNASSUME
Analytic Function
Arc Tangent Analytic Function: Returns the value of the angle having the given tangent. For a real argument, the result ranges from –90 to +90 degrees (–π/2 to +π/2 radians; –100 to +100 grads). The inverse of TAN is a relation, not a function, since TAN sends more than one argument to the same result. The inverse relation for TAN is expressed by ISOL as the general solution: ATAN(Z)+π*n1 The function ATAN is the inverse of a part of TAN, a part defined by restricting the domain of TAN such that:
Principal Solution (–1), Numerical Results (–3), Angle Mode (–17, –18)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| z | → | atan z |
| `symb` | → | `ATAN(symb)` |
ACOS, ASIN, ISOL, TAN
Command
Transforms an expression by replacing atan(x) subexpressions with the following: - x - asin - ------------------- - x 2 + 1-
An expression.
The transformed expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
ASIN2C, ACOS2S, ASIN2T
Analytic Function
Arc Hyperbolic Tangent Analytic Function: Returns the inverse hyperbolic tangent of the argument. For real arguments |x| > 1, ATANH returns the complex result obtained for the argument (x, 0). For a real argument x=±1, an Infinite Result exception occurs. If flag –22 is set (no error), the sign of the result (MAXR) matches that of the argument. The inverse of TANH is a relation, not a function, since TANH sends more than one argument to the same result. The inverse relation for TANH is expressed by ISOL as the general solution; ATANH(Z)+π*i*n1 The function ATANH is the inverse of a part of TANH, a part defined by restricting the domain of TANH such that:
Principal Solution (–1), Numerical Results (–3), Infinite Result Exception (–22)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| z | → | atanh z |
| `symb` | → | `ATANH(symb)` |
ACOSH, ASINH, ISOL, TANH
Command
Axes Tick-Mark Command: Sets the axes tick-mark annotation in the reserved variable PPAR. Given x, ATICK sets the tick-mark annotation to x units on both the x- and the y-axis. For example, 2 would place tick-marks every 2 units on both axes. Given #n, ATICK sets the tick-mark annotation to #n pixels on both the x- and the y-axis. For example, #5 would place tick-marks every 5 pixels on both axes. Given { x y }, ATICK sets the tick-mark unit annotation for each axis individually. For example, { 10 3 } would mark the x-axis at every multiple of 10 units, and the y-axis at every multiple of 3 units. Given { #n #m } ATICK sets the tick-mark pixel annotation for each axis individually. For example, {#6 #2 } would mark the x-axis every 6 pixels, and the y-axis every 2 pixels.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | |
| #n | → | |
| {xy} | → | |
| { #n #m } | → |
AXES, DRAX
Command
Attach Library Command: Attaches the library with the specified number to the current directory. Each library has a unique number. If a port number is specified, it is ignored. To use a library object, it must be in a port and it must be attached. A library object copied into RAM (such as through the PC Link) must be stored into a port using STO. Some libraries require you to ATTACH them. You can ascertain whether a library is attached to the current directory by executing LIBS. The number of libraries that can be attached to the HOME directory is limited only by the available memory. However, only one library at a time can be attached to any other directory. If you attempt to attach a second library to a non-HOME directory, the new library will overwrite the old one.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| nlibrary | → | |
| :nport :nlibrary | → |
DETACH, LIBS
Command
Concatenate two lists, a list and an element, or a vector and an element. Also creates a matrix from component row vectors.
Level 2/Argument 1: A vector, a list, a matrix, or a string. Level 1/Argument 2: A vector, a list, a matrix, or an element.
The matrix, list or string formed by combining the arguments. In the case of a string in level 2, AUGMENT acts exactly like “+” or “ADD”.
| Example 1: Append 3 to the list {1,2}: | |
|---|---|
| Command | AUGMENT({1,2},3) |
| Result | {1,2,3} |
| Example 2: Combine the rows [1,2,3] and [4,5,6] into a matrix: | |
| Command | AUGMENT([1,2,3],[4,5,6]) |
1 2 3 4 5 6 Result:
Command
Autoscale Command: Calculates a y-axis display range, or an x- and y-axis display range. The action of AUTO depends on the plot type as follows:
| Plot Type | Scaling Action |
|---|---|
| FUNCTION | Samples the equation in EQ at 40 values of the independent |
variable, equally spaced through the x-axis plotting range, discards points that return ±∞, then sets the y-axis display range to include the maximum, minimum, and origin.
| CONIC | Sets the y-axis scale equal to the x-axis scale. |
|---|---|
| POLAR | Samples the equation in EQ at 40 values of the independent |
variable, equally spaced through the plotting range, discards points that return ±∞, then sets both the x- and y-axis display ranges in the same manner as for plot type FUNCTION.
| PARAMETRIC | Same as POLAR. |
|---|---|
| TRUTH | No action. |
| BAR | Sets the x-axis display range from 0 to the number of elements in |
ΣDAT, plus 1. Sets the y-range to the minimum and maximum of the elements. The x-axis is always included.
HISTOGRAM Sets the x-axis display range to the minimum and maximum of
the elements in ΣDAT. Sets the y-axis display range from 0 to the number of rows in ΣDAT.
SCATTER Sets the x-axis display range to the minimum and maximum of
the independent variable column (XCOL) in ΣDAT. Sets the y- axis display range to the minimum and maximum of the dependent variable column (YCOL). AUTO does not affect 3D plots. AUTO actually calculates a y-axis display range and then expands that range so that the menu labels do not obscure the resultant plot. AUTO does not draw a plot — execute DRAW to do so.
None
DRAW, SCALEH, SCALE, SCLΣ, SCALEW, XRNG, YRNG
Command
Axes Command: Specifies the intersection coordinates of the x- and y-axes, tick-mark annotation, and the labels for the x- and y-axes. This information is stored in the reserved variable PPAR.
The argument for AXES (a complex number or list) is stored as the fifth parameter in the reserved variable PPAR. How the argument is used depends on the type of object it is:
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| (x, y) | → | |
| { (x, y) atick “x-axis label” “y-axis label” } | → |
The command sequence { (0,0) 2 "t" "y" } AXES LABEL specifies an axes intersection at (0,0), tick-mark annotation every 2 units, and puts the labels t and y PICT. The labels are positioned to identify the horizontal and vertical axes respectively.
ATICK, DRAW, DRAX, LABEL
Command
Converts a list to an array, or an array to a list.
A list or an array.
If the input is a list, returns the corresponding array. If the input is an array, returns the corresponding list.
Convert the following matrix to a list: 01 10
| Command | AXL([[0,1][1,0]]) |
|---|---|
| Result | {{0,1},{1,0}} |
AXM, AXQ
Command
Converts a numeric array (object type 3) to a symbolic matrix (object type 29), or a symbolic matrix to a numeric array.
A numeric array or a symbolic matrix.
The corresponding symbolic matrix or numeric array.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
AXL, AXQ
Command
Converts a square matrix into the associated quadratic form.
Level 2/Argument 1: An n×n matrix. Level 1/Argument 2: A vector containing n variables.
Level 2/Item 1: The corresponding quadratic form. Level 1/Item 2: The vector containing the variables.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Find the quadratic form, expressed in terms of x, y, and z, associated with the following matrix: 360 241 111
| Command | AXQ([[3,6,0][2,4,1][1,1,1]],[X,Y,Z]) |
|---|---|
| Result | {3*X^2+(8*Y+Z)*X+(4*Y^2+2*Z*Y+Z^2),[X,Y,Z]} |
AXL, AXM, GAUSS, QXA
Command
Bar Plot Type Command: Sets the plot type to BAR. When the plot type is BAR, the DRAW command plots a bar chart using data from one column of the current statistics matrix (reserved variable ΣDAT). The column to be plotted is specified by the XCOL command, and is stored in the first parameter of the reserved variable ΣPAR. The plotting parameters are specified in the reserved variable PPAR, which has the following form: { (xmin, ymin) (xmax, ymax) indep res axes ptype depend } For plot type BAR, the elements of PPAR are used as follows:
None
CONIC, DIFFEQ, FUNCTION, GRIDMAP, HISTOGRAM, PARAMETRIC, PARSURFACE, PCONTOUR, POLAR, SCATTER, SLOPEFIELD, TRUTH, WIREFRAME, YSLICE
Command
Draw Bar Plot Command: Plots a bar chart of the specified column of the current statistics matrix (reserved variable ΣDAT). The data column to be plotted is specified by XCOL and is stored as the first parameter in reserved variable ΣPAR. The default column is 1. Data can be positive or negative, resulting in bars above or below the axis. The y-axis is autoscaled, and the plot type is set to BAR. When BARPLOT is executed from a program, the resulting plot does not persist unless PICTURE, PVIEW (with an empty list argument), or FREEZE is subsequently executed.
None
A bar chart based on ΣDAT.
FREEZE, HISTPLOT, PICTURE, PVIEW, SCATRPLOT, XCOL
Command
Determines the basis of a sub-space of the n-space Rn.
A list of vectors defining a vector sub-space of Rn.
A list containing the vectors of a basis of the vector sub-space.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Find the vectors that form a basis of the sub-space defined by [1,2,3], [1,1,1], and [2,3,4]
| Command | BASIS({[1,2,3],[1,1,1],[2,3,4]}) |
|---|---|
| Result | {[1,0,-1],[0,1,2]} |
IBASIS
Command
Baud Rate Command: Specifies bit-transfer rate. Legal baud rates are 2400, 4800, 9600, 14400, 19200, 38400, 57600 and 115200 (default).
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| nbaudrate | → |
CKSM, PARITY, TRANSIO
Command
Beep Command: Sounds a tone at n hertz for x seconds. The frequency of the tone is subject to the resolution of the built-in tone generator. The minimum frequency is 1 Hz and the maximum frequency in 15000 Hz. An input that doesn’t round to an integer within this range will cause the BEEP command to be skipped. Durations greater than 1200 seconds are automatically changed to 1200 seconds.
Error Beep (–56)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| nfrequency | xduration | → |
HALT, INPUT, PROMPT, WAIT
Command
Best-Fitting Model Command: Executes LR with each of the four curve fitting models, and selects the model yielding the largest correlation coefficient. The selected model is stored as the fifth parameter in the reserved variable ΣPAR, and the associated regression coefficients, intercept and slope, are stored as the third and fourth parameters, respectively.
None
EXPFIT, LINFIT, LOGFIT, LR, PWRFIT
Command
Binary Mode Command: Selects binary base for binary integer operations. (The default base is decimal.) Binary integers require the prefix #. Binary integers entered and returned in binary base automatically show the suffix b. If the current base is not binary, binary numbers can still be entered by using the suffix b (the numbers are displayed in the current base, however). The current base does not affect the internal representation of binary integers as unsigned binary numbers.
Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12)
None
DEC, HEX, OCT, STWS, RCWS
Command
Sort into Frequency Bins Command: Sorts the elements of the independent column (XCOL) of the current statistics matrix (the reserved variable ΣDAT) into (nbins + 2) bins, where the left edge of bin 1 starts at value xmin and each bin has width xwidth. BINS returns a matrix containing the frequency of occurrences in each bin, and a 2-element array containing the frequency of occurrences falling below or above the defined range of x-values. The array can be stored into the reserved variable ΣDAT and used to plot a bar histogram of the bin data (for example, by executing BARPLOT). For each element x in ΣDAT, the nth bin count nfreq bin n is incremented, where: x – x m in n f r e q b in n = IP ------------------ - x w i d th
for xmin ≤ x ≤ xmax, where xmax = xmin + (nbins)(xwidth).
| L3/A1 | L2/A2 | L1/A3 | L2/I1 | L1/I2 | |
|---|---|---|---|---|---|
| xmin | xwidth | nbins | → | [[ nbin 1 ... nbin n ]] | [ nbin L nbin R] |
| L = Level; A = Argument; I = item | |||||
If the independent column of ΣDAT contains the following data: 7 2 3 1 4 6 9 0 1 1 3 5 13 2 6 9 5 8 5 1 2 5 BINS returns [[ 5 ][ 3 ][ 5 ][ 2 ][ 2 ]] and [ 1 1 ] The data has been sorted into 5 bins of width 2, starting at x-value 1 and ending at x-value 11. The first element of the matrix shows that 5 x-values (2 1 1 1 2) fell in bin 1, where bin 1 ranges from x-value 1 through 2.99999999999. The vector shows that one x-value was less than xmin (0), and one was greater than xmax (13).
BARPLOT, XCOL
Command
Blank Graphics Object Command: Creates a blank graphics object of the specified width and height.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| #nwidth | #mheight | → | grobblank |
→GROB, LCD→
Command Operation
Box Command: Draws in PICT a box whose opposite corners are defined by the specified pixel or user-unit coordinates.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| { #n1 #m1 } | { #n2 #m2 } | → | |
| (x1, y1) | (x2, y2) | → |
ARC, LINE, TLINE
Command
Buffer Length Command: Returns the number of characters in the calculator’s serial input buffer and a single digit indicating whether an error occurred during data reception. The digit returned is 1 if no framing, UART overrun, or input-buffer overflow errors occurred during reception, or 0 if one of these errors did occur. (The input buffer holds up to 255 bytes.) When a framing or overrun error occurs, data reception ceases until the error is cleared (which BUFLEN does); therefore, n represents the data received before the error. Use ERRM to see which error has occurred when BUFLEN returns 0 to level 1.
| Level 1/Argument 1 | Level 2/Item 1 | Level 1/Item 2 | |
|---|---|---|---|
| → | nchars | 0/1 |
CLOSEIO, OPENIO, SBRK, SRECV, STIME, XMIT
Command
Byte Size Command: Returns the number of bytes and the checksum for the given object. If the argument is a built-in object, then the size is 2.5 bytes and the checksum is #0. If the argument is a global name, then the size represents the name and its contents, while the checksum represents the contents only. The size of the name alone is (3.5 + n), where n is the number of characters in the name.
| Level 1/Argument 1 | Level 2/Item 1 | Level 1/Item 2 | |
|---|---|---|---|
| obj | → | #nchecksum | xsize |
Objects that decompile identically can have different byte sizes and checksums. For instance, {1} and 1 `A` STO A {} + both produce lists containing the number 1. However, the first list contains the built-in object 1 (for a size of 7.5 bytes), while the second list contains a RAM copy of 1 (for a size of 15.5 bytes).
MEM
Command
Binary to Real Command: Converts a binary integer to its floating-point equivalent.
If # n ≥ # 1000000000000 (base 10), only the 12 most significant decimal digits are preserved in the resulting mantissa.
Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| #n | → | n |
R→B
Command
Counted String Command: Enters C$ on the command line to help with the manual entry of a string object. Must be followed by a number indicating the number of characters to include in the strings, or an additional $ to indicate that the rest of the command line is a single string. There must be exactly one separator character after the second $ and before the body of the string. If the declared length is greater than the number of characters actually available, the string is automatically truncated to the correct length.
Command
Takes a list of cycles as an argument, and returns the equivalent permutation. In other words, finds a permutation from its cyclical decomposition.
A list of cycles equivalent to a permutation. For example, the list {1,3,5} defines a cycle C, such that C(1)=3, C(3)=5 and C(5)=1, while items 2 and 4 are not changed. This could be followed by {2,4} which defines a cycle C, such that C(2)=4, and C(4)=2.
A list representing the permutation equivalent to the cycles.
Convert the cycles given by {{1,3,5},{2,4}} into a permutation:
| Command | C2P({{1,3,5},{2,4}}) |
|---|---|
| Result | {3,4,5,2,1} |
P2C, CIRC
Command
Restores the default CAS mode settings. This command is almost equivalent to pressing L !RESET, then selecting “Reset all” and pressing !!OK!, when the CAS Modes input form is displayed. The difference is that CASCFG sets the modulus value to 13, whereas “Reset all” sets the modulus to 3.
Command
Displays a list of CAS operations. Selecting one with OK displays a description, related operations, an example of the operation, and the option to copy the example to the command line. More details are given in Appendix C and Appendix H of the User’s Guide. If level 1 of the stack contains a string, the list of CAS operations will be displayed beginning at this point.
HELP
Command
CASE Conditional Structure Command: Starts CASE … END conditional structure. The CASE … END structure executes a series of cases (tests). The first test that returns a true result causes execution of the corresponding true-clause, ending the CASE … END structure. A default clause can also be included: this clause executes if all tests evaluate to false. The CASE command is available in RPN programming only. You cannot use it in algebraic programming. The CASE … END structure has this syntax: CASE test-clause1 THEN true-clause1 END test-clause2 THEN true-clause2 END . . test-clausen THEN true-clausen END default-clause (optional) END When CASE executes, test-clause1 is evaluated. If the test is true, true-clause1 executes, then execution skips to END. If test-clause1 is false, test-clause2 executes. Execution within the CASE structure continues until a true clause is executed, or until all the test clauses evaluate to false. If the default clause is included, it executes if all test clauses evaluate to false.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| CASE | → | |
| THEN | T/F | → |
| END | → | |
| END | → |
The following program takes a numeric argument from the stack:
« → X « CASE
`X>0` THEN X NEG END `X<0` THEN X DUP + END `X==0` THEN 0 DOERR END END » »
END, IF, IFERR, THEN
Function
Ceiling Function: Returns the smallest integer greater than or equal to the argument.
Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | n |
| x_unit | → | n_unit |
| `symb` | → | `CEIL(symb)` |
FLOOR, IP, RND, TRNC
Command
Center Command: Adjusts the first two parameters in the reserved variable PPAR, (xmin, ymin) and (xmax, ymax), so that the point represented by the argument (x, y) is the plot center. On the HP 50g and 49g+, the center pixel is in row 40, column 65 when PICT is its default size (131 × 80). On the 48gII, the center pixel is in row 32, column 65 when PICT is its default size (131 × 64). If the argument is a real number x, CENTR makes the point (x,0) the plot center.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| (x, y) | → | |
| x | → |
SCALE
Command
Clear Flag Command: Clears the specified user or system flag. User flags are numbered 1 through 128. System flags are numbered –1 through –128. See Appendix C for a listing of the calculator’s system flags and their flag numbers.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| nflagnumber | → |
FC?, FC?C, FS?, FS?C, SF
Function
Percent Change Function: Returns the percent change from x to y as a percentage of x. If both arguments are unit objects, the units must be consistent with each other. The dimensions of a unit object are dropped from the result, but units are part of the calculation. For more information on using temperature units with arithmetic functions, refer to the keyword entry of +.
Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| x | y | → | 100(y – x)/x |
| x | `symb` | → | `%CH(x,symb)` |
| `symb` | x | → | `%CH(symb,x)` |
| `symb1` | `symb2` | → | `%CH(symb1, symb2)` |
| x_unit | y_unit | → | 100(y_unit – x_unit)/x_unit |
| x_unit | `symb` | → | `%CH(x_unit,symb)` |
| `symb` | x_unit | → | `%CH(symb,x_unit)` |
| Example 1: 1_m 500_cm %CH returns 400, because 500 cm represents an increase of 400% over 1 m. | |||
| Example 2: 100_K 150_K %CH returns 50. | |||
%, %T
Command
Chinese Remainder function. Solves a system of simultaneous polynomial congruences in the ring Z[x].
Level 2/Argument 1: A vector of the first congruence (expression and modulus). Level 1/Argument 2: A vector of the second congruence (expression and modulus).
A vector of the solution congruence (expression and modulus).
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Solve the following simultaneous congruences for the polynomial u: 2 u ≡ x + 1 (mod x+2) u ≡ x – 1 (mod x+3)
| Command | CHINREM([X^2+1,X+2],[X-1,X+3]) |
|---|---|
| Result | [X^3+2*X^2+5,-(X^2+5*X+6)] |
EGCD, ICHINREM
Command
Returns the Cholesky factorization of a square matrix.
A positive square matrix, M
An upper triangular matrix, P, such that tP*P=M. (tP is the transpose of P.)
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Find the Cholesky factorization of: 11 15
- -
CHOLESKY - 1 1 - - 15- Command: 1 1 0 2 Result:
Command
Create User-Defined Choose Box Command: Creates a user-defined choose box. CHOOSE creates a standard single-choice choose box based on the following specifications:
| Variable | Function |
|---|---|
| “prompt” | A message that appears at the top of choose box. If “prompt” is an |
empty string (“”), no message is displayed.
{c1 … cn} Definitions that appear within the choose box. A choice definition
(cx) can have two formats.
npos The position number of an item definition. This item is highlighted
when the choose box appears. If npos = 0, no item is highlighted, and the choose box can be used to view items only. If you choose an item from the choose box and press OK, CHOOSE returns the result (or the object itself if no result is specified) to level 2 and 1 to level 1. If you press −, CHOOSE returns 0. Also, if npos = 0, CHOOSE returns 0.
| L3/A1 | L2/A2 | L1/A3 | L2/I1 | L1/I2 | |
|---|---|---|---|---|---|
| “prompt” | { c1 ... cn } | npos | → | obj or result | “1” |
| “prompt” | { c1 ... cn } | npos | → | “0” | |
| L = Level; A = Argument; I = item | |||||
CHOOSE with the following three lines as input would produce a three-line choose box: "Select a Program" { { "Pie Chart" «PIE» } { "Inverse Function" «ROOTR» } { "Animate Taylor" «TSA» } } 1
INFORM, NOVAL
Command
Character Command: Returns a string representing the character corresponding to the character code n.
The character codes are an extension of ISO 8859/1. Codes 128 through 160 are unique to the calculator. See Appendix J for a complete list of characters and character codes. The default character ā is supplied for all character codes that are not part of the normal calculator’s display character set. Character code 0 is used for the special purpose of marking the end of the command line. Attempting to edit a string containing this character causes the error Can`t Edit Null Char. You can use the CHARS application to find the character code for any character used by the calculator. See “Additional Character Set” in Appendix D of the HP 50g User’s Guide.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| n | → | “string” |
NUM, POS, REPL, SIZE, SUB
Command
Composes two permutations.
Two lists, L1 and L2, representing two permutations. The composition L1○L2 is the permutation equivalent to performing permutation L2 first and L1 second. Level 2/Argument 1: L1 Level 1/Argument 2: L2
A list representing the single equivalent permutation, L = L1○L2
Compose the permutations given by {3,4,5,2,1} and {2,1,4,3,5}
| Command | CIRC({3,4,5,2,1},{2,1,4,3,5}) |
|---|---|
| Result | {4,3,2,5,1} |
C2P, P2C
Command
Checksum Command: Specifies the error-detection scheme. Legal values for nchecksum are as follows:
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| nchecksum | → |
BAUD, PARITY, TRANSIO
Command
Clear Command: Removes all objects from the stack or history. To recover a cleared stack or history, press …¯ (the right-shift of the Mkey) before executing any other operation. There is no programmable command to recover the stack or history.
| Leveln/Argument 1 ... Level 1/Argumentn | Leveln/Item 1 ... Level 1/Itemn | |
|---|---|---|
| objn ...obj1 | → |
CLVAR, PURGE
Command
Adjust System Clock Command: Adjusts the system time by x clock ticks, where 8192 clock ticks equal 1 second. If x is positive, x clock ticks are added to the system time. If x is negative, x clock ticks are subtracted from the system time. If X>10^12, it will be changed to 10^12 ticks (which is approximately 3.87 years).
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → |
→TIME
Command
Clear LCD Command: Clears (blanks) the stack display. The menu labels continue to be displayed after execution of CLLCD. When executed from a program, the blank display persists only until the keyboard is ready for input. To cause the blank display to persist until a key is pressed, execute FREEZE after executing CLLCD. (When executed from the keyboard, CLLCD automatically freezes the display.)
None
Evaluating « CLLCD 7 FREEZE » blanks the display (except the menu labels), then freezes the entire display.
DISP, FREEZE
Command
Close I/O Port Command: Closes the serial port, and clears the input buffer and any error messages for KERRM. When the calculator turns off, it automatically closes the serial port, but does not clear KERRM. Therefore, CLOSEIO is not needed to close the port, but can conserve power without turning off the calculator. Executing Kermit protocol commands automatically clears the input buffer; however, executing non-Kermit commands (such as SRECV and XMIT) does not. CLOSEIO also clears error messages from KERRM. This can be useful when debugging.
None
BUFLEN, OPENIO
Command
Purges the current statistics matrix (reserved variable ΣDAT).
None
RCLΣ, STOΣ, Σ+, Σ–
Command
Clear Variables Command: Provided for compatibility with the HP 28 series. CLUSR is the same as CLVAR. See CLVAR.
Command
Clear Variables Command: Purges all variables and empty subdirectories in the current directory.
None
PGDIR, PURGE
Command
Displays a menu of commands pertaining to complex numbers.
None
ARIT, DIFF, EXP&LN, SOLVER, TRIGO
Command
Column Norm Command: Returns the column norm (one-norm) of the array argument. The column norm of a matrix is the maximum (over all columns) of the sum of the absolute values of all elements in each column. For a vector, the column norm is the sum of the absolute values of the vector elements. For complex arrays, the absolute value of a given element (x, y) is
| 2 | 2 |
|---|---|
| x +y | . |
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| [ array ] | → | xcolumnnorm |
CROSS, DET, DOT, RNRM
Command
Matrix to Columns Command: Transforms a matrix into a series of column vectors and returns the vectors and a column count, or transforms a vector into its elements and returns the elements and an element count. →COL introduces no rounding error.
| Level 1/Argument 1 | Leveln+1/Item 1 ... | Level 2/Item 2 | Level 1/Item 3 | |
|---|---|---|---|---|
| [[ matrix ]] | → | [ vector ]col1 | [ vector ]coln | ncolcount |
| [ vector ] | → | element1 | elementn | nelementcount |
COL→, →ROW, ROW→ COL→
Command
Columns to Matrix Command: Transforms a series of column vectors and a column count into a matrix containing those columns, or transforms a sequence of numbers and an element count into a vector with those numbers as elements. All vectors must have the same length. The column or element count is rounded to the nearest integer.
| Ln+1/A1 ... | L2/A2 | L1/An+1 | Level 1/Item 1 | |
|---|---|---|---|---|
| [ vector ]col1 | [ vector ]coln | ncolcount | → | [[ matrix ]] |
| element1 | elementn | nelementcount | → | [ vector ] |
| L = Level; A = Argument; I = item | ||||
→COL, →ROW, ROW→
Command
Delete Column Command: Deletes column n of a matrix (or element n of a vector), and returns the modified matrix (or vector) and the deleted column (or element). n is rounded to the nearest integer.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 2/Item 1 | Level 1/Item 2 | |
|---|---|---|---|---|
| [[ matrix ]]1 | ncolumn | → | [[ matrix ]]2 | [ vector ]column |
| [ vector ]1 | nelement | → | [ vector ]2 | elementn |
COL+, CSWP, ROW+, ROW–
Command
Insert Column Command: Inserts an array (vector or matrix) into a matrix (or one or more elements into a vector) at the position indicated by nindex, and returns the modified array. The inserted array must have the same number of rows as the target array. nindex is rounded to the nearest integer. The original array is redimensioned to include the new columns or elements, and the elements at and to the right of the insertion point are shifted to the right.
| Level 3/Argument 1 | Level 2/Argument 2 | Level 1/Argument 3 | Level 1/Item 1 | |
|---|---|---|---|---|
| [[ matrix ]]1 | [[ matrix ]]2 | nindex | → | [[ matrix ]]3 |
| [[ matrix ]]1 | [ vector ]column | nindex | → | [[ matrix ]]2 |
| [ vector ]1 | nelement | nindex | → | [ vector ]2 |
COL–, CSWP, ROW+, ROW–
Command
Factorizes a polynomial or an integer. Almost identical to COLLECT.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `symb1` | → | `symb2` |
| x | → | x |
| (x, y) | → | (x, y) |
| Example 1: | COLCT(`5+X+9`) returns `X+14` | |
| Example 2: | COLCT(`X*1_m+X*9_cm`) returns `X*1.09_m` | |
| Example 3: | COLCT(`X^Z*Y*X^T*Y`) returns `Y^2*X^Z*X^T` | |
| Example 4: | COLCT(`X+3*X+Y+Y`) returns `4*X+2*Y` |
EXPAN, FACTOR, ISOL, QUAD, SHOW
Command
Factorizes a polynomial or an integer. This command is almost identical to the COLCT command and similar to the FACTOR command. Unlike FACTOR it does not factorize symbolically into square roots. It is included to ensure backward-compatibility with earlier calculators.
An expression or an integer
The factorized expression, or the integer expressed as the product of prime numbers.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). If complex inputs are given, complex mode must be set (flag –103 set).
Factorize the following: 2 x + 5x + 6
| Command | COLLECT(X^2+5*X+6) |
|---|---|
| Result | (X+2)(X+3) |
COLCT, EXPAND, FACTOR
Command
Column Sigma Command: Specifies the independent-variable and dependent-variable columns of the current statistics matrix (the reserved variable ΣDAT). COLΣ combines the functionality of XCOL and YCOL. The independent-variable column number xxcol is stored as the first parameter in the reserved variable ΣPAR (the default is 1). The dependent-variable column number xycol is stored as the second parameter in the reserved variable ΣPAR (the default is 2). COLΣ accepts and stores noninteger values, but subsequent commands that use these two parameters in ΣPAR will cause errors.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| xcol | ycol | → |
2 5 COLΣ sets column 2 in ΣDAT as the independent-variable column, sets column 5 as the dependent-variable column, and stores 2 and 5 as the first and second elements in ΣPAR.
BARPLOT, BESTFIT, CORR, COV, EXPFIT, HISTPLOT, LINFIT, LOGFIT, LR, PREDX, PREDY, PWRFIT, SCATRPLOT, XCOL, YCOL
Function
Combinations Function: Returns the number of possible combinations of n items taken m at a time. The following formula is used: n! C n, m = ------------------------------ m! ⋅ ( n – m )! The arguments n and m must each be less than 1012. If n<m, zero is returned.
Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| n | m | → | Cn;m |
| `symbn` | m | → | `COMB(symbn,m)` |
| n | `symbm` | → | `COMB(n, symbm)` |
| `symbn` | `symbm` | → | `COMB(symbn,symbm)` |
FACT, PERM, !
Command
Constant Array Command: Returns a constant array, defined as an array whose elements all have the same value.
The constant value is a real or complex number taken from argument 2/level 1. The resulting array is either a new array, or an existing array with its elements replaced by the constant, depending on the object in argument 1/level 2.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| { ncolumns } | zconstant | → | [ vectorconstant ] |
| { nrows mcolumns } | zconstant | → | [[ matrixconstant ]] |
| [ R-array ] | xconstant | → | [ R-arrayconstant ] |
| [ C-array ] | zconstant | → | [ C-arrayconstant ] |
| `name` zconstant → | |||
| Example 1: { 2 2 } 6 CON returns the matrix [[ 6 6 ][ 6 6 ]]. | |||
| Example 2: [ (2,4) (7,9) ] 3 CON returns the complex vector [ (3,0) (3,0) ]. | |||
IDN
Command
Condition Number Command: Returns the 1-norm (column norm) condition number of a square matrix. The condition number of a matrix is the product of the norm of the matrix and the norm of the inverse of the matrix. COND uses the 1-norm and computes the condition number of the matrix without computing the inverse of the matrix. The condition number expresses the sensitivity of the problem of solving a system of linear equations having coefficients represented by the elements of the matrix (this includes inverting the matrix). That is, it indicates how much an error in the inputs may be magnified in the outputs of calculations using the matrix. In many linear algebra computations, the base 10 logarithm of the condition number of the matrix is an estimate of the number of digits of precision that might be lost in computations using that matrix. A reasonable rule of thumb is that the number of digits of accuracy in the result is approximately MIN(12,15–log10(COND)).
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| [[ matrix ]]m×n | → | xconditionnumber |
The following program computes the above rule of thumb for the number of accurate digits: « DUP SIZE 1 GET LOG SWAP COND LOG + 11 SWAP - »
SNRM, SRAD, TRACE
Command
Conic Plot Type Command: Sets the plot type to CONIC. When the plot type is CONIC, the DRAW command plots the current equation as a second- order polynomial of two real variables. The current equation is specified in the reserved variable EQ. The plotting parameters are specified in the reserved variable PPAR, which has this form: { (xmin, ymin) (xmax, ymax) indep res axes ptype depend } For plot type CONIC, the elements of PPAR are used as follows:
None
BAR, DIFFEQ, FUNCTION, GRIDMAP, HISTOGRAM, PARAMETRIC, PARSURFACE, PCONTOUR, POLAR, SCATTER, SLOPEFIELD, TRUTH, WIREFRAME, YSLICE
Function
Conjugate Analytic Function: Conjugates a complex number or a complex array. Conjugation is the negation (sign reversal) of the imaginary part of a complex number. For real numbers and real arrays, the conjugate is identical to the original argument.
Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | x |
| (x, y) | → | (x, –y) |
| [ R-array ] | → | [ R-array ] |
| [ C-array ]1 | → | [ C-array ]2 |
| `symb` | → | `CONJ(symb)` |
| Example 1: | [ (3,4) (7,2) ] CONJ returns [ (3,-4) (7,-2) ] | |
| Example 2: | A square matrix A containing complex elements is said to be Hermitian if AH = A, where AH is | |
| the same as a normal transpose except that the complex conjugate of each element is used. The following program returns 1 if the input matrix is Hermitian, and a 0 if it is not. « DUP TRN CONJ SAME » | ||
ABS, IM, RE, SCONJ, SIGN
Command
Open Constants Library Command: Opens the Constants Library catalog.
None
CONST
Function
Constant Value Command: Returns the value of a constant. CONST returns the value of the specified constant. It chooses the unit type depending on flag 60: SI if clear, English if set, and uses the units depending on flag 61: units if clear, no units if set. See “Tables of Units and Constants” in appendix B of this reference for a list of the constants available in the Constants Library.
Units Type (60), Units Usage (61)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `name` | → | x |
CONLIB
Command
Displays a menu or list of CAS symbolic constants.
If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered list. If the flag is set, displays the operations as a menu of function keys.
None
ALGB, ARIT, DIFF, EXP&LN, INTEGER, MAIN, MATHS, MATR, MODULAR, POLYNOMIAL, REWRITE, TESTS, TRIGO
Command
Continue Program Execution Command: Resumes execution of a halted program. Since CONT is a command, it can be assigned to a key or to a custom menu.
None
The program « "Enter A, press { CONT }" { CONT } MENU PROMPT » displays a prompt message, builds a menu with the CONT command assigned to the first menu key, and halts the program for data input. After entering data, pressing %CONT% resumes program execution. (Note that pressing !æ is equivalent to pressing %CONT%.)
HALT, KILL, PROMPT
Command
Convert Units Command: Converts a source unit object to the dimensions of a target unit. The source and target units must be compatible. The number part x2 of the target unit object is ignored.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| x1_unitssource x2_unitstarget | → | x3_unitstarget |
UBASE, UFACT, →UNIT, UVAL
Command
Correlation Command: Returns the correlation coefficient of the independent and dependent data columns in the current statistics matrix (reserved variable ΣDAT). The columns are specified by the first two elements in the reserved variable ΣPAR, set by XCOL and YCOL, respectively. If ΣPAR does not exist, CORR creates it and sets the elements to their default values (1 and 2). The correlation is computed with the following formula: n ∑ ( xin – xn ) ( xin – xn )
1 1 2 2
i=1 ----------------------------------------------------------------------------------
n 2 n 2
∑ ( x in – xn ) ∑ ( xin – xn )
1 1 2 2
i=1 i=1
x in 1 x in 2
where is the ith coordinate value in column n1, is the ith coordinate value in the column
x n1 x n2
n2 , is the mean of the data in column n1, is the mean of the data in column n2, and n is the
number of data points.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | xcorrelation |
COLΣ, COV, PREDX, PREDY, XCOL, YCOL
Analytic Function
Cosine Analytic Function: Returns the cosine of the argument. For real arguments, the current angle mode determines the number’s interpretation as an angle, unless the angular units are specified. For complex arguments, cos(x + iy) = cosx coshy – i sinx sinhy. If the argument for COS is a unit object, then the specified angular unit overrides the angle mode to determine the result. Integration and differentiation, on the other hand, always observe the angle mode. Therefore, to correctly integrate or differentiate expressions containing COS with a unit object, the angle mode must be set to Radians (since this is a “neutral” mode).
Numerical Results (–3), Angle Mode (–17, –18)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| z | → | cos z |
| `symb` | → | `COS(symb)` |
| x_unitangular | → | cos (x_unitangular) |
ACOS, SIN, TAN
Analytic Function
Hyperbolic Cosine Analytic Function: Returns the hyperbolic cosine of the argument. For complex arguments, cosh(x + iy) = coshx cosy + i sinhx siny.
Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| z | → | cosh z |
| `symb` | → | `COSH(symb)` |
ACOSH, SINH, TANH
Command
Covariance Command: Returns the sample covariance of the independent and dependent data columns in the current statistics matrix (reserved variable ΣDAT). The columns are specified by the first two elements in reserved variable ΣPAR, set by XCOL and YCOL respectively. If ΣPAR does not exist, COV creates it and sets the elements to their default values (1 and 2). The covariance is calculated with the following formula: 1 n ----------- ∑ ( x in 1 – x n 1 ) ( x in 2 – x n 2 ) n – 1i = 1
where x in1 is the ith coordinate value in column n1, x in2 is the ith coordinate value in the column
| n2 , | is the |
|---|---|
| xn1mean of the data in column n1, | is thexnmean |
2 of the data in column n2, and n is the number of data points.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | xcovariance |
COLΣ, CORR, PCOV, PREDX, PREDY, XCOL, YCOL
Command
Carriage Right Command: Prints the contents, if any, of the printer buffer. When printing to the serial port (flag –34 set), CR sends to the printer a string that encodes the line termination method. The default termination method is carriage-return/linefeed. The string is the fourth parameter in the reserved variable PRTPAR. When using the HP 82240B Infrared Printer (flag –34 clear), CR leaves the printhead on the right end of the just printed line.
I/O Device (–33), Printing Device (–34), Double-Spaced Printing (–37), I/O Device for Wire (– 78)
None
DELAY, OLDPRT, PRLCD, PRST, PRSTC, PRVAR, PR1
Command
Create Directory Command: Creates an empty subdirectory with the specified name in the current directory. CRDIR does not change the current directory; evaluate the name of the new subdirectory to make it the current directory.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `global` | → |
HOME, PATH, PGDIR, UPDIR
Command
Cross Product Command: CROSS returns the cross product C = A × B of vectors A and B. The arguments must be vectors having two or three elements, and need not have the same number of elements. (The calculator automatically converts a two-element argument [ d1 d2 ] to a three-element argument [ d1 d2 0 ].)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| [ vector ]A | [ vector ]B | → | [ vector ]A × B |
CNRM, DET, DOT, RNRM
Command
Column Swap Command: Swaps columns i and j of the argument matrix and returns the modified matrix, or swaps elements i and j of the argument vector and returns the modified vector. Column numbers are rounded to the nearest integer. Vector arguments are treated as row vectors.
| Level 3/Argument 1 | Level 2/Argument 2 | Level 1/Argument 3 | Level 1/Item 1 | |
|---|---|---|---|---|
| [[ matrix ]]1 | ncolumni | ncolumnj | → | [[ matrix ]]2 |
| [ vector ]1 | nelementi | nelementj | → | [ vector ]2 |
COL+, COL–, RSWP
Function
Returns the curl of a three-dimensional vector function.
Level 2/Argument 1: A three-dimensional vector function of three variables. Level 1/Argument 2: An array comprising the three variables.
The curl of the vector function with respect to the specified variables.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Find the curl of the following vector function:
2 2 2
v = x yi + x yj + y zk
˜ ˜ ˜
Command: CURL([X^2*Y, X^2*Y, Y^2*Z],[X,Y,Z])
Result: [Z*2*Y,0,Y*2*X-X^2]
DIV, HESS, VPOTENTIAL
Function
Returns the cyclotomic polynomial of order n. This is the polynomial whose roots are all the nth roots of 1, except those that are also roots of 1 for smaller values of n. For example, if n is 4, the 4th roots of 1 are {1, i, -1, -i}, but 1 is the 1st root of 1 and –1 is a 2nd root of 1, so only i and -i are left, giving the polynomial (x-i)(x+i) = x2+1.
A non-negative integer n
The cyclotomic polynomial of order n.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
| Example: Find the 20th cyclotomic polynomial. | |
|---|---|
| Command | CYCLOTOMIC(20) |
X^8-X^6+X^4-X^2+1
Command
Cylindrical Mode Command: Sets Cylindrical coordinate mode. CYLIN clears flag –15 and sets flag –16. In Cylindrical mode, vectors are displayed as polar components. Therefore, a 3D vector would appear as [ R θ Z ].
None
RECT, SPHERE
Command
Complex to Pixel Command: Converts the specified user-unit coordinates to pixel coordinates. The user-unit coordinates are derived from the (xmin, ymin) and (xmax, ymax) parameters in the reserved variable PPAR.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| (x, y) | → | { #n, #m } |
PX→C C→R
Command
Complex to Real Command: Separates the real and imaginary parts of a complex number or complex array. The result in item 1/level 2 represents the real part of the complex argument. The result in item 2/ level 1 represents the imaginary part of the complex argument.
| Level 1/Argument 1 | Level 2/Item 1 | Level 1/Item 2 | |
|---|---|---|---|
| (x, y) | → | x | y |
| [ C-array ] | → | [R-array ]1 | [R-array ]2 |
R→C, RE, IM
Function
Darcy Friction Factor Function: Calculates the Darcy friction factor of certain fluid flows. DARCY calculates the Fanning friction factor and multiplies it by 4. xe/D is the relative roughness — the ratio of the conduit roughness to its diameter. yRe is the Reynolds number. The function uses different computation routines for laminar flow (Re ≤ 2100) and turbulent flow (Re > 2100). xe/D and yRe must be real numbers or unit objects that reduce to dimensionless numbers, and both numbers must be greater than 0.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| xe / D | yRe | → | xDarcy |
FANNING
Command
Date Command: Returns the system date.
Date Format (–42)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | date |
If the current date is May 12, 2010, if flag –42 is clear, and if the display mode is Standard, DATE returns 5.12201. (The trailing zeros are dropped.)
DATE+, DDAYS, TIME, TSTR
→DATE
Command
Set Date Command: Sets the system date to date. date has the form MM.DDYYYY or DD.MMYYYY, depending on the state of flag –42. MM is month, DD is day, and YYYY is year. If YYYY is not supplied, the current specification for the year is used. The range of allowable dates is January 1, 2000 to December 31, 2090. Inputs between January 1, 1991 and December 31, 1999 are silently rejected by →DATE; no error is reported and the system date is left unchanged.
Date Format (–42)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| date | → |
If flag –42 is set and the current system year is 2005, then 28.07 →DATE sets the system date as July 28, 2005.
→TIME
Command
Date Addition Command: Returns a past or future date, given a date in argument 1/level 2 and a number of days in argument 2/level 1. If xdays is negative, DATE+ calculates a past date. The range of allowable dates is October 15, 1582, to December 31, 9999.
Date Format (–42)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| date1 | xdays | → | datenew |
DATE, DDAYS
Operation
Debug Operation: Starts program execution, then suspends it as if HALT were the first program command. DBUG is programmable.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| « program » or `program name` | → |
HALT, NEXT
Command
Delta Days Command: Returns the number of days between two dates. If the argument 1/level 2 date is chronologically later than the argument 2/ level 1 date, the result is negative. The range of allowable dates is October 15, 1582, to December 31, 9999.
Date Format (–42)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| date1 | date2 | → | xdays |
DATE, DATE+
Command
Decimal Mode Command: Selects decimal base for binary integer operations. (The default base is decimal.) Binary integers require the prefix #. Binary integers entered and returned in decimal base automatically show the suffix d. If the current base is not decimal, then you can enter a decimal number by ending it with d. It will be displayed in the current base when it is entered. The current base does not affect the internal representation of binary integers as unsigned binary numbers.
Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12)
None
BIN, HEX, OCT, RCWS, STWS
Command
Decrement Command: Takes a variable, subtracts 1, stores the new value back into the original variable, and returns the new value. The contents of name must be a real number or an integer.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `name` | → | xnew |
| Example 1: | If 35.7 is stored in A, `A` DECR returns 34.7. | |
| Example 2: | The following program counts down from 100 to 0 and leaves the integers 100 to 0 on the stack: | |
| « 100 `A` STO WHILE A REPEAT `A` DECR END `A` PURGE » | ||
INCR, STO+, STO–
Function
Displays a greeting from the CAS team and dedication to all HP calculator users.
In algebraic mode, the message can be extended. Try: DEDICACE(Salutations)
Function
Defines a variable or a function. Works like the DEFINE command, except that it returns a result and can be included in an algebraic expression. Given an expression as input, DEF stores the expression, unlike STORE which evaluates the expression and stores the numerical value.
Level 1/Argument 1: An expression of the form name=expression or name(name1, … namen)=expression(name1,… name n) In the first case, name is the name of a variable, and expression is an expression or a number to be stored in the variable. If the variable does not exist, it is created in the current directory. In the second case, name is the name of a variable that will be treated as a function, name1 to namen are formal variables used to define inputs the function will take.
Level 1/Item 1: Unlike DEFINE, which returns NOVAL in Algebraic mode, and no result in RPN mode, DEF returns the expression used as the input.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Example 1: Define a new function that calculates:
(a-b)/(a+b)
| Command | DEF(NEW(A,B)=(A-B)/(A+B)) |
|---|---|
| Result | NEW(A,B)=(A-B)/(A+B) Example 2: Check that the newly defined function works: |
| Command | NEW(2,1) |
| Result | 1/3 |
DEFINE, STORE
Command
Define Variable or Function Command: Stores the expression on the right side of the = in the variable specified on the left side, or creates a user-defined function. If the left side of the equation is name only, DEFINE stores exp in the variable name. If the left side of the equation is name followed by parenthetical arguments name1 … namen, DEFINE creates a user-defined function and stores it in the variable name.
Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `name=exp` | → | |
| `name(name1 ... namen)=exp(name1 ... namen)` → | ||
Example 1: `A=2*X` DEFINE stores `2*X` in variable A.
Example 2: `A(X,Y)=2*X+3/Y` DEFINE creates a user-defined function A. The contents of A is
the program « → X Y `2*X+3/Y` » | ||
DEF, STO, UNASSIGN
Command
Degrees Command: Sets Degrees angle mode. DEG clears flags –17 and –18, and displays the DEG annunciator. In Degrees angle mode, real-number arguments that represent angles are interpreted as degrees, and real-number results that represent angles are expressed in degrees.
None
GRAD, RAD
Function
Returns the degree of a polynomial expression. Returns 0 for a constant expression, but –1 if the expression is zero.
Level 1/Argument 1: A polynomial expression or equation; all powers must be integers or real numbers with no fractional part.
Level 1/Item 1: An integer representing the highest power in the polynomial. If the input contains powers of more than one variable, including the current variable, returns the highest power of the current variable. If the input contains powers of more than one variable, not including the current variable, returns the highest power of the first symbolic variable (one that is not stored in the current directory path). If the input contains powers of more than one variable, and all the variables are stored in the current directory path, returns the highest power of any of the variables.
If exact mode is set (flag –105 clear), the result is returned as an integer, otherwise it is returned as a real number.
Example 1: Find the degree of the polynomial represented by:
x2-17=x3+2x
| Command | DEGREE(x^2-17=x^3+2*X) |
|---|---|
| Result | 3 |
Command
Delete Alarm Command: Deletes the specified alarm. If nindex is 0, all alarms in the system alarm list are deleted.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| nindex | → |
FINDALARM, RCLALARM, STOALARM
Command
Delay Command: Specifies how many seconds the calculator waits between sending lines of information to the printer. Setting flag –34 directs printer output to the serial port. In this case, flag –33 must be clear. If flag –34 is set and transmit pacing is enabled (nonzero) in reserved variable IOPAR, then XON/XOFF handshaking controls data transmission and the delay setting has no effect. xdelay specifies the delay time in seconds. The default delay is 0 seconds. The maximum delay is 6.9 seconds. (The sign of xdelay is ignored, so –4 DELAY is equivalent to 4 DELAY.) The delay setting is the first parameter in the reserved variable PRTPAR. A shorter delay setting can be useful when the calculator sends multiple lines of information to your printer (for example, when printing a program). To optimize printing efficiency, set the delay just longer than the time the printhead requires to print one line of information. If you set the delay shorter than the time to print one line, you may lose information. Also, as the batteries in the printer lose their charge, the printhead slows down, and, if you have previously decreased the delay, you may have to increase it to avoid losing information. (Battery discharge will not cause the printhead to slow to more than the 1.8-second default delay setting.)
I/O Device (–33), Printing Device (–34), I/O Device for Wire (–78)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| xdelay | → |
CR, OLDPRT, PRLCD, PRST, PRSTC, PRVAR, PR1
Command
Delete Key Assignments Command: Clears user-defined key assignments. The argument xkey is a real number rc.p specifying the key by its row number, its column number, and its plane (shift). For a definition of plane, see ASN. Specifying 0 for xkey clears all user key assignments and restores the standard key assignments. Specifying S as the argument for DELKEYS suppresses all standard key assignments on the user keyboard. This makes keys without user key assignments inactive on the user keyboard. (You can make exceptions using ASN, or restore them all using STOKEYS.) If you are stuck in User mode — probably with a “locked” keyboard — because you have reassigned or suppressed the keys necessary to cancel User mode, do a system halt (“warm start”): press and hold ‡ and C simultaneously, releasing C first. This cancels User mode. Deleted user key assignments still take up from 2.5 to 62.5 bytes of memory each. You can free this memory by packing your user key assignments by executing RCLKEYS 0 DELKEYS STOKEYS.
User-Mode Lock (–61) and User Mode (–62) affect the status of the user keyboard.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| xkey | → | |
| { xkey1, ... ,xkey n } | → | |
| 0 | → | |
| `S` | → |
ASN, RCLKEYS, STOKEYS
Command
Dependent Variable Command: Specifies the dependent variable (and its plotting range for TRUTH plots). The specification for the dependent variable name and its plotting range is stored in the reserved variable PPAR as follows:
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| `global` | → | ||
| { global } | → | ||
| { global, ystart, yend } | → | ||
| {ystart, yend } | → | ||
| ystart | yend | → |
INDEP
RPL Command
Depth Command: Returns a real number representing the number of objects present on the stack (before DEPTH was executed).
| Level n7Level 1 | Level 1 | |
|---|---|---|
| → | n |
CLEAR, DROPN
Function
Returns the partial derivatives of a function, with respect to the specified variables.
Level 2/Argument 1: A function or a list of functions. Level 1/Argument 2: A variable, or a vector of variables. The variable or variables must not exist as variables stored in the current directory nor directories above it.
The derivative, or a vector of the derivatives, of the function or functions.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Find the gradient of the following function of the spatial variables x, y, and z:
2 2
2x y + 3y z + zx
Command: DERIV(2*X^2*Y+3*Y^2*Z+Z*X, [X,Y,Z])
EXPAND(ANS(1))
Result: [4*Y*X+Z,2*X^2+6*Z*Y,X+3*Y^2]
DERVX, dn, ∂, POTENTIAL
Function
Returns the derivative of a function with respect to the current variable. This variable must not exist as a variable stored in the current directory path.
The function or list of functions to be differentiated.
The derivative, or a vector of the derivatives, of the function or functions.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
DERIV, dn, ∂
Function
Verbose alias for DERVX — differentiates the level-1 expression with respect to the current CAS variable VX. Provided so HP-family programs that spell out the name still work.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `f(VX)` | → | `d/dVX f` |
DERVX, DERIV, VX, SVX
Command
Solves certain first-order ordinary differential equations with respect to the current variable.
Level 2/Argument 1: A first-order differential equation. Level 1/Argument 2: The function to solve for.
The solution to the equation, either y as a function of x or x as a function of y, or x and y as functions of a parameter.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Solve the following differential equation: 3x y′ ( x ) + 2 y ( x ) = e
Command: DESOLVE(d1Y(X)+2*Y(X)=EXP(3*X),Y(X))
(See the description of dn and Chapter 16 of the User’s Guide for an explanation of the use of “d1” for a derivative.)
Result: {Y(X)=(1/5*EXP(5*X)+cC0)*(1/EXP(X)^2)}
dn, LDEC
Command
Determinant Function: Returns the determinant of a square matrix. The argument matrix must be square. DET computes the determinant of 1 × 1 and 2 × 2 matrices directly from the defining expression for the determinant. DET computes the determinant of a larger matrix by computing the Crout LU decomposition of the matrix and accumulating the product of the decomposition’s diagonal elements. Since floating-point division is used to do this, the computed determinant of an integer matrix is often not an integer, even though the actual determinant of an integer matrix must be an integer. DET corrects this by rounding the computed determinant to an integer value. This technique is also used for noninteger matrices with determinants having fewer than 15 nonzero digits: the computed determinant is rounded at the appropriate digit position to restore some or all of the accuracy lost to floating-point arithmetic. This refining technique can cause the computed determinant to exhibit discontinuity. To avoid this, you can disable the refinement by setting flag –54.
Tiny Element (–54)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| [[ matrix ]] | → | xdeterminant |
For a square matrix A, the minor of element aij is the determinant of the submatrix that remains after deleting row i and column j from the original matrix. Given a square matrix in level 3, i in level 2, and j in level 1, the following program, MINOR determines the minor of the submatrix:
« → M row col
« M row ROW- DROP col COL- DROP DET » » For example, entering [[ 1 2 3 ][ 4 5 6 ][ 7 8 9 ]] 2 3 MINOR returns -6.
CNRM, CROSS, DOT, RNRM
Command
Detach Library Command: Detaches the library with the specified number from the current directory. Each library has a unique number. If a port number is specified, it is ignored. A library object attached to a non-HOME directory is automatically detached (without using DETACH) whenever a new library object is attached there.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| nlibrary | → | |
| :nport :nlibrary | → |
ATTACH, LIBS, PURGE
Command
Vector to Matrix Diagonal Command: Takes an array and a specified dimension and returns a matrix whose major diagonal elements are the elements of the array. Real number dimensions are rounded to integers. If a single dimension is given, a square matrix is returned. If two dimensions are given, the proper order is { number of rows, number of columns }. No more than two dimensions can be specified. If the main diagonal of the resulting matrix has more elements than the array, additional diagonal elements are set to zero. If the main diagonal of the resulting matrix has fewer elements than the array, extra array elements are dropped.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| [ array ]diagonals | { dim } | → | [[ matrix ]] |
→DIAG
Command
Matrix Diagonal to Array Command: Returns a vector that contains the major diagonal elements of a matrix. The input matrix does not have to be square.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| [[ matrix ]] | → | [ vector ]diagonals |
DIAG→
Command
Applies a holomorphic operator to a diagonalizable matrix.
Level 2/Argument 1: A diagonalizable matrix. Level 1/Argument 2: An operator, expressed as a function. The function can be stored in a variable with DEF, or can be a program, or a single expression.
The matrix that results from applying the operator to the matrix.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). 11 02
Apply the operator ex to the matrix
- -
DIAGMAP - 1 1 , << → X<<EXP(X) >> >>-
- 0 2 -
Command: or DIAGMAP([[1,1],[0,2]],exp(X)) EXP ( 1 ) – EXP ( 1 ) + EXP ( 2 )
0 EXP ( 2 )
Command
Displays a menu or list containing the CAS commands for differential calculus, including commands for working with series.
If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered list. If the flag is set, displays the operations as a menu of function keys.
ALGB, ARIT, CONSTANTS, EXP&LN, INTEGER, MAIN, MATHS, MATR, MODULAR, POLYNOMIAL, REWRITE, TESTS, TRIGO
Command
Differential Equation Plot Type Command: Sets the plot type to DIFFEQ. When the plot type is DIFFEQ and the reserved variable EQ does not contain a list, the initial value problem is solved and plotted over an interval using the Runge–Kutta–Fehlberg (4,5) method. The plotting parameters are specified in the reserved variable PPAR, which has the following form: { (xmin, ymin) (xmax, ymax) indep res axes ptype depend } For plot type DIFFEQ, the elements of PPAR are used as follows:
– If axes contains any strings other than 0, 1 or n, the DIFFEQ plotter uses the default strings 0 and 1, and plots the independent variable on the horizontal axis and the dependent variable on the vertical.
None
AXES, CONIC, FUNCTION, PARAMETRIC, POLAR, RKFSTEP, RRKSTEP, TRUTH
Function
Creates an empty directory structure in run mode. Can be used as an alternative to CRDIR to create an empty directory by typing DIR `NAME` STO, which will create an empty directory `NAME` if it does not already exist in the current directory.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | DIR …END |
CRDIR
Command
Display Command: Displays obj in the nth display line. n ≤ 1 indicates the top line of the display. To facilitate the display of messages, strings are displayed without the surrounding " " delimiters. All other objects are displayed in the same form as would be used if the object were in level 1 in the multiline display format. If the object display requires more than one display line, the display starts in line n, and continues down the display either to the end of the object or the bottom of the display. The object displayed by DISP persists in the display only until the keyboard is ready
for input. The FREEZE command can be used to cause the object to persist in the display until a key is pressed.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| obj | n | → |
The program « "ENTER Data Now" 1 DISP 7 FREEZE HALT » displays ENTER Data Now at the top of the display, “freezes” the entire display, and halts.
DISPXY, FREEZE, HALT, INPUT, PROMPT
Command
Display Command: Displays obj at the specified screen coordinates using a specified font size. The list argument expects exactly two binary integers to specify the X and Y coordinates. The level one integer argument n will display the obj using a small font if n is 1 and using the system font if n is 2. To facilitate the display of messages, strings are displayed without the surrounding " " delimiters. All other objects are displayed in the same form as would be used if the object were in level 1 in the multiline display format. If the object display requires more than one display line, the display starts at coordinate #x #y, and continues down the display either to the end of the object or the bottom of the display. NOTE: DISPXY is not useful for displaying grobs. The object displayed by DISPXY persists in the display only until the keyboard is ready for input. The FREEZE command can be used to cause the object to persist in the display until a key is pressed.
| Level 3/Argument 1 | Level 2/Argument 2 | Level 1/Argument 3 | Level 1/Item 1 | |
|---|---|---|---|---|
| obj | { list } | n | → |
DISP, FREEZE, HALT, INPUT, PROMPT
Command
Applies one step of the distributive property of multiplication and division with respect to addition and subtraction. Used for single-stepping through a multi-step distribution.
An expression.
An equivalent expression that results from applying the distributive property of multiplication over addition one time.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Expand (X+1)( X-1)( X+2).
| Command | DISTRIB((X+1)*(X-1)*(X+2)) |
|---|---|
| Result | X*(X-1)*(X+2)+1*(X-1)*(X+2) |
FDISTRIB
Command
Returns the divergence of a vector function.
Level 2/Argument 1: An array representing a vector function. Level 1/Argument 2: An array containing the variables.
The divergence of the vector function with respect to the specified variables.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Find the divergence of the following vector function:
2 2 2
v = x y i + x yj + y zk
˜ ˜ ˜
Command: DIV([X^2*Y, X^2*Y, Y^2*Z],[X,Y,Z])
Result: Y*(2*X)+(X^2+Y^2)
CURL, HESS
Command
Performs Euclidean division on two expressions. Step-by-step mode is available with this command.
Level 2/Argument 1: The dividend. Level 1/Argument 2: The divisor.
Level 2/Item 1: The quotient. Level 1/Item 2: The remainder.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Step-by-step mode can be set (flag –100 set). Radians mode must be set (flag –17 set).
Perform the following division: 2 x +x+1 ---------------------- 2x + 4
| Command | DIV2(X^2+X+1,2*X+4) |
|---|---|
| Result | {1/2(X-1),3} |
Command
Performs Euclidean division on two expressions modulo the current modulus.
Level 2/Argument 1: The dividend. Level 1/Argument 2: The divisor.
Level 2/Item 1: The quotient. Level 1/Item 2: The remainder.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). 3 x +4 ------------- 2
Find the result of x – 1 , modulo 3.
| Command | DIV2MOD(X^3+4,X^2-1) |
|---|---|
| Result | {X X+1} |
Command
Returns a list of divisors of a polynomial or an integer.
A polynomial or an integer.
A list containing the expressions or integers that exactly divide into the input.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Find the divisors of the following polynomial: 2 x + 3x + 2
| Command | DIVIS(X^2+3*X+2) |
|---|---|
| Result | {1,X+1,X+2,X^2+3*X+2} |
DIV2
Function
Divides two expressions modulo the current modulus.
Level 2/Argument 1: The dividend. Level 1/Argument 2: The divisor.
The quotient of the terms modulo the current modulus.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Modulo 3, divide 5x2+4x+2 by x2+1.
| Command | DIVMOD(5*X^2+4*X+2,X^2+1) |
|---|---|
| Result | -((X^2-X+1)/X^2+1)) |
Command
Returns a Taylor polynomial for the quotient of two polynomial expressions.
Level 3/Argument 1: The numerator expression. Level 2/Argument 2: The denominator expression. Level 1/Argument 3: The degree of the Taylor polynomial.
The Taylor polynomial at x = 0 of the quotient of the two expressions, to the specified degree.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). Incremental power mode must be set (flag –114 set).
Find the fourth degree Taylor polynomial for the following: 3 x + 4x + 12 ----------------------------- 11 11x + 1
| Command | DIVPC(X^3+4*X+12,11*X^11+1,4) |
|---|---|
| Result | 12+4*X+X^3 |
TAYLOR0, TAYLR, SERIES dn
Function
Differential of a function with respect to its argument n. For example d1f(x,y) is the differential of f(x,y) with respect to x and d3g(y,z,t) is the differential of g(y,z,t) with respect to t. The second- order derivative of f(x,y) with respect to x is written d1d1f(x,y). The dn function is an alternative to the ∂ function; d1f(x,y) is the same as ∂x(f(x,y)). dn does not require brackets after it, it must be followed immediately by the function name, with no spaces. dn differentiates with respect to the whole of argument n, see the example. dn is mainly used for formal arguments, see the example in DESOLVE, but can be used to differentiate expressions, as in the example.
dn does not change its argument, it works like the negative sign placed before a number or an expression. If the argument can be differentiated, N will carry out the differentiation.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Differentiate the function sin(2x) with respect to its argument:
| Command | EVAL(d1SIN(2*X)) |
|---|---|
| Result | COS(2*X) |
(Note that the function was differentiated with respect to its argument 2x, not with respect to the variable x.)
DERIV, DERVX, DESOLVE, ∂
Command
DO Indefinite Loop Structure Command: Starts DO…UNTIL…END indefinite loop structure. DO … UNTIL … END executes a loop repeatedly until a test returns a true (nonzero) result. Since the test clause is executed after the loop clause, the loop is always executed at least once. The syntax is: DO loop-clause UNTIL test-clause END DO starts execution of the loop clause. UNTIL ends the loop clause and begins the test clause. The test clause must return a test result to the stack. END removes the test result from the stack. If its value is zero, the loop clause is executed again; otherwise execution resumes following END.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| DO | → | |
| UNTIL | → | |
| END | T/F → |
The following program counts down from 100 to 0 and leaves the integers 100 to 0 on the stack: « 100 `A` STO A DO `A` DECR UNTIL `A==0` END `A` PURGE »
END, UNTIL, WHILE
Command
Do Error Command: Executes a “user-specified” error, causing a program to behave exactly as if a normal error had occurred during program execution. DOERR causes a program to behave exactly as if a normal error has occurred during program execution. The error message depends on the argument provided to DOERR:
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| nerror | → | |
| #nerror | → | |
| “error” | → | |
| 0 | → |
The following program takes a number from the stack and returns an error if the number is greater than 10:
« → X « CASE `X>10` THEN "X IS TOO BIG" DOERR END END » »
ERRM, ERRN, ERR0
Command
Do to List Command: Applies commands, programs, or user-defined functions to lists. The number of lists, n, can be omitted when the first or level 1 argument is any of the following:
| Ln+2/A1 ... L3/An–2 | L2/An+1 | L1/An+2 | Level 1/Item 1 | |
|---|---|---|---|---|
| { list }1 ... { list }n | n | « program » | → | { results } |
| { list }1 ... { list }n | n | command | → | { results } |
| { list }1 ... { list }n | n | name | → | { results } |
| { list }1 ... | { list }n+1 | « program » | → | { results } |
| { list }1 ... | { list }n+1 | command | → | { results } |
| { list }1 ... | { list }n+1 | name | → | { results } |
| L = Level; A = Argument | ||||
{ 1 2 3 } { 4 5 6 } { 7 8 9 } 3 « + * » DOLIST returns { 11 26 45 }.
DOSUBS, ENDSUB, NSUB, STREAM
Command
For a function of the current variable, lists the domains of real numbers for which the function is defined and for which it is undefined. DOMAIN works for functions of more than one argument, for example DOMAIN (X*X), and for user defined functions, as in the example below. For functions which it does not recognize, DOMAIN returns the message “Unknown operator”.
Level 1/Item 1: A function, or an expression, in terms of the current variable.
Level 1/Item 1: A list with regions where the function is undefined marked by `?` and regions where the function is defined marked by +. Rational singularities, such as 0 in 1/x, are not listed.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Define a function f =√(a+1) by typing DEF(F(A)=√(A+1)). Then tabulate the domain over which it is defined and undefined.
Command: DOMAIN(F(X))
Result: {`-∞` `?` –1 + `+∞`}, showing that the function f is undefined for values from –∞ to –1 and is
defined from –1 to +∞.
SIGNTAB, TABVAR
Command
Do to Sublist Command: Applies a program or command to groups of elements in a list. The real number n can be omitted when the first argument is one of the following:
command ENDSUB. Both of these commands return an Undefined Local Name error if executed when DOSUBS is not active. DOSUBS returns the Invalid User Function error if the object at level 1/argument 3 is a user program that does not contain only one command and does not have a user-defined function structure. DOSUBS also returns the Wrong Argument Count error if the object at level 1/argument 3 is a command that does not accept 1 to 5 arguments of specific types (DUP, ROT, or →LIST, for example).
| Level 3/Argument 1 | Level 2/Argument 2 | Level 1/Argument 3 | Level 1/Item 1 | |
|---|---|---|---|---|
| { list }1 | n | « program » | → | { list }2 |
| { list }1 | n | command | → | { list }2 |
| { list }1 | n | name | → | { list }2 |
| { list }1 | « program » | → | { list }2 | |
| { list }1 | command | → | { list }2 | |
| { list }1 name → { list }2 | ||||
| Example 1: { A B C D E } « - » DOSUBS returns | ||||
| { `A-B` `B-C` `C-D` `D-E` }. | ||||
Example 2: { A B C } 2 « DUP * * » DOSUBS returns | ||||
| { `A*(B*B)` `B*(C*C)` }. | ||||
Example 3: Entering
{ 1 2 3 4 5 } « → a b | ||||
| « CASE `NSUB==1` THEN a END `NSUB==ENDSUB` THEN b END `a+b` EVAL END » » DOSUBS returns { 1 5 7 5 }. | ||||
DOLIST, ENDSUB, NSUB, STREAM
Command
Dot Product Command: Returns the dot product A•B of two arrays A and B, calculated as the sum of the products of the corresponding elements of the two arrays. Both arrays must have the same dimensions. Some authorities define the dot product of two complex arrays as the sum of the products of the conjugated elements of one array with their corresponding elements from the other array. The calculator uses the ordinary products without conjugation. If you prefer the alternative definition, apply CONJ to one array before using DOT.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| [ array A ] | [ array B ] | → | x |
[ 1 2 3 ][ 4 5 6 ] DOT returns 32 (by calculating 1 x 4 + 2 x 5 + 3 x 6).
CNRM, CROSS, DET, RNRM
Command Operation
Draw Plot Command: Plots the mathematical data in the reserved variable EQ or the statistical data in the reserved variable ΣDAT, using the specified x- and y-axis display ranges. The plot type determines if the data in the reserved variable EQ or the data in the reserved variable ΣDAT is plotted. DRAW does not erase PICT before plotting; execute ERASE to do so. DRAW does not draw axes; execute DRAX to do so. When DRAW is executed from a program, the graphics display, which shows the resultant plot, does not persist unless PICTURE, PVIEW (with an empty list argument), or FREEZE is subsequently executed.
Simultaneous or Sequential Plot (–28), Curve Filling (–31)
None
AUTO, AXES, DRAX, ERASE, FREEZE, PICTURE, LABEL, PVIEW
Command
Draws a 3D plot from the values in a specified matrix. The number of rows indicates the number of units along the x axis, the number of columns indicates the number of units along the y axis, and the values in the matrix give the magnitudes of the plotted points along the z axis. In other words, the coordinates of a plotted point are (r, c, v) where r is the row number, c the column number and v the value in the corresponding cell of the matrix. You can limit the points that are plotted by specifying a minimum value (vmin) and a maximum value (vmax). Values in the matrix outside this range are not plotted. If all values are included, the total number of points plotted is r × c. Once the plot has been drawn, you can rotate it in various ways by pressing the following keys: ™ and š rotate the plot around the x axis (in different directions) — and ˜ rotate the plot around the y axis (in different directions) Iand L rotate the plot around the z axis (in different directions)
| Level 3/Argument 1 | Level 2/Argument 2 | Level 1/Argument 3 | Level 1/Item 1 | |
|---|---|---|---|---|
| [[ matrix ]] | vmin | vmax | → |
FAST3D
Command
Draw Axes Command: Draws axes in PICT. The coordinates of the axes intersection are specified by AXES. Axes tick-marks are specified in PPAR with the ATICK, or AXES command. DRAX does not draw axes labels; execute LABEL to do so.
None
AXES, DRAW, LABEL
Function
Returns an equation for the line through two given points in a plane. For more than two points, LAGRANGE will fit a polynomial.
Level 2/Argument 1: The first point, in the form a+b *i, or (a,b), where a and b must be numbers, or variables or expressions that evaluate to numbers. Level 1/Argument 2: The second point, in the form c+d *i, or (c,d), where c and d must be numbers, or variables or expressions that evaluate to numbers.
Level 1/Item 1: An equation for the straight line through the two points. The general form is Y=(d-b)/(c-a)*(X-a)+b.
Numeric mode must not be set (flag –3 clear). Complex mode must be set (flag –103 set). In algebraic mode, if any of a, b, c, d are variables, they will be converted to their numeric values, even if “argument to symbolic” mode is set (flag –3 clear). In RPN mode, they will be returned as variables. If ALG mode is set and “constants to numeric” mode is selected (flag –2 set) π and e used in inputs will be converted to their real number approximations, otherwise they will be returned in symbolic form.
| Example 1: Find an equation for the straight line through the points (1, 2), (3, 4). | |
|---|---|
| Command | DROITE((1, 2), (3, 4)) |
| Result | Y=X-1.+2. |
| Example 2: Find a symbolic equation for the straight line through the points (π, e), (e, π). | |
| Command | With “constants to symbolic ” mode selected and exact mode set, type: |
DROITE(π+e*i, e+π*i)
Result: Y=(π-e)/(e-π)*(X-π)+e
LAGRANGE
RPL Command
Drop Object Command: Removes the level 1 object from the stack.
| Level 1 | Level 1 | |
|---|---|---|
| obj | → |
CLEAR, DROPN, DROP2
RPL Command
Drop 2 Objects Command: Removes the first two objects from the stack.
| Level 2 | Level 1 | Level 1 | |
|---|---|---|---|
| obj1 | obj2 | → |
CLEAR, DROP, DROPN
RPL Command
Drop n Objects Command: Removes the first n + 1 objects from the stack (the first n objects excluding the integer n itself).
| Leveln+1 ... Level 2 | Level 1 | Level 1 | |
|---|---|---|---|
| obj1 ... objn | n | → |
CLEAR, DROP, DROP2
Command
Delete Tag Command: DTAG removes all tags (labels) from an object. The leading colon is not shown for readability when the tagged object is on the stack. DTAG has no effect on an untagged object.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| tag:obj | → | obj |
LIST→, →TAG
RPL Command
Duplicate Object Command: DUP returns a copy of the argument (or the object on level 1).
| Level 1 | Level 2 | Level 1 | |
|---|---|---|---|
| obj | → | obj | obj |
DUPN, DUP2, PICK
RPL Command
Duplicate 2 Objects Command: DUP2 returns copies of the two objects on levels 1 and 2 of the stack.
| L2 | L1 | L4 | L3 | L2 | L1 | |
|---|---|---|---|---|---|---|
| obj2 | obj1 | → | obj2 | obj1 | obj2 | obj1 |
| L = Level | ||||||
DUP, DUPN, PICK
RPL Command
Duplicates an object twice. Same as DUP DUP.
| Level 1 | Level 3 | Level 2 | Level 1 | |
|---|---|---|---|---|
| obj | → | obj | obj | obj |
DUP, NDUPN, DUPN, DUP2
RPL Command
Duplicate n Objects Command: Takes an integer n from level 1 of the stack, and returns copies of the objects on stack levels 2 through n + 1.
| Li+1 | Li …L3 | L2 | L1 | Li+n | Li+n–1 ... L2 | L1 | |
|---|---|---|---|---|---|---|---|
| obj1 | obj2 … obji–1 | obji | n | → | obj1 | obj2 ... obji–1 | obji |
| L = Level | |||||||
DUP, DUP2, PICK
Function
Degrees to Radians Function: Converts a real number representing an angle in degrees to its equivalent in radians. This function operates independently of the angle mode.
Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | (π/180)x |
| `symb` | → | `D→R(symb)` |
R→D
Function
e Function: Returns the symbolic constant e or its numerical representation, 2.71828182846.
When evaluated, e returns its numerical representation if flag –2 or –3 is set; otherwise, e returns its symbolic representation. The number returned for e is the closest approximation to 12-digit accuracy. For exponentiation, use the expression `EXP(x)` rather than e^x, since the function EXP uses a special algorithm to compute the exponential to greater accuracy. Even though the calculator often displays `EXP(x)` as e^x, it’s still `EXP(x)` internally.
Symbolic Constants (–2), Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | `e` | |
| → | 2.71828182846 |
EXP, EXPM, i, LN, LNP1, MAXR, MINR, π
Command
Edit Command: Moves specified object to the command line where it can be edited.
None
EDITB, VISIT
Command
Edit Best Command: Opens the specified object in the most suitable editor. For example, if you use a matrix as the specified object, the command opens it in Matrix Writer.
None
EDIT, VISIT
Command
Given two polynomials, a and b, returns polynomials u, v, and c where: au+bv=c In the equation, c is the greatest common divisor of a and b.
Level 2/Argument 1: The expression corresponding to a in the equation. Level 1/Argument 2: The expression corresponding to b in the equation.
Level 3/Item 1: The result corresponding to c in the equation. Level 2/Item 2: The result corresponding to u in the equation. Level 1/Item 3: The result corresponding to v in the equation.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Find the polynomials for u, v, and c, where c is the greatest common divisor of a and b such that: 2 u(x + 1) + v(x – 1) = c
| Command | EGCD(X^2+1,X-1) |
|---|---|
| Result | {2,1,-(X+1)} |
IEGCD, ABCUV
Command
Eigenvalues and Eigenvectors Command: Computes the eigenvalues and right eigenvectors for a square matrix. The resulting vector EVal contains the computed eigenvalues. The columns of matrix EVec contain the right eigenvectors corresponding to the elements of vector EVal. The computed results should minimize (within computational precision): A ⋅ EVec – EVec ⋅ diag ( EVal ) ------------------------------------------------------------------------------ n⋅ A
where diag (EVal) denotes the n × n diagonal matrix containing the eigenvalues EVal.
| Level 1/Argument 1 | Level 2/Item 1 | Level 1/Item 2 | |
|---|---|---|---|
| [[matrix ]]A | → | [[matrix ]]EVec | [vector ]EVal |
EGVL
Command
Eigenvalues Command: Computes the eigenvalues of a square matrix. The resulting vector L contains the computed eigenvalues.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| [[matrix ]]A | → | [vector ]EVal |
EGV
Command
ELSE Command: Starts false clause in conditional or error-trapping structure. See the IF and IFERR keyword entries for more information.
None
IF, CASE, DO, ELSE, IFERR, REPEAT, THEN, UNTIL, WHILE
Command
END Command: Ends conditional, error-trapping, and indefinite loop structures.
See the IF, CASE, IFERR, DO, and WHILE keyword entries for more information.
None
IF, CASE, DO, ELSE, IFERR, REPEAT, THEN, UNTIL, WHILE
Command
Ending Sublist Command: Provides a way to access the total number of sublists contained in the list used by DOSUBS. Returns an Undefined Local Name error if executed when DOSUBS is not active.
None
The following program subtracts the number of elements in a list from each element in the list
« → a « a 1 « ENDSUB - » » DOSUBS »
DOSUBS, NSUB
Command
Engineering Mode Command: Sets the number display format to engineering mode, which displays one to three digits to the left of the fraction mark (decimal point) and an exponent that is a multiple of three. The total number of significant digits displayed is n + 1. Engineering mode uses n + 1 significant digits, where 0 ≤ n ≤ 11. (Values for n outside this range are rounded up or down.) A number is displayed or printed as follows: (sign) mantissa E (sign) exponent where the mantissa is of the form (nn)n.(n…) (with up to 12 digits total) and the exponent has one to three digits. A number with an exponent of –499 is displayed automatically in scientific mode.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| n | → |
The number 103.6 in Engineering mode with five significant digits (n=4) would appear as 103.60E0. This same number with one significant digit (n=0) would appear as 100.E0.
FIX, SCI, STD
Function
Replaces all coefficients in a polynomial that have an absolute value less than that held in the CASDIR variable EPS, with 0. The default value of EPS is 1E-10, which can be changed by storing a new number in the variable EPS in the CASDIR directory; this must be less than 1.
A polynomial.
The polynomial with conforming coefficients replaced with 0.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Replace with zero the terms smaller than EPS in the expression: 10-13x + 10-2
| Command | EPSX0(1E-13*X+.01) |
|---|---|
| Result | 0*X+.01 |
Command
Starts the Equation Library application.
None
MSOLVR, SOLVEQN
Command
Opens Equation Writer, where you can edit an expression. Puts an object into the Equation Writer.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| exp1 | → | exp2 |
EDIT, EDITB, VISIT, VISITB
Command
Equation to Stack Command: Separates an equation into its left and right sides. If the argument is an expression, it is treated as an equation whose right side equals zero.
| Level 1/Argument 1 | Level 2/Item 1 | Level 1/Item 2 | |
|---|---|---|---|
| `symb1=symb2` | → | `symb1` | `symb2` |
| z | → | z | 0 |
| `name` | → | `name` | 0 |
| `x_unit` | → | `x_unit` | 0 |
| `symb` | → | `symb` | 0 |
ARRY→, DTAG, LIST→, OBJ→, STR→
Command
Erase PICT Command: Erases PICT, leaving a blank PICT of the same dimensions.
None
DRAW
Command
Clear Last Error Number Command: Clears the last error number so that a subsequent execution of ERRN returns # 0h, and clears the last error message.
None
DOERR, ERRM, ERRN
Command
Error Message Command: Returns a string containing the error message of the most recent calculator error. ERRM returns the string for an error generated by DOERR. If the argument to DOERR was 0, the string returned by ERRM is ‘Interrupted’.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | “error message” |
The program « IFERR + THEN ERRM END » returns "Bad Argument Type" to level 1 if improper arguments (for example, a complex number and a binary integer) are in levels 1 and 2.
DOERR, ERRN, ERR0
Command
Error Number Command: Returns the error number of the most recent calculator error. If the most recent error was generated by DOERR with a string argument, ERRN returns #70000h. If the most recent error was generated by DOERR with a binary integer argument, ERRN returns that binary integer. (If the most recent error was generated by DOERR with a real number argument, ERRN returns the binary integer conversion of the real number.) The only exceptions to these rules are 0 DOERR and #0 DOERR, both of which set ERRN to #31Fh and ERRM to ‘Interrupted’.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | #nerror |
The program « IFERR + THEN ERRN END » returns # 202h to level 1 if improper arguments (for example, a complex number and a binary integer) are in levels 1 and 2.
DOERR, ERRM, ERR0
Function
For a given integer, returns the number of integers less than the integer that are co-prime with the integer. (Euler’s Φ function.)
A non-negative integer, or an expression that evaluates to a non-negative integer.
The number of positive integers, less than, and co-prime with, the integer.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Command
Evaluate Object Command: Evaluates the object. The following table describes the effect of the evaluation on different object types.
| Object Type | Effect of Evaluation |
|---|---|
| Local Name | Recalls the contents of the variable. |
| Global Name | Calls the contents of the variable: |
Program Enters each object in the program:
List Enters each object in the list:
Tagged If the tag specifies a port, recalls and evaluates the
specified object. Otherwise, puts the untagged object on the stack.
Algebraic Enters each object in the algebraic expression:
| Command, Function, XLIB Name | Evaluates the specified object. |
|---|---|
| Other Objects | Puts the object on the stack. |
To evaluate a symbolic argument to a numerical result, evaluate the argument in Numerical Results mode (flag –3 set) or execute →NUM on that argument.
Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| obj | → | (see above) |
→NUM, SYSEVAL
Command
Returns the left- and right-hand sides of an equation as discrete expressions.
An equation.
Level 2/Item 1: The expression to the left of the “=” sign in the original equation, or, if the input is an expression and not an equation, the independent variable. Level 1/Item 2: The expression to the right of the “=” sign in the original equation, or, if the input is an expression, the expression.
Numeric mode must not be set (flag –3 clear). In Algebraic mode (flag –95 set), the output expressions are evaluated (variables are replaced by numeric values) before the result is returned.
Split the following equation into its two component expressions: sin(x)=5x+y
| Command | EXLR(SIN(X)=5*X+Y) |
|---|---|
| Result | {SIN(X), 5*X+Y} |
FXND
Command
Displays a menu or list of the CAS exponential and logarithmic operations.
If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered list. If the flag is set, displays the operations as a menu of function keys.
ALGB, ARIT, CONSTANTS, DIFF, INTEGER, MAIN, MATHS, MATR, MODULAR, POLYNOMIAL, REWRITE, TESTS, TRIGO
Analytic Function
Exponential Analytic Function: Returns the exponential, or natural antilogarithm, of the argument; that is, e raised to the given power. EXP uses extended precision constants and a special algorithm to compute its result to full 12- digit precision for all arguments that do not trigger an underflow or overflow error. EXP provides a more accurate result for the exponential than can be obtained by using e Q. The difference in accuracy increases as z increases. For example:
| z | EXP(z) | ez |
|---|---|---|
| 3 | 20.0855369232 | 20.0855369232 |
| 10 | 22026.4657948 | 22026.4657949 |
| 100 | 2.68811714182E43 | 2.68811714191E43 |
| 500 | 1.40359221785E217 | 1.40359221809E217 |
| 1000 | 1.9707111402E434 | 1.9707111469E434 |
For complex arguments: e(x,y) = excosy + iexsiny
Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| z | → | ez |
| `symb` | → | `EXP(symb)` |
ALOG, EXPM, LN, LOG
Function
Converts expressions involving the exponential function into expressions with hyperbolic functions.
An expression
The rewritten expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). 5 ⋅ ln ( x )
Rewrite in terms of hyperbolic functions the expression e
| Command | EXP2HYP(EXP(5*LN(X))) |
|---|---|
| Result | SINH(5*LN(X))+COSH(5*LN(X)) |
Function
Simplifies expressions involving the composition of the exponential and logarithmic functions. Compare this to LNCOLLECT which combines logarithmic terms; the difference is shown in the results of the second example used here and for LNCOLLECT.
An expression
The simplified expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
| Example 1: Simplify the expression e 5·ln(x) | |
|---|---|
| Command | EXP2POW(EXP(5*LN(X))) |
5
| Result | X Example 2: Simplify the expression e n·ln(x) |
|---|---|
| Command | EXP2POW(EXP(N*LN(X))) |
N
Result: X
LNCOLLECT
Command
Expand Products Command: Rewrites an algebraic expression or equation by expanding products and powers. This command is similar to the old HP 48G series command, with minor modifications (such as adding RISCH for integration).
Numerical Results (–3), Exact Mode (–105)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | x |
| `symb1` | → | `symb2` |
| (x, y) | → | (x, y) |
| Example 1: | `A^(B+C)` EXPAN returns `A^C*A^B` | |
| Example 2: | `(X+Y)^2` EXPAN returns `X^2+2*Y*X+Y^2` |
COLCT, EXPAND, ISOL, QUAD, SHOW
Command
Expands and simplifies an algebraic expression. This command is similar to the EXPAN command (which is included to ensure backward-compatibility with the HP 48-series calculators), except that EXPAND does more a more in-depth analysis and often does a better job at simplifying an expression than EXPAN.
An expression, or an array of expressions.
The expanded and simplified expression or array of expressions.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Simplify the following expression: 2 ( x + 2x + 1 ) ------------------------------- x+1
| Command | EXPAND((X^2+2*X+1)/(X+1)) |
|---|---|
| Result | X+1 |
EXPAN
Function
Expands and simplifies an algebraic expression, or an array of expressions, modulo the current modulus.
An expression, or an array of expressions.
The expanded and simplified expression, or array of expressions, modulo the current modulus.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Expand the following expression and give the result modulo 3: ( x + 3 )( x + 4 )
| Command | EXPANDMOD((X+3)*(X+4)) |
|---|---|
| Result | X^2+X |
Command
Exponential Curve Fit Command: Stores EXPFIT as the fifth parameter in the reserved variable ΣPAR, indicating that subsequent executions of LR are to use the exponential curve fitting model. LINFIT is the default specification in ΣPAR.
None
BESTFIT, LR, LINFIT, LOGFIT, PWRFIT
Command
Transforms the trigonometric terms in an expression to exponential and logarithmic terms.
An expression
The transformed expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). Complex mode must be set (flag –103 set).
Transform the following expression and simplify the result using the EXPAND command: 2 2 cos ( x )
Command: EXPLN(2*COS(X^2))
EXPAND(ANS(1))
Result: (EXP(i*X^2)^2+1)/EXP(i*X^2)
SINCOS
Analytic Function
Exponential Minus 1 Analytic Function: Returns ex – 1. For values of x close to zero, EXPM(x) returns a more accurate result than does EXP(x)–1. (Using EXPM allows both the argument and the result to be near zero, and avoids an intermediate result near 1. The calculator can express numbers within 10–449 of zero, but within only 10–11 of 1.)
Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | ex – 1 |
| `symb` | → | `EXPM(symb)` |
EXP, LNP1
Command
Eye Point Command: Specifies the coordinates of the eye point in a perspective plot.
xpoint, ypoint, and zpoint are real numbers that set the x-, y-, and z-coordinates as the eye-point from which to view a 3D plot’s view volume. The y-coordinate must always be 1 unit less than the view volume’s nearest point (ynear of YVOL). These coordinates are stored in the reserved variable VPAR.
| Level 3/Argument 1 | Level 2/Argument 2 | Level 1/Argument 3 | Level 1/Item 1 | |
|---|---|---|---|---|
| xpoint | ypoint | zpoint | → |
NUMX, NUMY, XVOL, XXRNG, YVOL, YYRNG, ZVOL
Function
Black Body Emissive Power Function: Returns the fraction of total black-body emissive power at temperature xT between wavelengths 0 and ylambda. If units are not specified, ylambda has implied units of meters and xT has implied units of K. F0λ returns a dimensionless fraction.
Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| ylambda | xT | → | xpower |
| ylambda | `symb` | → | `F0λ(ylambda,symb)` |
| `symb` | xT | → | `F0λ(symb,xT)` |
| `symb1` | `symb2` | → | `F0λ(symb1,symb2)` |
Command
Factorial (Gamma) Function: FACT is the same as ! and is provided for compatibility with the HP 28. See !.
Numerical Results (–3), Underflow Exception (–20), Overflow Exception (–21)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| n | → | n! |
| x | → | Γ(x + 1) |
| `symb` | → | `(symb)!` |
COMB, PERM, !
Command
Factorizes a polynomial or an integer:
An expression or an integer.
The factorized expression, or the integer expressed as the product of prime numbers.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Results including complex terms are returned if complex mode is set (flag –103 set).
Factorize the following: 2 x + 5x + 6
| Command | FACTOR(X^2+5*X+6) |
|---|---|
| Result | (X+2)(X+3) |
EXPAN, EXPAND
Function
Factorizes a polynomial modulo the current modulus. The modulus must be less than 100, and a prime number, it can be changed by MODSTO.
The expression to be factorized.
The factorized expression modulo the current modulus.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Factorize the following expression modulo 3. x2+2
| Command | FACTORMOD(X^2+2) |
|---|---|
| Result | (X+1)*(X-1) |
MODSTO
Command
For a value or expression, returns a list of prime factors and their multiplicities.
A value or expression.
A list of prime factors of the value or expression, with each factor followed by its multiplicity expressed as a real number.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
| Example 1: Find the prime factors of 100. | |
|---|---|
| Command | FACTORS(100) |
| Result | {5 2. 2 2.} |
2
| Example 2: Find the irreducible factors of: x + 4x + 4 | |
|---|---|
| Command | FACTORS(X^2+4*X+4) |
| Result | {X+2,2.} |
Function
Fanning Friction Factor Function: Calculates the Fanning friction factor of certain fluid flows. FANNING calculates the Fanning friction factor, a correction factor for the frictional effects of fluid flows having constant temperature, cross-section, velocity, and viscosity (a typical pipe flow, for example). xx/D is the relative roughness (the ratio of the conduit roughness to its diameter). yRe is the Reynolds number. The function uses different computation routines for laminar flow (Re ≤ 2100) and turbulent flow (Re > 2100). xx/D and yRe must be real numbers or unit objects that reduce to dimensionless numbers, and both numbers must be greater than 0.
Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| xx/D | yRe | → | xfanning |
| xx/D | `symb` | → | `FANNING(xx/D,symb)` |
| `symb` | yRe | → | `FANNING(symb,yRe)` |
| `symb1` | `symb2` | → | `FANNING(symb1,symb2)` |
DARCY
Command
Fast 3D Plot Type Command: Sets the plot type to FAST 3D. When plot type is set to FAST3D, the DRAW command plots an image graph of a 3-vector- valued function of two variables. FAST3D requires values in the reserved variables EQ, VPAR, and PPAR. VPAR is made up of the following elements: { xleft,xright, ynear, yfar,zlow,zhigh,xmin,xmax, ymin, ymax,xeye, yeye,zeye,xstep, ystep } For plot type FAST3D, the elements of VPAR are used as follows:
None
BAR, CONIC, DIFFEQ, FUNCTION, GRIDMAP, HISTOGRAM, PARAMETRIC, PARSURFACE, PCONTOUR, POLAR, SCATTER, SLOPEFIELD, TRUTH, WIREFRAME, YSLICE
Command
From an array of roots and multiplicities/poles, returns a rational polynomial with a leading coefficient of 1, with the specified set of roots or poles, and with the specified multiplicities.
An array of the form [Root 1, multiplicity/pole 1, Root 2, multiplicity/pole 2, . . .] The multiplicity/pole must be an integer. A positive number signifies a multiplicity. A negative number signifies a pole.
The rational polynomial with the specified roots and multiplicities/poles. The polynomial is written using the current independent variable.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Find the rational polynomial corresponding to the following set of roots and poles: 1, 2, 3, –1
| Command | FCOEF([1,2,3,-1]) |
|---|---|
| Result | (X-1)^2/(X-3) |
FROOTS
Command
Flag Clear? Command: Tests whether the system or user flag specified by nflag number is clear, and returns a corresponding test result: 1 (true) if the flag is clear or 0 (false) if the flag is set.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| nflag number | → | 0/1 |
CF, FC?C, FS? FS?C, SF
Command
Flag Clear? Clear Command: Tests whether the system or user flag specified by nflag number is clear, and returns a corresponding test result: 1 (true) if the flag is clear or 0 (false) if the flag is set. After testing, clears the flag.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| nflag number | → | 0/1 |
If flag –44 is set, -44 FC?C returns 0 to level 1 and clears flag –44.
CF, FC?, FS? FS?C, SF
Command
Performs a full distribution of multiplication and division with respect to addition and subtraction in a single step.
An expression.
An equivalent expression that results from fully applying the distributive property of multiplication and division over addition and subtraction.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Expand (X+1)(X-1)(X+2):
| Command | FDISTRIB((X+1)*(X-1)*(X+2)) |
|---|---|
| Result | X*(X*X)+2*(X*X)+(-(X*(1*X))+-(2*(1*X)))+ (X*(X*1)+2*(X*1)+ |
(-(X*(1*1))+-(2*(1*1))))
DISTRIB
Command
Discrete Fourier Transform Command: Computes the one- or two-dimensional discrete Fourier transform of an array. If the argument is an N-vector or an N × 1 or 1 × N matrix, FFT computes the one-dimensional transform. If the argument is an M × N matrix, FFT computes the two-dimensional transform. M and N must be integral powers of 2. The one-dimensional discrete Fourier transform of an N-vector X is the N-vector Y where:
–1 2πi kn
– --------------
Yk = ∑ Xn e
, i = –1
n=0
for k = 0, 1, …, N – 1. The two dimensional discrete Fourier transform of an M × N matrix X is the M × N matrix Y where: M–1
–1 2 πik m 2πi ln
– ---------------- – -----------------
Y kl = ∑ ∑ xm n e M e
,i = –1
m=0 n=0
for k = 0, 1, …, M – 1 and l = 0, 1, …, N – 1. The discrete Fourier transform and its inverse are defined for any positive sequence length. However, the calculation can be performed very rapidly when the sequence length is a power of two, and the resulting algorithms are called the fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT). The FFT command uses truncated 15-digit arithmetic and intermediate storage, then rounds the result to 12-digit precision.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| [ array ]1 | → | [ array ]2 |
IFFT
Command
Opens File Manager.
None
Command
Find Alarm Command: Returns the alarm index nindex of the first alarm due after the specified time. If the input is a real number date, FINDALARM returns the index of the first alarm due after 12:00 AM on that date. If the input is a list { date time }, it returns the index of the first alarm due after that date and time. If the input is the real number 0, FINDALARM returns the first past-due alarm. For any of the three arguments, FINDALARM returns 0 if no alarm is found.
Date Format (–42)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| date | → | nindex |
| { date time } | → | nindex |
| 0 | → | nindex |
DELALARM, RCLALARM, STOALARM
Command
Finish Server Mode Command: Terminates Kermit Server mode in a device connected to the calculator. FINISH is used by a local Kermit device to tell a server Kermit (connected via the serial port or the IR port) to exit Server mode.
I/O Device flag (–33), I/O Messages (–39), I/O Device for Wire (–78)
None
BAUD, CKSM, KGET, PARITY, PKT, RECN, RECV, SEND, SERVER
Command
Fix Mode Command: Sets the number display format to fix mode, which rounds the display to n decimal places.
Fix mode shows n digits to the right of the fraction mark (decimal point), where 0 ≤ n ≤ 11. (Values for n outside this range are rounded to the nearest integer.) A number is displayed or printed as (sign) mantissa, where the mantissa can be of any form. However, the calculator automatically displays a number in scientific mode if either of the following is true:
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| n | → |
The number 103.6 in Fix mode to four decimal places would appear as 103.6000.
SCI, STD
Command
Evaluate Flash Function Command: Evaluates unnamed Flash functions. WARNING: Use extreme care when executing this function. Using FLASHEVAL with random addresses will almost always cause a memory loss. Do not use this function unless you know what you are doing. #nfunction is of the form ffffbbbh, where bbb is the bank ID, and ffff is the function number.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| #nfunction | → |
EVAL, LIBEVAL, SYSEVAL
Function
Floor Function: Returns the greatest integer that is less than or equal to the argument.
Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | n |
| x_unit | → | n_unit |
| `symb` | → | `FLOOR(symb)` |
| Example 1: | 3.2 FLOOR returns 3. | |
| Example 2: | -3.2 FLOOR returns –4. |
CEIL, IP, RND, TRNC
Function
Font Function: Returns the system FONT6 object. You use this in conjunction with the →FONT command to set the system font to type 6.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | Font object |
FONT7, FONT8, →FONT, FONT→
Function
Font Function: Returns the system FONT7 object. You use this in conjunction with the →FONT command to set the system font to type 7.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | Font object |
FONT6, FONT8, →FONT, FONT→
Function
Font Function: Returns the system FONT8 object. You use this in conjunction with the →FONT command to set the system font to type 8.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | Font object |
FONT6, FONT7, →FONT, FONT→
FONT→
Function
Returns the current system font.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | Font object |
FONT6, FONT7, FONT8, →FONT
Function
Set font Function: Sets the system font. You use this in conjunction with one of the three font commands to set the system font. Valid input is any font object (TYPE 30) of size 6, 7, or 8.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| Font object | → |
FONT6, FONT7, FONT8, FONT→
Command Operation
FOR Definite Loop Structure Command: Starts FOR … NEXT and FOR … STEP definite loop structures. Definite loop structures execute a command or sequence of commands a specified number of times.
| Level 2/ | Level 1 | Level 1/Item 1 | |
|---|---|---|---|
| FOR xstart | xfinish | → | |
| NEXT → | |||
| FOR xstart | xfinish | → | |
| STEP | xincrement | → | |
| STEP | `symbincrement` | → | |
It should be noted that FOR inputs may also be integers (object type 28) and binary integers (type 10). FOR actually runs fastest on binary integers, runs “normally” on reals and slightly slower on integers.
The following program sums all odd integers in the range 1 to 100: « 0 1 100 FOR I I + 2 STEP »
NEXT, START, STEP
Function
Returns the nth coefficient of a complex Fourier series expansion. The PERIOD variable must be in the CAS directory, CASDIR, or in current path, and set to hold L, the period of the input function. The expression is expanded in terms of the current CAS variable.
Level 1/Argument 2: An expression in terms of the current variable Level 2/Argument 1: The number, n, of the coefficient to return.
The nth Fourier coefficient of the expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). Complex mode must be set, that is, flag –103 must be set.
Obtain the Fourier coefficient as below, with the default value of 2π in the PERIOD variable in CASDIR, and simplify it with EXPAND:
Command: FOURIER(X^2,0)
EXPAND(ANS(1))
Result: 4/3* π^2
Function
Fractional Part Function: Returns the fractional part of the argument. The result has the same sign as the argument.
Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | y |
| x_unit | → | y_unit |
| `symb` | → | `FP(symb)` |
| Example 1: | -32.3 FP returns -.3. | |
| Example 2: | 32.3_m FP returns .3_m. |
IP
Command
Do not use this command, a carry-over from the HP 48SX for handling plug-in RAM cards.
Command
Freeze Display Command: Freezes the part of the display specified by ndisplay area, so that it is not updated until a key is pressed. Normally, the stack display is updated as soon as the calculator is ready for data input. For example, when HALT stops a running program, or when a program ends, any displayed messages are cleared. The FREEZE command “freezes” a part or all of the display so that it is not updated until a key is pressed. This allows, for example, a prompting message to persist after a program halts to await data input. ndisplay area is the sum of the value codes for the areas to be frozen:
| Display Area | Value Code |
|---|---|
| Status area | 1 |
| History/Stack/Command-line area | 2 |
| Menu area | 4 |
So, for example, 2 FREEZE freezes the history/stack/command-line area, 3 FREEZE freezes the status area and the history/stack/command-line area, and 7 FREEZE freezes all three areas. Values of ndisplay area ≥ 7 or ≤ 0 freeze the entire display (are equivalent to value 7). To freeze the graphics display, you must freeze the status and stack/command-line areas (by entering 3), or the entire display (by entering 7).
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| ndisplayarea | → | |
| Example 1: | This program: | |
| « "Ready for data" 1 DISP 1 FREEZE HALT » displays the contents of the string in the top line of the display, then freezes the status area so that the string contents persist in the display after HALT is executed. | ||
Example 2: This program: | ||
| « { # 0d # 0d } PVIEW 7 FREEZE » selects the graphics display and then freezes the entire display so that the graphics display persists after the program ends. (If FREEZE was not executed, the stack display would be selected after the program ends.) To use FREEZE with PVIEW (or any graphics display), you must enter 3 or 7. | ||
None
CLLCD, DISP, HALT
Command
For a rational polynomial, returns an array of its roots and poles, with their corresponding multiplicities. This is the inverse of FCOEF and uses the same notation for roots and poles.
A rational polynomial.
An array of the form [Root 1, Multiplicity 1, Root 2, Multiplicity 2, . . .] A negative multiplicity indicates a pole.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). If complex mode is set (flag –103 set), FROOTS looks for complex solutions as well as real solutions. If approximate mode is set (flag –105 set) FROOTS searches for numeric roots.
FCOEF
Command
Flag Set? Command: Tests whether the system or user flag specified by nflag number is set, and returns a corresponding test result: 1 (true) if the flag is set or 0 (false) if the flag is clear.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| nflag number | → | 0/1 |
CF, FC?, FC?C, FS?C, SF
Command
Flag Set? Clear Command: Tests whether the system or user flag specified by nflag number is set, and returns a corresponding test result: 1 (true) if the flag is set or 0 (false) if the flag is clear. After testing, clears the flag.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| nflag number | → | 0/1 |
If flag –44 is set, -44 FS?C returns 1 to level 1 and clears flag –44.
CF, FC?, FC?C, FS?, SF
Command
Function Plot Type Command: Sets the plot type to FUNCTION. When the plot type is FUNCTION, the DRAW command plots the current equation as a real- valued function of one real variable. The current equation is specified in the reserved variable EQ. The plotting parameters are specified in the reserved variable PPAR, which has the form: { (xmin, ymin) (xmax, ymax) indep res axes ptype depend } For plot type FUNCTION, the elements of PPAR are used as follows:
otherwise, the values in (xmin, ymin) and (xmax, ymax)(the display range) are used. Lines are drawn between plotted points unless flag –31 is set. If EQ contains an expression or program, the expression or program is evaluated in Numerical Results mode for each value of the independent variable to give the values of the dependent variable. If EQ contains an equation, the plotting action depends on the form of the equation, as shown in the following table.
| Form of Current Equation | Plotting Action |
|---|---|
| expr = expr | Each expression is plotted separately. The intersection of |
the two graphs shows where the expressions are equal.
| name = expr | Only the expression is plotted. |
|---|---|
| indep = constant | A vertical line is plotted. |
If flag –28 is set, all equations are plotted simultaneously. If the independent variable in the current equation represents a unit object, you must specify the units by storing a unit object in the corresponding variable in the current directory. For example, if the current equation is X+3_m, and you want X to represent some number of inches, you would store 1_in (the number part of the unit object is ignored) in X. For each plotted point, the numerical value of the independent variable is combined with the specified unit (inches in this example) before the current equation is evaluated. If the result is a unit object, only the number part is plotted.
Simultaneous Plotting (–28), Curve Filling (–31)
None
BAR, CONIC, DIFFEQ, FAST3D, GRIDMAP, HISTOGRAM, PARAMETRIC, PARSURFACE, PCONTOUR, POLAR, SCATTER, SLOPEFIELD, TRUTH, WIREFRAME, YSLICE
Command
Splits an object into a numerator and a denominator.
A fraction, or an object that evaluates to a fraction.
The object split into numerator and denominator. Level 2/Item 1: The numerator. Level 1/Item 2: The denominator.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Return the numerator and the denominator of the following expression: 2 (x – 3) ------------------ z+4
| Command | FXND((X-3)^2/(Z+4)) |
|---|---|
| Result | {(X-3)^2, Z+4} |
EXLR
Function
Evaluate the Γ function at the given point. For a positive integer x, Γ(x) is equal to (x +1)! GAMMA differs from the FACT and ! functions because it allows complex arguments. The Γ function is defined by
+∞ – t x–1
Γ(x ) = ∫ e ⋅t dt
0 .
A real or complex number, x.
Γ(x). If the input x is an integer greater than 100, returns the symbolic expression GAMMA(x).
If the Underflow Exception (–20) or Overflow Exception (–21) flags are set then underflow or overflow conditions give errors, otherwise they give zero or the maximum real number the calculator can express. Complex mode must be set (flag –103 set) if x is complex.
FACT, PSI, Psi, !
Command
Returns the diagonal representation of a quadratic form.
Level 2/Argument 1: The quadratic form. Level 1/Argument 2: A vector containing the independent variables.
Level 4/Item 1: An array of the coefficients of the diagonal. Level 3/Item 2: A matrix, P, such that the quadratic form is represented as PTDP, where the diagonal matrix D contains the coefficients of the diagonal representation. Level 2/Item 3: The diagonal representation of the quadratic form. Level 1/Item 4: The vector of the variables.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Find the Gaussian symbolic quadratic form of the following: 2 x + 2axy
| Command | GAUSS(X^2+2*A*X*Y,[X,Y]) |
|---|---|
| Result | {[1,-A^2], [[1,A][0,1]], -(A^2*Y^2)+(A*Y+X)^2,[X,Y]} |
AXQ, QXA
Command
Returns a set of polynomials that are a Gröbner basis G of the ideal I generated from an input set of polynomials F.
Level 2/Argument 1: A vector F of polynomials in several variables. Level 1/Argument 2: A vector giving the names of the variables.
Level 1/Item 1: A vector containing the resulting set G of polynomials. The command attempts to order the polynomials as given in the vector of variable names.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Find a Gröbner basis of the ideal polynomial generated by the polynomials: x2 + 2xy2, xy + 2y3 – 1
| Command | GBASIS([X^2 + 2*X*Y^2, X*Y + 2*Y^3 – 1], [X,Y]) |
|---|---|
| Result | [X, 2*Y^3-1] |
Note this is not the minimal Gröbner basis, as the leading coefficient of the second term is not 1; the algorithm used avoids giving results with fractions.
GREDUCE
Function
Returns the greatest common divisor of two objects.
Level 2/Argument 1: An expression, or an object that evaluates to a number. Level 1/Argument 2: An expression, or an object that evaluates to a number.
The greatest common divisor of the two objects.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Find the greatest common divisor of 2805 and 99.
| Command | GCD(2805,99) |
|---|---|
| Result | 33 |
GCDMOD, EGCD, IEGCD, LCM
Function
Finds the greatest common divisor of two polynomials modulo the current modulus.
Level 2/Argument 1: A polynomial expression. Level 1/Argument 2: A polynomial expression.
The greatest common divisor of the two expressions modulo the current modulus.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Find the greatest common divisor of 2x^2+5 and 4x^2-5x, modulo 13.
| Command | GCDMOD(2X^2+5,4X^2-5X) |
|---|---|
| Result | -(4X-5) |
GCD
Command
Get Element Command: Returns from the argument 1/level 2 array or list (or named array or list) the real or complex number zget or object objget whose position is specified in argument 2/level 1. For matrices, nposition is incremented in row order.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| [[ matrix ]] | nposition | → | zget |
| [[ matrix ]] | { nrow, mcolumn } | → | zget |
| `namematrix` | nposition | → | zget |
| `namematrix` | { nrow, mcolumn } | → | zget |
| [ vector ] | nposition | → | zget |
| [ vector ] | {nposition } | → | zget |
| `namevector` | nposition | → | zget |
| `namevector` | {nposition } | → | zget |
| { list } | nposition | → | objget |
| { list } | {nposition } | → | objget |
| `namelist` | nposition | → | objget |
| `namelist` {nposition } → objget | |||
| Example 1: [[ 2 3 7 ][ 3 2 9 ][ 2 1 3 ] { 2 3 } GET returns 9. | |||
| Example 2: [[ 2 3 7 ][ 3 2 9 ][ 2 1 3 ] 8 GET returns 1. | |||
| Example 3: { A B C D E } { 1 } GET returns `A`. | |||
GETI, PUT, PUTI
Command
Get and Increment Index Command: Returns from the argument 1/level 2 array or list (or named array or list) the real or complex number zget or object objget whose position is specified in argument 2/level 1, along with the first (level 2) argument and the next position in that argument. For matrices, the position is incremented in row order.
Index Wrap Indicator (–64)
| L2/A1 | L1/A2 | L3/I1 | L2/I2 | L1/I3 | |
|---|---|---|---|---|---|
| [[ matrix ]] | nposition1 | → | [[ matrix ]] | nposition2 | zget |
| [[ matrix ]] | { nrow, mcolumn }1 | → | [[ matrix ]] | { nrow, mcolumn }2 | zget |
| `namematrix` | nposition1 | → | `namematrix` | nposition2 | zget |
| `namematrix` | { nrow, mcolumn }1 | → | `namematrix` | { nrow, mcolumn }2 | zget |
| [ vector ] | nposition | → | [ vector ] | nposition2 | zget |
| [ vector ] | {nposition1 } | → | [ vector ] | {nposition2 } | zget |
| `namevector` | nposition1 | → | `namevector | nposition2 | zget |
| `namevector` | {nposition1 } | → | `namevector | {nposition2 } | zget |
| { list } | nposition1 | → | { list } | nposition2 | objget |
| { list } | {nposition1 } | → | { list } | {nposition2 } | objget |
| `namelist` | nposition1 | → | `namelist` | nposition2 | objget |
| `namelist` | {nposition1 } | → | `namelist` | {nposition2 } | objget |
| L = Level; A = Argument; I = Item | |||||
GET, PUT, PUTI
Command
Graphics OR Command: Superimposes grob1 onto grobtarget or PICT, with the upper left corner pixel of grob1 positioned at the specified coordinate in grobtarget or PICT. GOR uses a logical OR to determine the state (on or off) of each pixel in the overlapping portion of the argument graphics object. If the first argument (stack level 3) is any graphics object other than PICT, then grobresult is returned to the stack. If the first argument (level 3) is PICT, no result is returned to the stack. Any portion of grob1 that extends past grobtarget or PICT is truncated.
| Level 3/Argument 1 | Level 2/Argument 2 | Level 1/Argument 3 | Level 1/Item 1 | |
|---|---|---|---|---|
| grobtarget | { #n #m } | grob1 | → | grobresult |
| grobtarget | (x, y) | grob1 | → | grobresult |
| PICT | { #n #m } | grob1 | → | |
| PICT | (x, y) | grob1 | → |
GXOR, REPL, SUB
Command
Grads Mode Command: Sets Grads angle mode. GRAD clears flag –17 and sets flag –18, and displays the GRD annunciator. In Grads angle mode, real-number arguments that represent angles are interpreted as grads, and real-number results that represent angles are expressed in grads.
None
DEG, RAD
Command
Finds an orthonormal base of a vector space with respect to a given scalar product.
Level 2/Argument 1: A vector representing a basis of a vector space. Level 1/Argument 2: A function that defines a scalar product in that space. This can be given as a program, or as the name of a variable containing the definition of the function.
An orthonormal base of the vector space with respect to the given scalar product.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Find an orthonormal base for the vector space with base [1, 1+X] with respect to the scalar product defined by : 1 P ⋅ Q = ∫ P ( x ) ⋅ Q ( x ) dx –1
Command: GRAMSCHMIDT([1,1+X], « → P Q « PREVAL(INTVX(P*Q),-1,1) » »)
1 X
------ -------------- 1 2 -- ⋅ 6 3 Result:
Command
Picture Environment Command: Selects the Picture environment GRAPH is provided for compatibility with the HP 28 series. GRAPH is the same as PICTURE; see its listing for details.
Command
Reduces a polynomial with respect to a Gröbner basis.
Level 3/Argument 1: A vector of polynomials in several variables. Level 2/Argument 2: A vector of polynomials that is a Gröbner basis in the same variables. Level 1/Argument 3: A vector giving the names of the variables.
Level 1/Item 1: A vector containing the input polynomial reduced with respect to the Gröbner basis, up to a constant; as with GBASIS, fractions in the result are avoided.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Reduce the polynomial: x2y – xy – 1 with respect to the Gröbner basis (obtained in the example for GBASIS): x, 2y3 – 1
| Command | GREDUCE(X^2*Y–X*Y–1, [X,2*Y^3–1], [X,Y]) |
|---|---|
| Result | -1 |
Note this is the remainder of the input polynomial modulo the term x in the Gröbner basis
GBASIS
Command
GRIDMAP Plot Type Command: Sets the plot type to GRIDMAP. When plot type is set GRIDMAP, the DRAW command plots a mapping grid representation of a 2-vector-valued function of two variables. GRIDMAP requires values in the reserved variables EQ, VPAR, and PPAR. VPAR has the following form: {xleft, xright, ynear, yfar, zlow, zhigh, xmin, xmax, ymin, ymax, xeye, yeye, zeye, xstep, ystep} For plot type GRIDMAP, the elements of VPAR are used as follows:
None
BAR, CONIC, DIFFEQ, FUNCTION, HISTOGRAM, PARAMETRIC, PARSURFACE, PCONTOUR, POLAR, SCATTER, SLOPEFIELD, TRUTH, WIREFRAME, YSLICE
Command
Stack to Graphics Object Command: Creates a graphics object from a specified object, where the argument nchar size specifies the character size of the object. nchar size can be 0, 1 (small), 2 (medium), or 3 (large). nchar size = 0 is the same as nchar size = 3, except for unit objects and algebraic objects, where 0 specifies the Equation Writer application picture.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| obj | ncharsize | → | grob |
This program: « `Y=3*X^2` 0 →GROB PICT STO { } PVIEW » returns a graphics object to the stack representing the Equation Writer application picture of `Y=3*X^2`, then stores the graphics object in PICT and shows it in the graphics display with scrolling activated.
→LCD, LCD→
Command
Enters GROB on the command line to help with the manual entry of a graphic object.
Command
Combines two graphic objects by appending the second argument onto the bottom of the first.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| GROB1 | GROB2 | → | GROB3 |
Command
Graphics Exclusive OR Command: Superimposes grob1 onto grobtarget or PICT, with the upper left corner pixel of grob1 positioned at the specified coordinate in grobtarget or PICT. GXOR is used for creating cursors, for example, to make the cursor image appear dark on a light background and light on a dark background. Executing GXOR again with the same image restores the original picture. GXOR uses a logical exclusive OR to determine the state of the pixels (on or off) in the overlapping portion of the argument graphics objects. Any portion of grob1 that extends past grobtarget or PICT is truncated. If the first (level 3) argument (the target graphics object) is any graphics object other than PICT, then grobresult is returned to the stack. If the first (level 3) argument is PICT, no result is returned to the stack.
| Level 3/Argument 1 | Level 2/Argument 2 | Level 1/Argument 3 | Level 1/Item 1 | |
|---|---|---|---|---|
| grobtarget | { #n, #m } | grob1 | → | grobresult |
| grobtarget | (x, y) | grob1 | → | grobresult |
| PICT | { #n, #m } | grob1 | → | |
| PICT | (x, y) | grob1 | → |
This program: « ERASE PICT NEG PICT { # 0d # 0d }
GROB 5 x 5 11A040A011 GXOR LASTARG GXOR » turns on (makes dark) every pixel in PICT, then superimposes a 5 x 5 graphics object on PICT at pixel coordinates { # 0d # 0d }. Each on-pixel in the 5 by 5 graphics object turns off (makes light) the corresponding pixel in PICT. Then, the original picture is restored by executing GXOR again with the same arguments.
GOR, REPL, SUB
Command
Multiply Height Command: Multiplies the vertical plot scale by xfactor. *H is provided for compatibility with the HP 48. *H is the same as SCALEH; see its listing for details.
Command
Performs an element by element multiplication of two matrices (Hadamard product).
Level 2/Argument 1: Matrix 1. Level 1/Argument 2: Matrix 2. The matrices must have the same order.
The matrix representing the result of the multiplication.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Find the Hadamard product of the following two matrices:
| 3 –1 2 | 2 3 0 |
|---|---|
| 0 1 4 | 1 5 2 |
and
| Command | HADAMARD([[3,-1,2][0,1,4]],[2,3,0][1,5,2]]) |
|---|---|
| Result | [[6,-3,0][0,5,8]] |
Command
Transforms an expression by replacing sin(x), cos(x) and tan(x) subexpressions with tan(x/2) terms.
An expression
The transformed expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
TAN2CS2, TAN2SC2
Command
Halt Program Command: Halts program execution. Program execution is halted at the location of the HALT command in the program. The HLT annunciator is turned on. Program execution is resumed by executing CONT (that is, by pressing !æ). Executing KILL cancels all halted programs.
None
CONT, KILL
Command
First Listed Element Command: Returns the first element of a list or string.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| { obj1, ... ,objn } | → | obj1 |
| “string” | → | “element1” |
| Example 1: | "Dead" HEAD returns "D". | |
| Example 2: | The following program takes a list of coordinates { A B C } that define a right triangle, and finds | |
| the length of the hypotenuse AC: « DUP HEAD SWAP REVLIST HEAD - ABS » For example, entering { (0,0) (0,3) (3,4) } returns 5. | ||
TAIL
Command
Header size: Returns the current size of the header in lines.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | Header size |
→HEADER
Command
Header size: Sets the current size of the header in lines: to 0, 1, or 2 lines.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| Header size | → |
HEADER→
Command
Similar to CASCMD, displays a list of CAS operations. Selecting one with OK displays help for it, an example of the operation, and the option to copy the example to the command line. More details are given in Appendix C and Appendix H of the User’s Guide.
CASCMD
Function
Returns the nth Hermite polynomial.
A non-negative integer.
The corresponding polynomial expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Find the Hermite polynomial with degree 4.
| Command | HERMITE(4) |
|---|---|
| Result | 16*X^4-48*X^2+12 |
LEGENDRE, TCHEBYCHEFF
Command
Returns the Hessian matrix and the gradient of an expression with respect to the specified variables.
Level 2/Argument 1: An expression. Level 1/Argument 2: A vector of the variables.
Level 3/Item 1: The Hessian matrix with respect to the specified variables. Level 2/Item 2: The gradient with respect to the variables. Level 1/Item 3: The vector of the variables.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Find the Hessian matrix, and the gradient with respect to each variable, of the expression: t2 + 2tu2.
| Command | HESS(T^2+2*T*U^2, [T, U]) |
|---|---|
| Result | {[[2, 2*(2*U)], [2*(2*U), 2*(2*T)]], [2*T+2*U^2, 2*T*(2*U)], [T, U]} |
CURL, DIV
Command
Hexadecimal Mode Command: Selects hexadecimal base for binary integer operations. (The default base is decimal.) Binary integers require the prefix #. Binary integers entered and returned in hexadecimal base automatically show the suffix h. If the current base is not hexadecimal, then you can enter a hexadecimal number by ending it with h. It will be displayed in the current base when it is entered. The current base does not affect the internal representation of binary integers as unsigned binary numbers.
Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12)
None
BIN, DEC, OCT, RCWS, STWS
Command
Returns a square Hilbert matrix of the specified order.
A positive integer, representing the order.
The Hilbert matrix of the specified order.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Find the order 3 Hilbert matrix.
Command: HILBERT(3)
1 1 1 -- -- 2 3 1 1 1 -- -- -- 2 3 4 1 1 1 -- -- -- 3 4 5
CON, IDN, RANM, VANDERMONDE
Command
Histogram Plot Type Command: Sets the plot type to HISTOGRAM. When the plot type is HISTOGRAM, the DRAW command creates a histogram using data from one column of the current statistics matrix (reserved variable ΣDAT). The column is specified by the first parameter in the reserved variable ΣPAR (using the XCOL command). The plotting parameters are specified in the reserved variable PPAR, which has the form: { (xmin, ymin) (xmax, ymax) indep res axes ptype depend } For plot type HISTOGRAM, the elements of PPAR are used as follows:
None
BAR, CONIC, DIFFEQ, FUNCTION, GRIDMAP, PARAMETRIC, PARSURFACE, PCONTOUR, POLAR, SCATTER, SLOPEFIELD, TRUTH, WIREFRAME, YSLICE
Command
Draw Histogram Plot Command: Plots a frequency histogram of the specified column in the current statistics matrix (reserved variable ΣDAT). The data column to be plotted is specified by XCOL and is stored as the first parameter in the reserved variable ΣPAR. If no data column is specified, column 1 is selected by default. The y-axis is autoscaled and the plot type is set to HISTOGRAM. HISTPLOT plots relative frequencies, using 13 bins as the default number of partitions. The RES command lets you specify a different number of bins by specifying the bin width. To plot a frequency histogram with numerical frequencies, store the frequencies in ΣDAT and execute BINS and then BARPLOT. When HISTPLOT is executed from a program, the graphics display, which shows the resultant plot, does not persist unless PICTURE, PVIEW (with an empty list argument), or FREEZE is subsequently executed.
None
BARPLOT, BINS, FREEZE, PICTURE, PVIEW, RES, SCATRPLOT, XCOL
Command
Hours-Minutes-Seconds Minus Command: Returns the difference of two real numbers, where the arguments and the result are interpreted in hours-minutes-seconds format. The format for HMS (a time or an angle) is H.MMSSs, where:
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| HMS1 | HMS2 | → | HMS1 – HMS2 |
HMS→, →HMS, HMS+
Command
Hours-Minutes-Seconds Plus Command: Returns the sum of two real numbers, where the arguments and the result are interpreted in hours-minutes-seconds format.
The format for HMS (a time or an angle) is H.MMSSs, where:
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| HMS1 | HMS2 | → | HMS1 + HMS2 |
HMS→, →HMS, HMS–
Command
Hours-Minutes-Seconds to Decimal Command: Converts a real number in hours-minutes- seconds format to its decimal form (hours or degrees with a decimal fraction). The format for HMS (a time or an angle) is H.MMSSs, where:
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| HMS | → | x |
→HMS, HMS+, HMS–
Command
Decimal to Hours-Minutes-Seconds Command: Converts a real number representing hours or degrees with a decimal fraction to hours-minutes-seconds format. The format for HMS (a time or an angle) is H.MMSSs, where:
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | HMS |
HMS→, HMS+, HMS–
Command
HOME Directory Command: Makes the HOME directory the current directory.
None
CRDIR, PATH, PGDIR, UPDIR
Command
Executes a Horner scheme on a polynomial. That is, for a given polynomial P, and a number r, HORNER returns QUOT(P/(x–r)), r and also P(r)
Level 2/Argument 1: A polynomial, P. Level 1/Argument 2: A number, r.
Level 3/Item 1: QUOT(P/(x–r)) Level 2/Item 2: r Level 1/Item 3: P(r), the remainder of the division process.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
For r = 3, find the result of executing a Horner scheme on the following polynomial: 2 x +x+1
| Command | HORNER(X^2+X+1,3) |
|---|---|
| Results | (X+4,3,13) |
Function
i Function: Returns the symbolic constant i or its numerical representation, (0, 1).
Symbolic Constants (–2), Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | `i` | |
| → | (0,1) |
e, MAXR, MINR, π
Command
Returns a solution in integers u and v of au + bv = c, where a, b, and c are integers.
Level 3/Argument 1: the value of a. Level 2/Argument 2: the value of b. Level 1/Argument 3: the value of c.
Level 2/Item 1: The value for u. Level 1/Item 2: The value for v.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Find a solution in integers of the equation: 6a + 11b = 3
| Command | IABCUV(6,11,3) |
|---|---|
| Result | {6,-3} |
ABCUV, IEGCD
Command
Determines the basis of the intersection between two vector spaces.
Two lists of vectors
A list of vectors.
Exact mode must be set (flag –105 clear).
Find a vector of a basis of the intersection of the vector sub-spaces defined by [1, 2] and [2, 4]
| Command | IBASIS({[1,2]}, {[2,4]}) |
|---|---|
| Result | {[1,2]} |
BASIS
Function
Returns the nth Bernoulli number for a given integer n.
Level 1/Argument 1: an integer.
Level 1/Item 1: The corresponding nth Bernoulli number for the integer. For numbers greater than about 40 the calculation can take a long time.
Numeric mode must not be set (flag –3 clear).
Command
Performs integration by parts on a function. The function must be able to be represented as a product of two functions, where the antiderivative of one of the functions is known: f(x) = u(x).v’(x) Note that the command is designed for use in RPN mode only.
Level 2: The integrand expressed as a product of two functions, u(x).v’(x) Level 1: The antiderivative of one of the component functions, v(x).
Level 2: u(x)v(x) Level 1: -u`(x)v(x)
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Use integration by parts to calculate the following: ∫ x cos ( x ) dx Command 1: Apply the IBP command in RPN mode: Level 2: X*COS(X) Level 1: SIN(X)
Result: Level 2: SIN(X)*X
Level 1: -SIN(X) Command 2: Apply the INTVX command to level 1, -SIN(X)
Result: Level 2: SIN(X)*X
Level 1: COS(X) Command 3: Press + to add the result to the value at level 2 to obtain the final result.
Result: SIN(X)*(X)+COS(X)
INTVX, INT, PREVAL, RISCH
Command
Solves a system of two congruences in integers using the Chinese Remainder theorem.
Level 2/Argument 1: A vector of the first value and the modulus. Level 1/Argument 2: A vector of the second value and the modulus.
A vector of the solution.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Solve the following system of congruences: x ≡ 2 Modulo 3 x ≡ 1 Modulo 5
| Command | ICHINREM([2,3],[1,5]) |
|---|---|
| Results | [-4, 15] |
CHINREM
Command
Identity Matrix Command: Returns an identity matrix; that is, a square matrix with its diagonal elements equal to 1 and its off-diagonal elements equal to 0. The result is either a new square matrix, or an existing square matrix with its elements replaced by the elements of the identity matrix, according to the argument.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| n | → | [[ R-matrixidentity ]] |
| [[ matrix ]] | → | [[ matrixidentity ]] |
| `name` | → | [[ matrixidentity ]] |
CON
Command
For two integers, a and b, returns the integer part of a/b, and the remainder, r.
Level 2/Argument 1: a. Level 1/Argument 2: b.
Level 2/Item 1: The integer part of a/b. Level 1/Item 2: The remainder.
Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Return the integer part and the remainder of 11632/864.
| Command | IDIV2(11632,864) |
|---|---|
| Result | {13,400} |
DIV2, IQUOT
Command
Given two integers x and y, returns three integers, a, b, and c, such that: ax+by=c where c is the GCD of x and y.
Level 2/Argument 1: x. Level 1/Argument 2: y.
Level 3/Item 1: c. Level 2/Item 2: a. Level 1/Item 3: b. Note the order, c is first.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Find a, b and c such that a18 + b24 = c, where c is the GCD of 18 and 24.
| Command | IEGCD(18,24) |
|---|---|
| Result | {6,-1,1} |
ABCUV, EGCD, IABCUV
Command Operation
IF Conditional Structure Command: Starts IF … THEN … END and IF … THEN … ELSE … END conditional structures. Conditional structures, used in combination with program tests, enable a program to make decisions.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| IF | → | |
| THEN | T/F | → |
| END IF | ||
| THEN | T/F | → |
| ELSE → | ||
| END → | ||
CASE, ELSE, END, IFERR, THEN
Command
If Error Conditional Structure Command: Starts IFERR … THEN … END and IFERR … THEN … ELSE … END error trapping structures. Error trapping structures enable program execution to continue after a “trapped” error occurs.
3 The key buffer is cleared. 4 If any or all of the display is “frozen” (by FREEZE), that state is cancelled. 5 If Last Arguments is enabled, the arguments to the command that caused the error are returned to the stack. 6 Program execution jumps to the error clause. The commands in the error clause are executed only if an error is generated during execution of the trap clause.
Last Arguments (–55)
None
The following program uses IFERR much like the built-in linear system of equations solver. The program takes a result vector and a matrix of coefficients and returns a least-squares solution to the equations.
« → a b « IFERR a b / THEN LSQ END » »
CASE, ELSE, END, IF, THEN
Command
Inverse Discrete Fourier Transform Command: Computes the one- or two-dimensional inverse discrete Fourier transform of an array. If the argument is an N-vector or an N × 1 or 1 × N matrix, IFFT computes the one-dimensional inverse transform. If the argument is an M × N matrix, IFFT computes the two-dimensional inverse transform. M and N must be integral powers of 2. The one-dimensional inverse discrete Fourier transform of an N-vector Y is the N-vector X where: 2πik n
–1 --------------
1
X n = --- ∑ Y k e ,i = –1
k=0
for n = 0, 1, …, N – 1. The two-dimensional inverse discrete Fourier transform of an M × N matrix Y is the M × N matrix X where: M – 1
– 1 2πi km 2πi ln
---------------- ----------------- 1 X mn = -------- ∑ ∑ Y kl e M e
, i = –1
M k = 0 l = 0
for m = 0, 1, …, M – 1 and n = 0, 1, …, N – 1. The discrete Fourier transform and its inverse are defined for any positive sequence length. However, the calculation can be performed very rapidly when the sequence length is a power of two, and the resulting algorithms are called the fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT). The IFFT command uses truncated 15-digit arithmetic and intermediate storage, then rounds the result to 12-digit precision.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| [ array ]1 | → | [ array ]2 |
FFT
Command
IF-THEN Command: Executes obj if T/F is nonzero. Discards obj if T/F is zero. IFT lets you execute in stack syntax the decision-making process of the IF … THEN … END conditional structure. The “true clause” is obj in argument 2 (level 1).
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| T/F | obj | → | It depends! |
« X 0 > "Positive" IFT » puts "Positive" in level 1 if X contains a positive real number.
IFTE
Function
IF-THEN-ELSE Function: Executes the obj in argument 2 or level 2 if T/F is nonzero. Executes the obj in argument 3 or level 1 if T/F is zero. IFTE lets you execute in stack syntax the decision-making process of the IF … THEN … ELSE … END conditional structure. The “true clause” is objtrue in argument 2 or level 2. The “false clause” is objfalse in argument 3 or level 1. IFTE is also allowed in algebraic expressions, with the following syntax: IFTE(test,true-clause,false-clause) When an algebraic containing IFTE is evaluated, its first argument test is evaluated to a test result. If it returns a nonzero real number, true-clause is evaluated. If it returns zero, false-clause is evaluated.
| Level 3/Argument 1 | Level 2/Argument 2 | Level 1/Argument 3 | Level 1/Item 1 | |
|---|---|---|---|---|
| T/F | objtrue | objfalse | → | It depends! |
| Example 1: The command sequence X 0 Š "Positive" "Negative" IFTE leaves | ||||
| "Positive" on the stack if X contains a non-negative real number, or "Negative" if X contains a negative real number. | ||||
Example 2: The algebraic `IFTE(X‹0,SIN(X)/X,1)` returns the value of sin(x)/x, even for x = 0, | ||||
| which would normally cause an Infinite Result error. | ||||
IFT
Function
Returns the inverse Laplace transform of an expression. The expression must evaluate to a rational fraction.
A rational expression.
The inverse Laplace transformation of the expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). 1
Find the inverse Laplace transform of:------------------2 (x – 5 )
| Command | ILAP(1/(X-5)^2) |
|---|---|
| Result | X*EXP(5*X) |
LAP, LAPL
Function
Imaginary Part Function: Returns the imaginary part of its complex argument. If the argument is an array, IM returns a real array, the elements of which are equal to the imaginary parts of the corresponding elements of the argument array. If the argument array is real, all of the elements of the result array are zero.
Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | 0 |
| (x, y) | → | y |
| [ R-array ] | → | [ R-array ] |
| [ C-array ] | → | [ R-array ] |
| `symb` | → | `IM(symb)` |
C→R, RE, R→C
Command
Computes the basis of the image (also called the range) of a linear application f.
A matrix representing a linear application f in terms of the standard basis.
A list of vectors representing a basis of the image of f.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). 112 213 314
Find the image of
| Command | IMAGE([1,1,2] [2,1,3] [3,1,4]) |
|---|---|
| Result | {[1,0,-1] [0,1,2]} |
BASIS, KER
Command
Increment Command: Takes a variable, adds 1, stores the new value back into the original variable, and returns the new value. The value in name must be a real number or an integer.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `name` | → | xincrement |
If 35.7 is stored in A, `A` INCR returns 36.7.
DECR
Command
Independent Variable Command: Specifies the independent variable and its plotting range. The specification for the independent variable name and its plotting range is stored as the third parameter in the reserved variable PPAR. If the argument to INDEP is a:
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| `global` | → | ||
| { global } | → | ||
| { global xstart xend } | → | ||
| {xstart xend } | → | ||
| xstart | xend | → |
DEPND
Command
User-Defined Dialog Box Command: Creates a user-defined input form (dialog box). INFORM creates a standard dialog box based upon the following specifications:
| Variable | Function |
|---|---|
| “title” | Title. This appears at the top of the dialog box. |
| Variable | Function |
| {s1 s2 … sn} | Field definitions. A field definition (sx) can have two formats: “label”, a field |
label, or { “label” “helpInfo” type0 type1 … typen }, a field label with optional help text that appears near the bottom of the screen, and an optional list of valid object types for that field. If object types aren’t specified, all object types are valid. For information about object types, see the TYPE command. When creating a multi-column dialog box, you can span columns by using an empty list as a field definition. A field that appears to the left of an empty field automatically expands to fill the empty space.
format Field format information. This is the number col or a list of the form { col tabs
}: col is the number of columns the dialog box has, and tabs optionally specifies the number of tab stops between the labels and the highlighted fields. This list can be empty. col defaults to 1 and tabs defaults to 3.
{ resets } Default values displayed when RESET is selected. Specify reset values in the
list in the same order as the fields were specified. To specify no value, use the NOVAL command as a place holder. This list can be empty.
{ init } Initial values displayed when the dialog box appears. Specify initial values in
the list in the same order as the fields were specified. To specify no value, use the NOVAL command as a place holder. This list can be empty.
If you exit the dialog box by selecting OK or `, INFORM returns the field values { vals } in item 1 or level 2, and puts a 1 in item 2 or level 1. (If a field is empty, NOVAL is returned as a place holder.) If you exit the dialog box by selecting CANCEL or B, INFORM returns 0.
| L5/A1 | L4/A2 | L 3 A3 | L2/A4 | L1/A5 | L2/I1 | L1/I2 | |
|---|---|---|---|---|---|---|---|
| “title” | {s1 s2 ... sn } | format | {resets } | {init } | → { vals } | 1 | |
| “title” | {s1 s2 ... sn } | format | {resets } | {init } | → | 0 | |
| L = Level; A = Argument; I = item | |||||||
Place the following five lines on the stack and run INFORM: "The Title" { { "ONE" "Name?" 2 } { } { "TWO" "Age?" } { "THREE" "Lucky numbers?" 5 } } { 2 } { NOVAL NOVAL { 1 2 3 } } { "Charlotte" NOVAL { 4 5 6 } }
CHOOSE, INPUT, NOVAL, TYPE
Command
Input Command: Prompts for data input to the command line and prevents the user access to stack operations. When INPUT is executed, the stack or history area is blanked and program execution is suspended for data input to the command line. The contents of “stack prompt” are displayed at the top of the screen. Depending on the second argument (level 1), the command line may also contain the contents of a string, or it may be empty. Pressing ` resumes program execution and returns the contents of the command line in string form.
In its general form, the second argument (level 1) for INPUT is a list that specifies the content and interpretation of the command line. The list can contain one or more of the following parameters, in any order:
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| “stack prompt” | “command-line prompt” | → | “result” |
| “stack prompt” | { listcommand-line } | → | “result” |
PROMPT, STR→
Function
Calculates the antiderivative of a function for a given variable, at a given point.
Level 3/Argument 1: A function. Level 2/Argument 2: The variable to obtain the derivative with respect to. Level 1/Argument 3: The point at which to calculate the antiderivative. This point can be a variable or an expression.
The antiderivative of the function for the given variable, at the point you specified.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Find the integral of sin(x) with respect to x, at the point where x=y.
| Command | INT(SIN(X),X,Y) |
|---|---|
| Result | -COS(Y) |
INTVX, RISCH
Command
Displays a menu or list of CAS integer operations.
If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered list. If the flag is set, displays the operations as a menu of function keys.
ALGB, ARIT, CONSTANTS, DIFF, EXP&LN, MAIN, MATHS, MATR, MODULAR, POLYNOMIAL, REWRITE, TESTS, TRIGO
Function
Finds the antiderivative of a function symbolically, with respect to the current default variable.
An expression.
The antiderivative of the expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Find the antiderivative of the following: 2 x ln x
| Command | INTVX(X^2*LN(X)) |
|---|---|
| Result | 1/3*X^3*LN(X)+(-1/9)*X^3 |
IBP, RISCH, PREVAL
Analytic function
Inverse (1/x) Analytic Function: Returns the reciprocal or the matrix inverse. For a complex argument (x, y), the inverse is the complex number:
- x –y -
2, 2 - ---------------- 2 ----------------2 - -x +y x +y - Matrix arguments must be square (real or complex). The computed inverse matrix A-1 satisfies A × A-1 = In, where In is the n × n identity matrix.
Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| z | → | 1/z |
| [[ matrix ]] | → | [[ matrix ]]–1 |
| `symb` | → | `INV(symb)` |
| x_unit | → | 1/x_1/unit |
SINV, /
Function
Performs modular inversion on an object modulo the current modulus.
An object.
The modular inverse of the object.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Solve the following for x, modulo the default modulus, 13. ( 2x ≡ 1 )
| Command | INVMOD(2) |
|---|---|
| Result | -6 |
Function
Integer Part Function: Returns the integer part of its argument. The result has the same sign as the argument.
Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | n |
| x_unit | → | n_unit |
| `symb` | → | `IP(symb)` |
32.3_m IP returns 32_m.
FP
Function
Returns the integer quotient (or Euclidean quotient) of two integers. That is, given two integers, a and b, returns the integer q, such that: a = qb + r, and 0 ≤ r < b
Level 2/Argument 1: The dividend. Level 1/Argument 2: The divisor.
The integer quotient.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
QUOT, IDIV2
Function
Returns the remainder of an integer division.
Level 2/Argument 1: The numerator. Level 1/Argument 2: The denominator.
The remainder.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
IDIV2
Command
Isolate Variable Command: Returns an algebraic symb2 that rearranges symb1 to “isolate” the first occurrence of variable global. The result symb2 is an equation of the form global = expression. If global appears more than once, then symb2 is effectively the right side of an equation obtained by rearranging and solving symb1 to isolate the first occurrence of global on the left side of the equation. If symb1 is an expression, it is treated as the left side of an equation symb1 = 0. If global appears in the argument of a function within symb1, that function must be an analytic function, that is, a function for which the calculator provides an inverse. Thus ISOL cannot solve IP(x)=0 for x, since IP has no inverse. ISOL is identical to SOLVE.
Principal Solution (–1), Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| `symb1` | `global` | → | `symb2` |
COLCT, EXPAN, QUAD, SHOW, SOLVE
Command
Determine the characteristics of a 2-d or 3-d linear isometry.
A square matrix representing a linear isometry.
A vector and/or an angle that represent the symmetry of the matrix, and 1 (for a direct isometry) or –1 (for an indirect isometry).
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Example 1: Analyze the isometry given by the matrix
0 –1 –1 0
| Command | ISOM([[0,-1] [-1,0]]) |
|---|---|
| Result | { [1, 1] –1}, meaning the matrix represents a symmetry in the line y = –x, and this is an indirect |
isometry.
1 – 3 -- --------- 2 2
| 3 | 1 |
|---|---|
| ------ | -- |
| 2 | 2 |
| Example 2: | Analyze the isometry given by the matrix |
| Command: | ISOM([[1/2, -√3/2][√3/2, 1/2]]) |
| Result: | { π/3, 1 }, meaning the matrix represents a rotation of π/3 radians, and this is a direct isometry. |
MKISOM
Function
Tests if a number is prime. For numbers of the order of 1014 or greater (to be exact, greater than 341550071728321), tests if the number is a pseudoprime; this has a chance of less than 1 in 1012 of wrongly identifying a number as a prime.
An object that evaluates to an integer or a whole real number.
1 (True) if the number is prime, 0 (False) if it is not.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
NEXTPRIME, PREVPRIME
Function
Converts an integer into a real number.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). The flags affect the output only if the input is not an integer.
Level 1/Argument 1: An integer or real number.
Level 1/Item 1: The integer converted to a real number.
→NUM, R→I, XNUM
Command
Diagonalization, or Jordan cycle decomposition, of a matrix. Computes the eigenvalues, eigenvectors, minimum polynomial, and characteristic polynomial of a matrix.
An n × n matrix.
Level 4/Item 1: The minimum polynomial. Level 3/Item 2: The characteristic polynomial. Level 2/Item 3: A list of characteristic spaces tagged by the corresponding eigenvalue (either a
vector or a list of Jordan chains, each of them ending with an "Eigen:"-tagged eigenvector). Level 1/Item 4: An array of the eigenvalues, with multiplicities
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Perform the following diagonalization:
| Command | JORDAN([1,1][1,1]) |
|---|---|
| Result | {X^2-2*X, |
X^2-2*X, {0: [1,-1]}, 2: [1,1]} [0,2]}
Command
Computes the basis of the kernel of a linear application f.
A matrix representing a linear application f in terms of the standard basis.
A list of vectors representing a basis of the kernel (also called the nullspace) of f.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). 112 213 314
Find the kernel of
| Command | KER([1,1,2][2,1,3][3,1,4]) |
|---|---|
| Result | {[1,1,-1]} |
BASIS, IMAGE
Command
Kermit Error Message Command: Returns the text of the most recent Kermit error packet. If a Kermit transfer fails due to an error packet sent from the connected Kermit device to the calculator, then executing KERRM retrieves and displays the error message. (Kermit errors not in packets are retrieved by ERRM rather than KERRM.)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | “error message” |
FINISH, KGET, PKT, RECN, RECV, SEND, SERVER
Command
Key Command: Returns a test result and, if a key is pressed, returns the row-column location xn m of that key. KEY returns a false result (0) to item 2 (stack level 1) until a key is pressed. When a key is pressed, it returns a true result (1) to item 2 (stack level 1) and xn m to item 1 (stack level 2). The result xn m is a two- or three-digit number that identifies the row and column location of the key just pressed.
Unlike WAIT, which returns a three-digit number that identifies alpha and shifted keyboard planes, KEY returns the row-column location of any key pressed, including !, …, and ~.
| Level 1/Argument 1 | Level 2/Item 1 | Level 1/Item 2 | |
|---|---|---|---|
| → | xn m | 1 | |
| → | 0 |
The program « DO UNTIL KEY END 81 SAME » returns 1 to the stack if the ! key is pressed while the indefinite loop is running.
WAIT, KEYEVAL
Command
Actions the specified key press. You input a number, in the format ab.c, that represents the key. In the number ab.c:
| 2: Left-shift function. | 21: Left shift-and-hold function. |
|---|---|
| 3. Right-shift function. | 31: Right shift-and-hold function. |
| 4. Alpha-function. | 41: Alpha shift-and-hold function. |
| 5. Alpha-left-shift function. | 51: Alpha-left-shift-and-hold function. |
| 6. Alpha-right-shift function. | 61: Alpha-right-shift-and-hold function. |
The sign of the input controls whether USER mode key assignments are used. Positive inputs specify the USER mode key definition. Negative inputs specify the default system keyboard.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| nn.n | → |
Turn the calculator off using a command.
| Command | KEYEVAL(101.3) |
|---|---|
| Result | The calculator is turned off. |
Command
Sets a new keytime value. Keytime is the time after a keypress during which further keypresses will not be actioned. It is measured in ticks, with valid values between 0 and 4096 ticks. If you experience key bounce, you can increase the value of keytime. If you experience lost keystrokes when rapidly hitting the same key in succession, you can decrease the value of keytime. The default is 1138 ticks.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| time | → |
KEYTIME→
KEYTIME→
Command
Displays the current keytime value. Keytime is the time after a keypress during which further keypresses will not be actioned. It is measured in ticks. If you experience key bounce, you can increase the value of keytime.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | time |
→KEYTIME
Command
Kermit Get Command: Used by a local Kermit to get a Kermit server to transmit the named object(s). To rename an object when the local device gets it, include the old and new names in an embedded list. For example, {{ AAA BBB }} KGET gets the variable named AAA but changes its name to BBB. {{ AAA BBB } CCC } KGET gets AAA as BBB and gets CCC under its own name. (If the original name is not legal on the calculator, enter it as a string.)
I/O Device (–33), RECV Overwrite (–36), I/O Messages (–39), I/O Device for Wire (–78)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `name` | → | |
| “name” | → | |
| { nameold namenew } | → | |
| { name1 ... namen } | → | |
| {{ nameold namenew } name ... } → | ||
BAUD, CKSM, FINISH, PARITY, RECN, RECV, SEND, SERVER, TRANSIO
Command
Cancel Halted Programs Command: Cancels all currently halted programs. If KILL is executed within a program, that program is also canceled. Canceled programs cannot be resumed. KILL cancels only halted programs and the program from which KILL was executed, if any. Commands that halt programs are HALT and PROMPT. Suspended programs cannot be canceled. Commands that suspend programs are INPUT and WAIT.
None
CONT, DOERR, HALT, PROMPT
Command
Label Axes Command: Labels axes in PICT with x- and y-axis variable names and with the minimum and maximum values of the display ranges. The horizontal axis name is chosen in the following priority order: 1. If the axes parameter in the reserved variable PPAR is a list, then the x-axis element from that list is used.
2. If axes parameter is not a list, then the independent variable name in PPAR is used. The vertical axis name is chosen in the following priority order: 1. If the axes parameter in PPAR is a list, then the y-axis element from that list is used. 2. If axes is not a list, then the dependent variable name from PPAR is used.
None
AXES, DRAW, DRAX
Command
Returns the interpolating polynomial of minimum degree for a set of pairs of values. For two pairs, DROITE will fit a straight line.
A two × n matrix of the n pairs of values.
The polynomial that results from the Lagrange interpolation of the data.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Find an interpolating polynomial for the data (1,6), (3,7), (4,8), (2,9)
| Command: | LAGRANGE([[1,3,4,2][6,7,8,9]]) |
|---|---|
| 3 | 2 |
8x – 63x + 151 x – 60 -------------------------------------------------------
Result: 6
DROITE
Command
Language: Returns the language that is currently set. 0 for English, 1 for French, and 2 for Spanish.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | value |
→LANGUAGE →LANGUAGE
Command
Language: Sets the language for things such as error messages: 0 for English, 1 for French, and 2 for Spanish.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| value | → |
LANGUAGE→
Function
Performs a Laplace transform on an expression with respect to the current default variable.
An expression.
The Laplace transform of the expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Find the Laplace transform of ex.
| Command | LAP(EXP(X)) |
|---|---|
| Result | 1/(X-1) |
ILAP, LAPL
Command
Returns the Laplacian of a function with respect to a list of variables.
Level 2/Argument 1:An expression. Level 1/Argument 2: A vector of variables.
The Laplacian of the expression with respect to the variables.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Find, and simplify, the Laplacian of the following expression: x e cos ( zy )
Command: LAPL(EXP(X)*COS(Z*Y),[X,Y,Z])
EXPAND(ANS(1))
Result: -((Y^2+Z^2-1)*EXP(X)*COS(Z*Y))
LAP, ILAP
Command
Returns copies of the arguments of the most recently executed command. LAST is provided for compatibility with the HP 28S. LAST is the same as LASTARG.
Last Arguments (–55)
| Level 1 | Level n | 7 | Level 1 | |
|---|---|---|---|---|
| → | objn | … | obj1 |
ANS, LASTARG
Command
Returns copies of the arguments of the most recently executed command. The objects return to the same stack levels that they originally occupied. Commands that take no arguments leave the current saved arguments unchanged. When LASTARG follows a command that evaluates an algebraic expression or program, the last arguments saved are from the evaluated algebraic expression or program, not from the original command.
Last Arguments (–55)
| Level 1 | Level n | 7 | Level 1 | |
|---|---|---|---|---|
| → | objn | … | obj1 |
ANS, LAST
Command
LCD to Graphics Object Command: Returns the current stack and menu display as a 131 × 80 (on the HP 50g and 49g+) or 131 × 64 (on the HP 48gII) graphics object.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | grob |
LCD→ PICT STO PICTURE returns the current display to level 1 as a graphics object, stores it in PICT, then shows the image in the Picture environment.
→GROB, →LCD
Command
Graphics Object to LCD Command: Displays the specified graphics object with its upper left pixel in the upper left corner of the display. If the graphics object is larger than 131 × 72 (on the HP 50g and 49g+) or 131 × 56 (on the HP 48gII), it is truncated.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| grob | → |
BLANK, →GROB, LCD→
Function
Returns the least common multiple of two objects.
Level 2/Argument 1: An expression, a number, or object that evaluates to a number. Level 1/Argument 2: An expression, a number, or object that evaluates to a number.
The least common multiple of the objects.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Find the least common multiple of the following two expressions: 2 x –1 x–1
| Command | LCM(X^2-1,X-1) |
|---|---|
| Results | X^2-1 |
GCD
Command
From a program with two arguments, builds a matrix with the specified number of rows and columns, with aij = f(i,j).
Level 3/Argument 1: The number of rows you want in the resulting matrix. Level 2/Argument 2: The number of columns you want in the resulting matrix. Level 1/Argument 3: A program that uses two arguments. An expression with the two variables I, J can be used instead.
The resulting matrix.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Build a 2 × 3 matrix with aij=i+2j.
Command: LCXM(2,3,« →I J `I+2*J`»)
3 5 7 4 6 8 Result:
Command
Solves a linear differential equation with constant coefficients, or a system of first order linear differential equations with constant coefficients.
Level 2/Argument 1: For a single equation, the function forming the right hand side of the equation. For a system of equations, an array comprising the terms not containing the dependent variables. Level 1/Argument 2: For one equation, the auxiliary polynomial. For a system of equations, the matrix of coefficients of the dependent variables.
The solution.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Solve 2sin(x), with the auxiliary polynomial x2+1:
| Command | LDEC(2*SIN(X),X^2+1) |
|---|---|
| Result | COS(X)*(cC0 -X)+(cC1 — -1)*SIN(X) |
DESOLVE
Function
Returns the nth degree Legendre polynomial.
An integer, n.
The nth Legendre polynomial.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Find the Legendre polynomial with degree 4.
| Command | LEGENDRE(4) |
|---|---|
| Result | (35*X^4-30*X^2+3)/8 |
HERMITE, TCHEBYCHEFF
Function
Returns the greatest common divisor of a list of expressions or values.
A list of expressions or values.
Level 2/Item 1: The list of elements. Level 1/Item 2: The greatest common divisor of the elements.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
GCD
Command
Evaluate Library Function Command: Evaluates unnamed library functions. WARNING: Use extreme care when executing this function. Using LIBEVAL with random addresses will almost always cause a memory loss. Do not use this function unless you know what you are doing. #nfunction is of the form lllfffh, where lll is the library number, and fff the function number.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| #nfunction | → |
EVAL, FLASHEVAL, SYSEVAL
Command
Libraries Command: Lists the title, number, and port of each library attached to the current directory. The title of a library often takes the form LIBRARY-NAME : Description. A library without a title is displayed as " ".
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | {“title”, nlib, nport, ...,“title”, nlib, nport } |
ATTACH, DETACH lim
Function
Returns the limit of a function as its argument approaches a specified value. Expands and simplifies an algebraic expression.
Level 2/Argument 1: An expression. Level 1/Argument 2: An expression of the form x = y, where x is the variable and y is the value at which the limit is to be evaluated. If the variable approaching a value is the current CAS variable, it is sufficient to give its value alone. The ∞ symbol provided by the calculator can be used to set the limiting value at plus or minus infinity.
The limit of the expression at the limit point.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Find the following limit:
n n
- lim - x--------------- –y
- x → y- x – y
Command: lim((X^N-Y^N)/(X-Y), X=Y)
Result: N*EXP(N*LN(Y))/Y
SERIES
Function
Returns the limit of a function as its argument approaches a specified value. This function is identical to the lim function, described above, and is included to ensure backward-compatibility with the HP 49G calculator.
Command
Linearizes expressions involving exponential terms.
An expression.
The linearized expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Linearize the following expression: x y 4 x(e e )
| Command | LIN(X*(EXP(X)*EXP(Y))^4) |
|---|---|
| Result | X*EXP(4X+4Y) |
TEXPAND
Command Operation
Draw Line Command: Draws a line in PICT between the input coordinates.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| (x1, y1) | (x2, y2) | → | |
| { #n1, #m1} | { #n2, #m2} | → |
This program: « (0,0) (2,3) LINE { # 0d # 0d } PVIEW 7 FREEZE » draws a line in PICT between two user-unit coordinates, displays PICT with pixel coordinate { # 0d # 0d } at the upper left corner of the picture display, and freezes the display.
ARC, BOX, TLINE
Command
Regression Model Formula Command: Returns an expression representing the best fit line according to the current statistical model, using X as the independent variable name, and explicit values of the slope and intercept taken from the reserved variable ΣPAR. For each curve fitting model, the following table indicates the form of the expression returned by ΣLINE, where m is the slope, x is the independent variable, and b is the intercept.
| Model | Form of Expression |
|---|---|
| LINFIT | mx + b |
| LOGFIT | m ln(x) + b |
| EXPFIT | bemx |
| PWRFIT | bxm |
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | `symbformula` |
If the current model is EXPFIT, and if the slope is 5 and the intercept 3, ΣLINE returns `3*EXP(5*X)`.
BESTFIT, COLΣ, CORR, COV, EXPFIT, LINFIT, LOGFIT, LR, PREDX, PREDY, PWRFIT, XCOL, YCOL
Command
Linear Curve Fit Command: Stores LINFIT as the fifth parameter in the reserved variable ΣPAR, indicating that subsequent executions of LR are to use the linear curve fitting model. LINFIT is the default specification in ΣPAR.
None
BESTFIT, EXPFIT, LOGFIT, LR, PWRFIT
Function
Linear Test Function: Tests whether an algebraic is structurally linear for a given variable. If any two subexpressions containing a variable (name) are combined only with addition and subtraction, and any subexpression containing the variable is at most multiplied or divided by another factor not containing the variable, the algebraic (symb) is determined to be linear for that variable. LININ returns a 1 if the algebraic is linear for the variable, and a 0 if not.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| `symb` | `name` | → | 0/1 |
| Example 1: `(X+1)*(Y^-2^Z)+(X/(3-Z^3)` `X` LININ returns 1. | |||
| Example 2: `(X^2-1)/(X+1)` `X` LININ returns 0. | |||
| (Although this equation yields a linear equation when factored, LININ tests the equation as described above.) | |||
Command
Solves a system of linear equations.
Level 2/Argument 1: An array of equations. Level1/Argument 2: A vector of the variables to solve for.
Level 3/Item 1: The system of equations, as a list containing the inputs as above. Level 2/Item 2: A list of the pivot points. Level 1/Item 3: The solution.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
DESOLVE, SOLVE, MSLV
Command
List to Stack Command: Takes a list of n objects and returns each object to a separate level, and returns the total number of objects to item n+1 (stack level 1). The command OBJ→ also provides this function.
Level 1/Argument 1 Leveln+1/Item1 ... Level2/Itemn Level1/Itemn+1
{ obj1, ...,objn } → obj1 ... objn n
ARRY→, DTAG, EQ→, →LIST, OBJ→, STR→
Command
Stack to List Command: Takes n specified objects and returns a list of those objects.
| Leveln+1/Argument1 7Level2/Argumentn | Level1/Argumentn+1 | Level 1/Item 1 | |
|---|---|---|---|
| obj1 … objn n | → | { obj1, … ,objn } |
The program « DEPTH →LIST `A` STO » combines the entire contents of the stack into a list that is stored in variable A.
→ARRY, LIST→, →STR, →TAG, →UNIT
ΔLIST
Command
List Differences Command: Returns the first differences of the elements in a list. Adjacent elements in the list must be suitable for mutual subtraction.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| { list } | → | { differences } |
| Example 1: | { 4 20 1 17 60 91 } ›LIST returns { 16 -19 16 43 31 }. | |
| Example 2: | { A B C 1 2 3 } ›LIST returns { `B-A` `C-B` `1-C` 1 1 }. | |
| Example 3: | { `A+3` `X/5` `Y^4` } ›LIST returns { `X/5-(A+3)` `Y^4-X/5` }. |
ΣLIST, ΠLIST, STREAM
Command
List Product Command: Returns the product of the elements in a list. The elements in the list must be suitable for mutual multiplication.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| { list } | → | product |
| Example 1: | { 5 8 2 } œLIST returns 80. | |
| Example 2: | { A B C 1 } œLIST returns `A*B*C`. |
ΣLIST, ΔLIST, STREAM
Command
List Sum Command: Returns the sum of the elements in a list. The elements in the list must be suitable for mutual addition.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| { list } | → | sum |
| Example 1: | { 5 8 2 } ΣLIST returns 15. | |
| Example 2: | { A B C 1 } ΣLIST returns `A+B+C+1`. |
ΠLIST, ΔLIST, STREAM
Analytic function
Natural Logarithm Analytic Function: Returns the natural (base e) logarithm of the argument.
For x = 0 or (0, 0), an Infinite Result exception occurs, or, if flag –22 is set, –MAXR is returned. The inverse of EXP is a relation, not a function, since EXP sends more than one argument to the same result. The inverse relation for EXP is the general solution: LN(Z)+2*π*i*n1 The function LN is the inverse of a part of EXP, a part defined by restricting the domain of EXP such that: each argument is sent to a distinct result, and each possible result is achieved. The points in this restricted domain of EXP are called the principal values of the inverse relation. LN in its entirety is called the principal branch of the inverse relation, and the points sent by LN to the boundary of the restricted domain of EXP form the branch cuts of LN. The principal branch used by the calculator for LN was chosen because it is analytic in the regions where the arguments of the real-valued inverse function are defined. The branch cut for the complex-valued natural log function occurs where the corresponding real-valued function is undefined. The principal branch also preserves most of the important symmetries. The graphs below show the domain and range of LN. The graph of the domain shows where the branch cut occurs: the heavy solid line marks one side of the cut, while the feathered lines mark the other side of the cut. The graph of the range shows where each side of the cut is mapped under the function. These graphs show the inverse relation LN(Z)+2*π*i*n1 for the case n1=0. For other values of n1, the horizontal band in the lower graph is translated up (for n1 positive) or down (for n1 negative). Taken together, the bands cover the whole complex plane, which is the domain of EXP.
You can view these graphs with domain and range reversed to see how the domain of EXP is restricted to make an inverse function possible. Consider the vertical band in the lower graph as the restricted domain Z = (x,y). EXP sends this domain onto the whole complex plane in the range W = (u,v) = EXP(x,y) in the upper graph.
Principal Solution (–1), Numerical Results (–3), Infinite Result Exception (–22)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| z | → | ln z |
| `symb` | → | `LN(symb)` |
ALOG, EXP, ISOL, LNP1, LOG
Command
Returns the variable names contained in a symbolic expression.
A symbolic expression.
Level 2/Argument 1: The original expression. Level 1/Argument 2: A vector containing the variable names. The variable names are sorted by length, longest first, and ones of equal length are sorted alphabetically.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
List the variables in the expression COS(B)/2*A + MYFUNC(PQ) + 1/T.
| Command | LNAME(COS(B)/2*A + MYFUNC(PQ) + INV(T)) |
|---|---|
| Result | {COS(B)/2*A + MYFUNC(PQ) + 1/T, [MYFUNC,PQ,A,B,T]} |
LVAR
Command
Simplifies an expression by collecting logarithmic terms. For symbolic powers does not perform the same simplification as EXP2POW; compare example 2 here with example 2 for EXP2POW.
An expression.
The simplified expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Example 1: Simplify the following expression:
2(ln(x)+ln(y))
| Command | LNCOLLECT(2(LN(X)+LN(Y)) |
|---|---|
| Result | LN(X^2*Y) Example 2: Compare the effect of LNCOLLECT with the effect of EXP2POW on the expression e n·ln(x) |
| Command | LNCOLLECT(EXP(N*LN(X)) |
| Result | EXP(N*LN(X)) |
EXP2POW, TEXPAND
Analytic function
Natural Log of x Plus 1 Analytic Function: Returns ln(x + 1). For values of x close to zero, LNP1(x) returns a more accurate result than does LN(x+1). Using LNP1 allows both the argument and the result to be near zero, and it avoids an intermediate result near 1. The calculator can express numbers within 10-449 of zero, but within only 10–11 of 1. For values of x < –1, an Undefined Result error results. For x=–1, an Infinite Result exception occurs, or, if flag –22 is set, LNP1 returns –MAXR.
Numerical Results (–3), Infinite Result Exception (–22)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | ln (x + 1) |
| `symb` | → | `LNP1(symb)` |
EXPM, LN
Command
Creates one or more local variables. This command is intended mainly for use in Algebraic mode; it can not be single stepped when a program containing it is being debugged in Algebraic mode.
Level 1/Argument 1: A list of one or more local variable names (names beginning with the local variable identifier ←), each one followed by an equals sign and the value to be stored in it. Any variable not followed by an equal sign and a value is set equal to zero.
Level 1/Item 1: The input list.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Create local variables ←A and ←B and store the values 0 in the first and 2 in the second.
| Command | LOCAL({←A,←B=2}) |
|---|---|
| Result | {←A,←B=2} |
DEF, STORE, UNBIND
Analytic function
Common Logarithm Analytic Function: Returns the common logarithm (base 10) of the argument. For x=0 or (0, 0), an Infinite Result exception occurs, or, if flag –22 is set (no error), LOG returns –MAXR. The inverse of ALOG is a relation, not a function, since ALOG sends more than one argument to the same result. The inverse relation for ALOG is the general solution: LOG(Z)+2*π*i*n1/2.30258509299 The function LOG is the inverse of a part of ALOG, a part defined by restricting the domain of ALOG such that 1) each argument is sent to a distinct result, and 2) each possible result is achieved. The points in this restricted domain of ALOG are called the principal values of the inverse relation. LOG in its entirety is called the principal branch of the inverse relation, and the points sent by LOG to the boundary of the restricted domain of ALOG form the branch cuts of LOG. The principal branch used by the calculator for LOG(z) was chosen because it is analytic in the regions where the arguments of the real-valued function are defined. The branch cut for the complex-valued LOG function occurs where the corresponding real-valued function is undefined. The principal branch also preserves most of the important symmetries. You can determine the graph for LOG(z) from the graph for LN (see LN) and the relationship log z = ln z / ln 10.
Principal Solution (–1), Numerical Results (–3), Infinite Result Exception (–22)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| z | → | log z |
| `symb` | → | `LOG(symb)` |
ALOG, EXP, ISOL, LN
Command
Logarithmic Curve Fit Command: Stores LOGFIT as the fifth parameter in the reserved variable ΣPAR, indicating that subsequent executions of LR are to use the logarithmic curve-fitting model. LINFIT is the default specification in ΣPAR.
None
BESTFIT, EXPFIT, LINFIT, LR, PWRFIT
Command
LQ Factorization of a Matrix Command: Returns the LQ factorization of an m × n matrix. LQ factors an m × n matrix A into three matrices:
| Level 1/Argument 1 | Level 3/Item 1 | Level 2/Item 2 | Level 1/Item 3 | |
|---|---|---|---|---|
| [[ matrix ]]A | → | [[ matrix ]]L | [[ matrix ]]Q | [[ matrix ]]P |
LSQ, QR
Command
Linear Regression Command: Uses the currently selected statistical model to calculate the linear regression coefficients (intercept and slope) for the selected dependent and independent variables in the current statistics matrix (reserved variable ΣDAT). The columns of independent and dependent data are specified by the first two elements in the reserved variable ΣPAR, set by XCOL and YCOL, respectively. (The default independent and dependent columns are 1 and 2.) The selected statistical model is the fifth element in ΣPAR. LR stores the intercept and slope (untagged) as the third and fourth elements, respectively, in ΣPAR. The coefficients of the exponential (EXPFIT), logarithmic (LOGFIT), and power (PWRFIT) models are calculated using transformations that allow the data to be fitted by standard linear regression. The equations for these transformations appear in the table below, where b is the intercept and m is the slope. The logarithmic model requires positive x-values (XCOL), the exponential model requires positive y-values (YCOL), and the power model requires positive x- and y-values.
| Model | Transformation |
|---|---|
| Logarithmic | y = b + m ln(x) |
| Exponential | ln(y) = ln(b) + mx |
| Power | ln(y) = ln(b) + m ln(x) |
Level 1/Argument 1 Level 2/Item 1 Level 1/Item 2
→
Intercept: x1 Slope: x2
BESTFIT, COLΣ, CORR, COV, EXPFIT, ΣLINE, LINFIT, LOGFIT, PREDX, PREDY, PWRFIT, XCOL, YCOL
Command
Least Squares Solution Command: Returns the minimum norm least squares solution to any system of linear equations where A × X = B. If B is a vector, the resulting vector has a minimum Euclidean norm ||X|| over all vector solutions that minimize the residual Euclidean norm ||A × X – B||. If B is a matrix, each column of the resulting matrix, Xi, has a minimum Euclidean norm ||Xi|| over all vector solutions that minimize the residual Euclidean norm ||A × Xi – Bi||. If A has less than full row rank (the system of equations is underdetermined), an infinite number of solutions exist. LSQ returns the solution with the minimum Euclidean length. If A has less than full column rank (the system of equations is overdetermined), a solution that satisfies all the equations may not exist. LSQ returns the solution with the minimum residuals of A × X – B.
Singular Values (–54)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| [ array ]B | [[ matrix ]]A | → | [ array ]x |
| [[ matrix ]]B | [[ matrix ]]A | → | [[ matrix ]]x |
LQ, RANK, QR, /
Command
LU Decomposition of a Square Matrix Command: Returns the LU decomposition of a square matrix. When solving an exactly determined system of equations, inverting a square matrix, or computing the determinant of a matrix, the calculator factors a square matrix into its Crout LU decomposition using partial pivoting. The Crout LU decomposition of A is a lower-triangular matrix L, an upper-triangular matrix U with ones on its diagonal, and a permutation matrix P, such that P × A = L × U. The results satisfy P × A ≅ L × U.
| Level 1/Argument 1 | Level 3/Item 1 | Level 2/Item 2 | Level 1/Item 3 | |
|---|---|---|---|---|
| [[ matrix ]]A | → | [[ matrix ]]L | [[ matrix ]]U | [[ matrix ]]P |
DET, INV, LSQ, /
Command
Returns a list of variables in an algebraic object. Differs from LNAME above in that functions of variables, such as COS(X) or LN(AB) are returned, instead of the variable names, X or AB. INV() and SQ() are not treated as functions. Compare the example here with the same example in LNAME.
An algebraic object.
Level 2/Item 1: The algebraic object. Level 1/Item 2: A list which includes both the original expression and a vector containing the variable names. Variable names include functions of variables, as described above. The names are sorted by length, longest first, and ones of equal length are sorted alphabetically.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
List the variables and function names in the expression COS(B)/2*A + MYFUNC(PQ) + 1/T.
| Command | LVAR(COS(B)/2*A + MYFUNC(PQ) + INV(T)) |
|---|---|
| Result | {COS(B)/2*A + MYFUNC(PQ) + 1/T, [MYFUNC(PQ),COS(B),A,T]} |
LNAME
Command
Returns details of a square matrix, including the information needed to obtain the adjoint matrix. The adjoint matrix is obtained by multiplying the inverse matrix by the determinant.
A square matrix
Level 4/Item 1: The determinant. Level 3/Item 2: The formal inverse. Level 2/Item 3: The matrix coefficients of the polynomial, p, defined by (xi–a)p(x)=m(x)i, where a is the matrix, and m is the characteristic polynomial of a. Level 1/Item 4: The characteristic polynomial.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Obtain the adjoint matrix of: 0 –1 1 0
| Command | MAD([[0, -1][1, 0]]) |
|---|---|
| Result | {1,[[0, 1][-1, 0]],{[[1, 0][0, 1]], [[0, -1][1, 0]]}, X^2+1} |
The determinant is 1, so the adjoint is the second item[[0, 1][-1, 0]].
LNAME
Command
Displays the main menu (or list) of CAS operations. This displays the CASCFG command, the ALGB, ARIT, DIFF, EXP&LN, MATHS MATR, REWRITE and TRIGO menu commands described in this part of the Command Reference, and the CMPLX and SOLVER menu commands described in the Full Command and Function Reference (Chapter 3). Other menus are not shown because they are within the submenus given by MAIN. More details are given in Appendix K of the User’s Guide.
If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a list. If the flag is set, displays the operations as a menu of function keys.
ALGB, ARIT, CONSTANTS, DIFF, EXP&LN, INTEGER, MATHS, MATR, MODULAR, POLYNOMIAL, REWRITE, TESTS, TRIGO
Function
Mantissa Function: Returns the mantissa of the argument.
Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | ymant |
| `symb` | → | `MANT(symb)` |
SIGN, XPON
Command
Applies a specified program to a list of objects or values. If one of the objects is a list, MAP will apply the program recursively to the items in the inner list.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| {list}1 | «program» | → | {list}2 |
{ 1 2 { 3 4 } } « →STR » MAP returns { "1" "2" { "3" "4" } }.
Command
Match Pattern Down Command: Rewrites an expression that matches a specified pattern. ↓MATCH rewrites expressions or subexpressions that match a specified pattern `symbpat`. An optional condition, `symbcond`, can further restrict whether a rewrite occurs. A test result is also returned to indicate if command execution produced a rewrite; 1 if it did, 0 if it did not.
The pattern `symbpat` and replacement `symbrepl` can be normal expressions; for example, you can replace .5 with `SIN(π/6)`. You can also use a “wildcard” in the pattern (to match any subexpression) and in the replacement (to represent that expression). A wildcard is a name that begins with &, such as the name `&A`, used in replacing `SIN(&A+&B)` with `SIN(&A)*COS(&B)+COS(&A)*SIN(&B)`. Multiple occurrences of a particular wildcard in a pattern must match identical subexpressions. ↓MATCH works from top down; that is, it checks the entire expression first. This approach works well for expansion. An expression expanded during one execution of ↓MATCH will contain additional subexpressions, and those subexpressions can be expanded by another execution of ↓MATCH. Several expressions can be expanded by one execution of ↓MATCH provided none is a subexpression of any other.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 2/Item 1 | ||
|---|---|---|---|---|
| Level 1/Item | ||||
| `symb1` | { `symbpat` `symbrepl` } | → | `symb2` | 0/1 |
| `symb1` { `symbpat` `symbrepl` `symbcond` } → `symb2` 0/1 | ||||
| Example 1: .5 { .5 `SIN(π/6)` } ↓MATCH returns `SIN(π/6)` to level 2 and 1 to level | ||||
| 1. Example 2: `SIN(U+V)` { `SIN(&A+&B)` `SIN(&A)*COS(&B)+COS(&A)*SIN(&B)` } ↓MATCH returns `SIN(U)*COS(V)+COS(U)*SIN(V)` to level 2 and 1 to level 1. Example 3: This sequence: `SIN(5*Z)` { `SIN(&A+&B)` `Σ(K=0,&A,COMB(&A,K)*SIN(K*π)*COS(&B^(&A-K)*SIN(&B)^K)` `ABS(IP(&A))==&A` } ↓MATCH returns `Σ(K=0,5,COMB(5,K)*SIN(K*π)*COS(Z^(5-K)*SIN(Z)^K)` to level 2 and 1 to level 1. | ||||
↑MATCH
Command
Bottom-Up Match and Replace Command: Rewrites an expression. ↑MATCH rewrites expressions or subexpressions that match a specified pattern `symbpat`. An optional condition, `symbcond`, can further restrict whether a rewrite occurs. A test result is also returned to indicate if command execution produced a rewrite; 1 if it did, 0 if it did not. The pattern `symbpat` and replacement `symbrepl` can be normal expressions; for example, you can replace `SIN(π/6)` with `1/2`. You can also use a “wildcard” in the pattern (to match any subexpression) and in the replacement (to represent that expression). A wildcard is a name that begins with &, such as the name `&A`, used in replacing `SIN(&A+π)` with `–SIN(&A)`. Multiple occurrences of a particular wildcard in a pattern must match identical subexpressions. ↑MATCH works from bottom up; that is, it checks the lowest level (most deeply nested) subexpressions first. This approach works well for simplification. A subexpression simplified during one execution of ↑MATCH will be a simpler argument of its parent expression, so the parent expression can be simplified by another execution of ↑MATCH. Several subexpressions can be simplified by one execution of ↑MATCH provided none is a subexpression of any other.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 2/Item 1 | Level 1/Item 2 | |
|---|---|---|---|---|
| `symb1` | { `symbpat`, `symbrepl` } | → | `symb2` | 0/1 |
| `symb1` | { `symbpat`, `symbrepl`, `symbcond` } → | `symb2` 0/1 | ||
| Example 1: This sequence: `SIN(π/6)` { `SIN(π/6)` `1/2` } ↑MATCH returns | ||||
| `1/2` to level 2 and 1 (indicating a replacement was made) to level 1. | ||||
Example 2: This sequence: `SIN(X+π)` { `SIN(&A+π)` `-SIN(&A)` } ↑MATCH | ||||
| returns `-SIN(X)` to level 2 and 1 to level 1. | ||||
Example 3: This sequence: `W+ƒ(SQ(5))` { `ƒ(SQ(&A))` `&A` `&AŠ0` } ↑MATCH | ||||
| returns `W+5` to level 2 and 1 to level 1. | ||||
↓MATCH
Command
Displays a menu or list of CAS mathematics submenus. Details are given in Appendix J of the User’s Guide.
If the CHOOSE boxes flag is clear (flag –117 clear), displays the submenus as a list. If the flag is set, displays the submenus as a menu of function keys.
ALGB, ARIT, CONSTANTS, DIFF, EXP&LN, INTEGER, MAIN, MATR, MODULAR, POLYNOMIAL, REWRITE, TESTS, TRIGO
Command
Displays a menu or list containing the CAS commands for matrix operations.
If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered list. If the flag is set, displays the operations as a menu of function keys.
ALGB, ARIT, CONSTANTS, DIFF, EXP&LN, INTEGER, MAIN, MATHS, MODULAR, POLYNOMIAL, REWRITE, TESTS, TRIGO
Function
Maximum Function: Returns the greater of two inputs.
Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| x | y | → | max(x,y) |
| x | `symb` | → | `MAX(x, symb)` |
| `symb` | x | → | `MAX(symb, x)` |
| `symb1` | `symb2` | → | `MAX(symb1, symb2)` |
| x_unit1 | y_unit2 | → | max(x_unit1, y_unit2) |
| Example 1: 10 -23 MAX returns 10. | |||
| Example 2: -10 -23 MAX returns -10. | |||
| Example 3: 1_m 9_cm MAX returns 1_m. | |||
MIN
Function
Maximum Real Function: Returns the symbolic constant MAXR or its numerical representation 9.99999999999E499. MAXR is the largest real number that can be represented by the calculator.
Symbolic Constants (–2), Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | `MAXR` | |
| → | 9.99999999999E499 |
e, i, MINR, π
Command
Maximum Sigma Command: Finds the maximum coordinate value in each of the m columns of the current statistical matrix (reserved value ΣDAT). The maxima are returned as a vector of m real numbers, or as a single real number if m = 1.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | xmax | |
| → | [xmax1 xmax2 ... xmaxm ] |
BINS, MEAN, MINΣ, SDEV, TOT, VAR
Command
Make Calculated Value Command: Designates a variable as a calculated variable for the multiple- equation solver. MCALC designates a single variable, a list of variables, or all variables as calculated values.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `name` | → | |
| { list } | → | |
| "ALL" | → |
MUSER
Command
Mean Command: Returns the mean of each of the m columns of coordinate values in the current statistics matrix (reserved variable ΣDAT). The mean is returned as a vector of m real numbers, or as a single real number if m = 1. The mean is computed from the formula: 1 n -- ∑ x i ni = 1
where xi is the ith coordinate value in a column, and n is the number of data points.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | xmean | |
| → | [xmean1, xmean2, ..., xmeanm ] |
BINS, MAXΣ, MINΣ, SDEV, TOT, VAR
Command
Memory Available Command: Returns the number of bytes of available RAM. The number returned is only a rough indicator of usable available memory, since recovery features (LASTARG= !î, …¯, and !®) consume or release varying amounts of memory with each operation. Before it can assess the amount of memory available, MEM must remove objects in temporary memory that are no longer being used. This clean-up process (also called “garbage collection”) also occurs automatically at other times when memory is full. Since this process can slow down calculator operation at undesired times, you can force it to occur at a desired time by executing MEM. In a program, execute MEM DROP.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | x |
BYTES
Command Operation
Display Menu Command: Displays a built-in menu or a library menu, or defines and displays a custom menu. A built-in menu is specified by a real number xmenu. The format of xmenu is mm.pp, where mm is the menu number and pp is the page of the menu. If pp doesn’t correspond to a page of the specified menu, the first page is displayed. Library menus are specified in the same way as built-in menus, with the library number serving as the menu number. Custom menus are specified by a list of the form { "label-object" action-object } or a name containing a list (namedefinition). Either argument is stored in reserved variable CST, and the custom menu is subsequently displayed. MENU takes any object as a valid argument and stores it in CST. However, the calculator can build a custom menu only if CST contains a list or a name containing a list. Thus, if an object other
than a list or name containing a list is supplied to MENU, a Bad Argument Type error will occur when the calculator attempts to display the custom menu. A full list of all menus can be found in Appendix H of this reference.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| xmenu | → | |
| { listdefinition } | → | |
| `namedefinition` | → | |
| obj | → | |
| Example 1: | 5 MENU displays the first page of the MTH MATR NORM menu. | |
| Example 2: | 48.02 MENU displays the second page of the UNITS MASS menu. | |
| Example 3: | { A 123 "ABC" } MENU displays the custom menu defined by the list argument. | |
| Example 4: | `MYMENU` MENU displays the custom menu defined by the name argument. |
RCLMENU, TMENU
Command
Displays a function key menu of computer algebra commands in a specified range.
Level 2/Argument 1: The number of the first command in the range to be displayed. Level 1/Argument 2: The number of the last command in the range to be displayed. Arguments below 0 are treated as 0; arguments above 140 are treated as 140.
On the function key menu, the computer algebra commands in the range specified. NOVAL is returned in Algebraic mode. This list gives the number of each operation that can be displayed by the command. The complete menu below can be generated by MENUXY(0,140). Items 127 through to 135 allow access from the top row of keys to CAS menus.
Number Operation
0-5 EXPAND FACTOR SUBST DERVX INTVX lim
6-11 TAYLOR0 SERIES SOLVEVX PLOT PLOTADD IBP
12-17 PREVAL RISCH DERIV DESOLVE LAP ILAP
18-23 LDEC TEXPAND LIN TSIMP LNCOLLECT EXPLN
24-29 SINCOS TLIN TCOLLECT TRIG TRIGCOS TRIGSIN
30-35 TRIGTAN TAN2SC HALFTAN TAN2SC2 ATAN2S ASIN2T
36-41 ASIN2C ACOS2S DIV2 IDIV2 QUOT IQUOT
42-47 REMAINDER IREMAINDER GCD LCM EGCD IEGCD
48-53 ABCUV IABCUV LGCD SIMP2 PARTFRAC PROPFRAC
54-59 PTAYL HORNER EULER PA2B2 CHINREM ICHINREM
60-65 ISPRIME? NEXTPRIME PREVPRIME SOLVE ZEROS FCOEF
66-71 FROOTS FACTORS DIVIS TRAN HADAMARD rref
72-77 REF AXM AXL QXA AXQ GAUSS
78-83 SYLVESTER PCAR JORDAN MAD LINSOLVE VANDERMONDE
84-89 HILBERT LCXM DIV CURL LAPL HESS
90-95 LEGENDRE TCHEBYCHEFF HERMITE LAGRANGE FOURIER SIGNTAB
96-101 TABVAR TABVAL DIVPC TRUNC SEVAL TEVAL
102-107 MAP XNUM XQ REORDER LVAR FXND
108-113 EXLR LNAME ADDTMOD SUBTMOD MULTMOD DIVMOD
114-119 DIV2MOD POWMOD INVMOD GCDMOD EXPANDMOD FACTORMOD
120-125 RREFMOD MODSTO MENUXY KEYEVAL GROBADD SCROLL
126-131 CASCFG MAIN ALGB CMPLX TRIGO MATR
132-137 DIFF ARIT SOLVER EXP&LN EPSX0 ?
138-140 ∞ PROMPTSTO VER
Display a menu containing ATAN2S, ASIN2T, ASIN2C and ACOS2S.
| Command | MENUXY(34,37) |
|---|---|
| Result | The four functions are displayed above the A to D keys. In Algebraic mode, NOVAL is |
returned as item 1.
MENU, TMENU
Command
Do not use this command, a carry-over from the HP 48SX for handling plug-in RAM cards.
Function
Minimum Function: Returns the lesser of two inputs.
Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| x | y | → | min(x,y) |
| x | `symb` | → | `MIN(x, symb)` |
| `symb` | x | → | `MIN(symb, x)` |
| `symb1` | `symb2` | → | `MIN(symb1, symb2)` |
| x_unit1 | y_unit2 | → | min(x_unit1, y_unit2) |
| Example 1: 10 23 MIN returns 10. | |||
| Example 2: -10 -23 MIN returns -23. | |||
| Example 3: 1_m 9_cm MIN returns 9_cm. | |||
MAX
Command
Starts the MINEHUNT game. In this game, you are standing in the upper-left corner of an 8x16 battlefield grid. Your mission is to travel safely to the lower-right corner, avoiding invisible mines along the way. The game tells you how many mines are under the eight squares adjacent to your position.
Use the number or arrow keys to cross the battlefield one square at a time (use 7, 9, 1, and 3to move diagonally.) You can exit the game at any time by pressing −(the $ key). To interrupt and save a game, press K. This creates a variable MHpar in the current directory and ends the game. If MHpar exists when you start MINEHUNT, the interrupted game resumes and MHpar is purged. You can change the number of mines in the battlefield by creating a variable named Nmines containing the desired number. Nmines must contain a real number (1 to 64). If Nmines is negative, the mines are visible during the game (allowing you to cheat).
None.
Command
Minifont: Returns the font that is set as the minifont.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | Font object |
→MINIFONT →MINIFONT
Command
Minifont: Sets the font that is used as the minifont.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| Font object | → |
MINIFONT→
Command
Multiple-equation Menu Initialization Command. Creates the reserved variable Mpar, which includes the equations in EQ and the variables in these equations.
MITM, MROOT, MSOLVR
Function
Minimum Real Function: Returns the symbolic constant MINR or its numerical representation, 1.00000000000E–499. MINR is the smallest positive real number that can be represented by the calculator.
Symbolic Constants (–2), Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | `MINR` | |
| → | 1.00000000000E–499 |
e, i, MAXR, π
Command
Minimum Sigma Command: Finds the minimum coordinate value in each of the m columns of the current statistics matrix (reserved variable ΣDAT). The minima are returned as a vector of m real numbers, or as a single real number if m = 1.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | xmin | |
| → | { xmin 1 xmin 2 … xmin m } |
BINS, MAXΣ, MEAN, SDEV, TOT, VAR
Command
Multiple-equation Menu Item Order Command. Changes multiple equation menu titles and order. The argument list contains the variable names in the order you want. Use "" to indicate a blank label. You must include all variables in the original menu and no others.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| "title" | { list } | → |
MINIT
Command
Returns the matrix representation for a given isometry.
Level 2/Argument 1: For a 3-d isometry, a list of the characteristic elements of the isometry. For a 2-d isometry, the characteristic element of the isometry (either an angle or a vector). Level 1/Argument 2: +1 for a direct isometry or –1 for an indirect isometry.
The matrix that represents the given isometry.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
| Example 1: Find the matrix for a rotation of π/2 radians in two dimensions | |
|---|---|
| Command | MKISOM(π/2, 1) |
0 –1 1 0 Result:
Example 2: Find the matrix for a rotation with axis [1 1 1] and angle π/3 radians combined with a reflection in
the plane x + y + z = 0
Command: MKISOM({ [1, 1, 1],π/3}, -1) then simplify with EXPAND(ANS(1))
0 –1 0 0 0 –1 –1 0 0 Result:
ISOM
Function
Modulo Function: Returns a remainder defined by: x mod y = x – y floor (x/y) Mod (x, y) is periodic in x with period y. Mod (x, y) lies in the interval [0, y) for y > 0 and in (y, 0] for y < 0. Algebraic syntax: argument 1 MOD argument 2
Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| x | y | → | x mod y |
| x | `symb` | → | `MOD(x, symb)` |
| `symb` | x | → | `MOD(symb, x)` |
| `symb1` | `symb2` | → | `MOD(symb1, symb2)` |
FLOOR, /
Command
Changes the modulo setting to the specified number. The number that you set is reflected in the CAS Modes input form. Negative numbers are replaced by their positive value, 0 and 1 are replaced by 2.
The modulo value that you want to set, an integer or an expression that evaluates to an integer.
The modulo setting is changed to the specified number. In Algebraic mode, NOVAL is returned as argument 1.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Command
Displays a menu or list of the CAS modulo operations.
If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered list. If the flag is set, displays the operations as a menu of function keys.
ALGB, ARIT, CONSTANTS, DIFF, EXP&LN, INTEGER, MAIN, MATHS, MATR, POLYNOMIAL, REWRITE, TESTS, TRIGO
Function
Returns the molecular weight for the specified molecular formula. It takes the formula as a string (such as "H2O") or name (with certain restrictions, such as `H2O`). It returns the molecular weight. It chooses to use or not use units according to the Units Usage flag (flag 61: SI units if clear, no units if set). You can store a molecular formula in a variable, then use the variable name with MOLWT. You should do this when you want to use MOLWT in an expression and the formula contains parentheses or matches a command name. You must take care when naming a variable that contains a formula string or name. Make sure the variable name isn’t a valid formula — for example, start the variable name with a lowercase letter. (If the variable name is a valid formula, using MOLWT with the variable name returns the molecular weight for the variable name, not for the formula it contains.)
Units Usage (61)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `name` | → | x or x_unit |
| “string” | → | x or x_unit |
| Example 1: | The command sequence "CH3C6H2(NO2)3" MOLWT returns | |
| `227.133_g/gmol` when flag 61 is clear. | ||
Example 2: The command sequence `C12H17ClN4OS` MOLWT returns 300.8055 when flag 61 | ||
| is set. | ||
PERINFO, PERTBL, PTPROP
Command
Multiple Roots Command: Uses the multiple-equation solver to solve for one or more variables using the equations in EQ. Given a variable name, MROOT returns the found value; with "ALL" MROOT stores a found value for each variable but returns nothing.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `name` | → | x |
| "ALL" | → |
MCALC, MUSER
Command
Message Box Command: Creates a user-defined message box. MSGBOX displays “message” in the form of a standard message box. Message text too long to appear on the screen is truncated. You can use spaces and new-line characters (…ë) to control word-wrapping and line breaks within the message. Program execution resumes when the message box is exited by selecting OK or CANCL.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| “message” | → |
CHOOSE, INFORM, PROMPT
Command
Numerically approximates a solution to a system of equations. Searches for a solution accurate to 12 digits, regardless of the display setting. Underdetermined and overdetermined systems are rejected. Complex solutions will be looked for if any of the inputs contain complex values. If a single expression or equation is to be solved, use SOLVE instead, or for linear equations, use LINSOLVE. This command is similar to MSOLVR, but is more appropriate for use with the CAS as it automates the solution instead of working through a menu. Step-by-step mode is available with this command.
Level 3/Argument 1: A vector containing the equations or expressions (assumed equal to zero) to solve. Level 2/Argument 2: A vector containing the variables to solve for Level 1/Argument 3: A vector containing initial guesses
Level 3/Item 1: The vector containing the equations to solve. Level 2/Item 2: The vector containing the variables to solve for Level 1/Item 3: A vector representing an approximate solution to the system of equations.
Exact mode must be set (flag –105 clear), The calculator will set approximate mode and will look for approximate results if exact results are not found. Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). Complex mode must be set (flag –103 set) if complex results are wanted. Step-by-step mode can be set (flag –100 set).
Find x and y values, allowing for complex solutions, that solve the following two equations. The first equation is an expression equal to zero, so only the expression needs to be given. Setting the second expression equal to a complex number forces the solver to look for complex solutions: sin(x)+y=0, x+sin(y)=1:
Command: MSLV(`[SIN(X)+Y, X+SIN(Y)=(1,0)]`, `[X,Y]`, [0,0])
Results: (`[SIN(X)+Y, X+SIN(Y)=(1,0)]`, `[X,Y]`, [(1.82384112611,0.),
(-.968154636174,0.)])
DESOLVE, LINSOLVE, MSOLVR, SOLVE
Command
Multiple Equation Solver Command: Gets the multiple-equation solver variable menu for the set of equations defined by Mpar. The multiple-equation solver application can solve a set of two or more equations for unknown variables by finding the roots of each equation, one at a time. The Multiple-Equation Solver uses the list of equations stored in EQ. “Equations” in this context includes programs, expressions, and variable names that evaluate to a single value. The Multiple- Equation Solver requires that EQ contain more than one equation — that is, the HP Solve application would include the NXEQ menu label for EQ. The solver uses EQ to create a reserved
variable Mpar that is used during the solution process. Mpar contains the equation set plus additional information. See appendix D, “Reserved Variables”, for information about Mpar.
None
EQNLIB, MCALC, MINIT, MITM, MROOT, MSLV, MUSER
Function
Performs modular multiplication of two objects, modulo the current modulus.
Level 2/Argument 1: A number or an expression. Level 1/Argument 2: A number or an expression.
The result of modular multiplication of the two objects, modulo the current modulus.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Find the product of 2x and 38x2, modulo the default modulus, 3.
| Command | MULTMOD(2*X,38*X^2) |
|---|---|
| Result | X^3 |
Command
Make User-Defined Variable Command: Designates a variable as user-defined for the multiple- equation solver. MUSER designates a single variable, a list of variables, or all variables as user-defined.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `name` | → | |
| { list } | → | |
| "ALL" | → |
MCALC
Command
Sets the number of program lines displayed on the screen. The default value on the calculator is 9. On the HP 50g and 49g+ a value of 12 should be set for →NDISP, which will allow more of these models’ taller screen to be used when the font is FONT7, FONT6, or the MINIFONT. Also, note that the →NDISP setting is reset to 9 at every warmstart. Including << 12 →NDISP >> in `STARTUP` will automatically reset the value to 12.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| n | → |
Command
Normal Distribution Command: Returns the normal probability distribution (bell curve) at x based on the mean m and variance v of the normal distribution. NDIST is calculated using this formula: 2 (x – m) – ------------------- 2v e ndist ( m, v, x ) = -------------------- 2πv
| Level 3/Argument 1 | Level 2/Argument 2 | Level 1/Argument 3 | Level 1/Item 1 | |
|---|---|---|---|---|
| m | v | x | → | ndist(m, v, x) |
UTPN
RPL command
Duplicates an object n times, and returns n.
| Level 2 | Level 1 | Leveln+1 … Level2 | Level1 | |
|---|---|---|---|---|
| obj | n | → | obj … obj | n |
To make a list of 100 “X”s, run "X" 100 NDUPN →LIST.
DUP, DUPDUP, DUPN, DUP2
Analytic function
Negate Analytic Function: Changes the sign or negates an object. Negating an array creates a new array containing the negative of each of the original elements. Negating a binary number takes its two’s complement (complements each bit and adds 1). Negating a graphics object “inverts” it (toggles each pixel from on to off, or vice-versa). If the argument is PICT, the graphics object stored in PICT is inverted.
Numerical Results (–3), Binary Integer Wordsize (–5 through –10)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| z | → | –z |
| #n1 | → | #n2 |
| [ array ] | → | [ –array ] |
| `symb` | → | `–(symb)` |
| x_unit | → | –x_unit |
| grob1 | → | grob2 |
| PICT1 | → | PICT2 |
ABS, CONJ, NOT, SIGN
Command
New Object Command: Creates a new copy of the specified object. NEWOB has two main uses:
Last Arguments (–55). In order for NEWOB to immediately release the memory occupied by the original copy, flag –55 must be set so that the copy is not saved as a last argument.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| obj | → | obj |
| Example 1: | :0:BKUP1 RCL NEWOB :0:BKUP1 PURGE recalls and purges the backup object | |
| BKUP1. | ||
Example 2: 3 GET NEWOB retrieves the third element out of a list on the stack, recovering the memory | ||
| occupied by the whole list. | ||
MEM, PURGE
Command
NEXT Command: Ends definite loop structures. See the FOR and START keyword entries for more information.
None
FOR, START, STEP NEXT
Operation
NEXT Operation: Returns but does not execute the next one or two steps of a program.
None
SST, SST↓
Function
Given an integer, returns the next prime number larger than the integer. Like ISPRIME?, it uses a pseudoprime check for large numbers.
An integer or an expression that evaluates to an integer.
The next prime number larger than the integer.
Find the closest, larger prime number to 145.
| Command | NEXTPRIME(145) |
|---|---|
| Result | 149 |
ISPRIME?, PREVPRIME
RPL command
Drops the (n–1)th argument, where n is the number of arguments or items on the stack. (that is, the object on level 2 of the stack). This is equivalent to executing SWAP followed by DROP in RPN mode.
| Level 2 | Level 1 | Level 1 | |
|---|---|---|---|
| obj1 | obj2 | → | obj2 |
333 222 1 NIP returns 333 1
DUP, DUPDUP, DUPN, DUP2
Function
NOT Command: Returns the one’s complement or logical inverse of the argument. When the argument is a binary integer or string, NOT complements each bit in the argument to produce the result.
Numerical Results (–3), Binary Integer Wordsize (–5 through –10)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| #n1 | → | #n2 |
| T/F | → | 0/1 |
| “string1” | → | “string2” |
| `symb` | → | `NOT symb` |
AND, OR, XOR
Command
INFORM Place Holder/Result Command: Place holder for reset and initial values in user-defined dialog boxes. NOVAL is returned when a field is empty.
NOVAL is used to mark an empty field in a user-defined dialog box created with the INFORM command. INFORM defines fields sequentially. If default values are used for those fields, the defaults must be defined in the same order as the fields were defined. To skip over (not provide defaults for) some of the fields, use the NOVAL command. After INFORM terminates, NOVAL is returned if a field is empty and OK or ` is selected.
None
INFORM
Command
Number of Rows Command: Returns the number of rows in the current statistical matrix (reserved variable ΣDAT).
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | nrows |
ΣX, ΣXY, ΣX2, ΣY, ΣY2
Command
Number of Sublist Command: Provides a way to access the current sublist position during an iteration of a program or command applied using DOSUBS. Returns an Undefined Local Name error if executed when DOSUBS is not active.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | nposition |
DOSUBS, ENDSUB
Command
Evaluate to Number Command. Evaluates a symbolic argument object (other than a list) and returns the numerical result. →NUM repeatedly evaluates a symbolic argument until a numerical result is achieved. The effect is the same as evaluating a symbolic argument in Numerical Result Mode (flag –3 set).
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| objsymb | → | z |
EVAL
Command
Character Number Command: Returns the character code n for the first character in the string. The character codes are an extension of ISO 8859/1. Codes 128 through 159 are unique to the calculators.
The number of a character can be found by accessing the Characters tool (…±) and highlighting that character. The number appears near the bottom of the screen. These are also listed in Appendix J of this manual.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| “string” | → | n |
CHR, POS, REPL, SIZE, SUB
Command
Number of X-Steps Command: Sets the number of x-steps for each y-step in 3D perspective plots. The number of x-steps is the number of independent variable points plotted for each dependent variable point plotted. This number must be 2 or more. This value is stored in the reserved variable VPAR. YSLICE is the only 3D plot type that does not use this value.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| nx | → |
NUMY
Command
Number of Y-Steps Command: Sets the number of y-steps across the view volume in 3D perspective plots. The number of y-steps is the number of dependent variable points plotted across the view volume. This number must be 2 or more. This value is stored in the reserved variable VPAR.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| ny | → |
NUMX
Command
Object to Stack Command: Separates an object into its components. For some object types, the number of components is returned as item n+1 (stack level 1). If the argument is a complex number, list, array, or string, OBJ→ provides the same functions as C→R, LIST→, ARRY→, and STR→, respectively. For lists, OBJ→ also returns the number of list elements. If the argument is an array, OBJ→ also returns the dimensions { m n } of the array, where m is the number of rows and n is the number of columns. For algebraic objects, OBJ→ returns the arguments of the top-level (least-nested) function (arg1 … argn), the number of arguments of the top-level function (n), and the name of the top-level function (function). If the argument is a string, the object sequence defined by the string is executed.
| Level 1/Argument 1 | Leveln+1/Item1 | Level2/Itemn | Level1/Itemn+1 | ||
|---|---|---|---|---|---|
| (x, y) | → | x | y | ||
| { obj1, ... ,objn } | → | obj1 | … | objn | n |
| [ x1, ... ,xn ] | → | x1 | … | xn | {n} |
| [[ x1 1, ... ,xm n ]] | → | x1 1 | … | xm n | { m, n } |
| “obj” | → | evaluated object | |||
| `symb` | → | arg1 ... argn | … | n | `function` |
| x_unit | → | x | 1_unit | ||
| :tag:obj | → | obj | “tag” |
The command sequence `„(0,1,SIN(X),X)` OBJ→ returns:
6: 0 first argument
5: 1 second argument
4: `SIN(X)` third argument
3: `X` fourth argument
2: 4 number of arguments for „
1: „ function name
ARRY→, C→R, DTAG, EQ→, LIST→, R→C, STR→, →TAG
Command
Octal Mode Command: Selects octal base for binary integer operations. (The default base is decimal.) Binary integers require the prefix #. Binary integers entered and returned in octal base automatically show the suffix o. If the current base is not octal, enter an octal number by ending it with o. It will be displayed in the current base when entered. The current base does not affect the internal representation of binary integers as unsigned binary numbers.
Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12)
None
BIN, DEC, HEX, RCWS, STWS
Command
Off Command: Turns off the calculator. When executed from a program, that program will resume execution when the calculator is turned on. This provides a programmable “autostart.” ( i.e., a programmable …ç).
None
CONT, HALT, KILL
Command
Modifies the remapping string in the reserved variable PRTPAR so that the extended character set of the calculator matches that of the HP 82240A Infrared Printer.
The character set in the HP 82240A Infrared Printer does not match the character set of the calculator:
CR, DELAY, PRLCD, PRST, PRSTC, PRVAR, PR1
Command
Open I/O Port Command: Opens a serial port using the I/O parameters in the reserved variable IOPAR. Since all Kermit-protocol commands automatically effect an OPENIO first, OPENIO is not normally needed, but can be used if an I/O transmission does not work. OPENIO is necessary for interaction with devices that interpret a closed port as a break. OPENIO is also necessary for the automatic reception of data into the input buffer using non- Kermit commands. If the port is closed, incoming characters are ignored. If the port is open, incoming characters are automatically placed in the input buffer (up to 255 characters). These characters can be detected with BUFLEN, and can be read out of the input buffer using SRECV. If the port is already open, OPENIO does not affect the data in the input buffer. However, if the port is closed, executing OPENIO clears the data in the input buffer. For more information, refer to the reserved variable IOPAR in appendix D, “Reserved Variables”.
I/O Device (–33), I/O Device for Wire (–78)
None
BUFLEN, CLOSEIO, SBRK, SRECV, STIME, XMIT
Function
OR Function: Returns the logical OR of two arguments. When the arguments are binary integers or strings, OR does a bit-by-bit (base 2) logical comparison.
| bit1 | bit2 | bit1 OR bit2 |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
Numerical Results (–3), Binary Integer Wordsize (–5 through –10)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| #n1 | #n2 | → | #n3 |
| “string1” | “string2” | → | “string3” |
| T/F1 | T/F2 | → | 0/1 |
| T/F | `symb` | → | `T/F OR symb` |
| `symb` | T/F | → | `symb OR T/F` |
| `symb1` | `symb2` | → | `symb1 OR symb2` |
AND, NOT, XOR
Command
Order Variables Command: Reorders the variables in the current directory (shown in the VAR menu) to the order specified. The names that appear first in the list will be the first to appear in the VAR menu. Variables not specified in the list are placed after the reordered variables. If the list includes the name of a large subdirectory, there may be insufficient memory to execute ORDER.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| { global1 ... globaln } | → |
VARS
RPL command
Over Command: Returns a copy to stack level 1 of the object in level 2.
| Level 2 | Level 1 | Level 3 | Level 2 | Level 1 | |
|---|---|---|---|---|---|
| obj1 | obj2 | → | obj1 | obj2 | obj1 |
PICK, ROLL, ROLLD, ROT, SWAP
Command
Takes a list representing a permutation as an argument, and returns the permutation decomposed into lists that represent cycles.
A list representing a permutation. For example, the list {3,1,2,5,4} defines a permutation P, such that P(1)=3, P(2)=1, P(3)=2, P(4)=5, and P(5)=4
Level 2/Item 1:A list of cycles equivalent to the permutation. For example, the list {3,1,2,5,4} defines a cycle C, such that C(3)=1, C(1)=2, C(2)=5, C(5)=4, and C(4)=3 Level 1, Item 2: The signature of the permutation, 1 or –1.
Convert the permutation given by {3,4,5,2,1} into cycles:
| Command | P2C({3,4,5,2,1}) |
|---|---|
| Result | {{{1,3,5},{2,4}},-1} |
C2P, CIRC
Function
Takes a prime number, p, such that p=2 orp ≡ 1 modulo 4, and returns a Gaussian integer a + ib such that p = a2 + b2. This function is useful for factorizing Gaussian integers.
A prime number, p, such that p=2 orp ≡ 1 modulo 4
A Gaussian integer a+ib such that p=a2+b2
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Complex mode must be set (flag –103 set).
GAUSS
Command
Parametric Plot Type Command: Sets the plot type to PARAMETRIC. When the plot type is PARAMETRIC, the DRAW command plots the current equation as a complex-valued function of one real variable. The current equation is specified in the reserved variable EQ. The plotting parameters are specified in the reserved variable PPAR, which has the following form: { (xmin, ymin), (xmax, ymax), indep, res, axes, ptype, depend } For plot type PARAMETRIC, the elements of PPAR are used as follows:
Simultaneous Plotting (–28), Curve Filling (–31)
None
BAR, CONIC, DIFFEQ, FUNCTION, GRIDMAP, HISTOGRAM, PARSURFACE, PCONTOUR, POLAR, SCATTER, SLOPEFIELD, TRUTH, WIREFRAME, YSLICE
Command
Parity Command: Sets the parity value in the reserved variable IOPAR. Legal values are shown below. A negative value means the calculator does not check parity on bytes received during Kermit transfers or with SRECV. Parity is still used during data transmission, however.
| n-Value | Meaning |
|---|---|
| 0 | no parity (the default value) |
| 1 | odd parity |
| 2 | even parity |
| 3 | mark |
| 4 | space |
For more information, refer to the reserved variable IOPAR in appendix D, “Reserved Variables”.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| nparity | → |
BAUD, CKSM, TRANSIO
Command
PARSURFACE Plot Type Command: Sets plot type to PARSURFACE. When plot type is set to PARSURFACE, the DRAW command plots an image graph of a 3- vector-valued function of two variables. PARSURFACE requires values in the reserved variables EQ, VPAR, and PPAR. VPAR is made up of the following elements: { xleft, xright, ynear, yfar, zlow, zhigh, xmin, xmax, ymin, ymax, xeye, yeye, zeye, xstep, ystep } For plot type PARSURFACE, the elements of VPAR are used as follows:
None
BAR, CONIC, DIFFEQ, FAST3D, FUNCTION, GRIDMAP, HISTOGRAM, PARAMETRIC, PCONTOUR, POLAR, SCATTER, SLOPEFIELD, TRUTH, WIREFRAME, YSLICE
Command
Performs partial fraction decomposition on a partial fraction.
An algebraic expression.
The partial fraction decomposition of the expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Perform a partial fraction decomposition of the following expression: 1 ------------- 2 x –1
| Command | PARTFRAC(1/(X^2-1)) |
|---|---|
| Result | 1/2/(X-1)+-1/2/(X+1) |
PROPFRAC
Command
Current Path Command: Returns a list specifying the path to the current directory. The first directory is always HOME, and the last directory is always the current directory. If a program needs to switch to a specific directory, it can do so by evaluating a directory list, such as one created earlier by PATH.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | { HOME directory-name1 ... directory-namen } |
CRDIR, HOME, PGDIR, UPDIR
Command
Returns the characteristic polynomial of an n × n matrix.
A square matrix.
The characteristic polynomial of the matrix.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Find the characteristic polynomial of the following matrix: 5 8 16 4 1 8 – 4 – 4 – 11
| Command | PCAR([[5,8,16][4,1,8][-4,-4,-11]]) |
|---|---|
| Result | X^3+5*X^2+3*X-9 |
JORDAN, PMINI
Command
Monic Polynomial Coefficients Command: Returns the coefficients of a monic polynomial (a polynomial with a leading coefficient of 1) having specific roots. The argument must be a real or complex array of length n containing the polynomial’s roots. The result is a real or complex vector of length n+1 containing the coefficients listed from highest order to lowest, with a leading coefficient of 1.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| [ array ]roots | → | [ array ]coefficients |
Find the polynomial that has the roots 2, –3, 4, –5:
| Command | [ 2 –3 4 –5 ] PCOEF |
|---|---|
| Result | [ 1 2 –25 –26 120 ], representing the polynomial x4 + 2x3 - 25x2 - 26x + 120. |
PEVAL, PROOT
Command
PCONTOUR Plot Type Command: Sets the plot type to PCONTOUR. When plot type is set PCONTOUR, the DRAW command plots a contour-map view of a scalar function of two variables. PCONTOUR requires values in the reserved variables EQ, VPAR, and PPAR. VPAR is made up of the following elements: { xleft xright ynear yfar zlow zhigh xmin xmax ymin ymax xeye yeye zeye xstep ystep } For plot type PCONTOUR, the elements of VPAR are used as follows:
None
BAR, CONIC, DIFFEQ, FUNCTION, GRIDMAP, HISTOGRAM, PARAMETRIC, PARSURFACE, POLAR, SCATTER, SLOPEFIELD, TRUTH, WIREFRAME, YSLICE
Command
Population Covariance Command: Returns the population covariance of the independent and dependent data columns in the current statistics matrix (reserved variable ΣDAT). The columns are specified by the first two elements in reserved variable ΣPAR, set by XCOL and YCOL respectively. If ΣPAR does not exist, PCOV creates it and sets the elements to their default values (1 and 2). The population covariance is calculated with the following formula: 1 n -- ∑ ( xkn1 – x n 1 ) ( x kn2 – x n2 ) nk = 1
x kn 1 n 1 x kn 2
where is the kth coordinate value in column , is the kth coordinate value in the
n x n1 xn n
column 2 , n1 is the mean of the data in column , 2 is the mean of the data in column 2 ,
and n is the number of data points.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | xpcovariance |
COLΣ, CORR, COV, PREDX, PREDY, XCOL, YCOL
Command
PICT Dimension Command: Replaces PICT with a blank PICT of the specified dimensions. If the arguments are complex numbers, PDIM changes the size of PICT and makes the arguments the new values of (xmin, ymin) and (xmax, ymax) in the reserved variable PPAR. Thus, the scale of a subsequent plot is not changed. If the arguments are binary integers, PPAR remains unchanged, so the scale of a subsequent plot is changed. PICT cannot be smaller than 131 pixels wide × 80 pixels high on the HP 50g and 49g+ (64 pixels high on the HP 48gII) nor wider than 2048 pixels (height is unlimited).
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| (xmin, ymin) | (xmax, ymax) | → | |
| #nwidth | #mheight | → |
PMAX, PMIN
Command
Displays the Periodic Table version and copyright information. It doesn’t affect the stack.
None
MOLWT, PERTBL, PTPROP
Function
Permutations Function: Returns the number of possible permutations of n items taken m at a time. The formula used to calculate Pn,m is: n! P n, m = ------------------- ( n – m )!
The arguments n and m must each be less than 1012. If n < m, zero is returned.
Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| n | m | → | Pn,m |
| `symbn` | m | → | `PERM(symbn,m)` |
| n | `symbm` | → | `PERM(n, symbm)` |
| `symbn` | `symbm` | → | `PERM(symbn,symbm)` |
COMB, FACT, !
Command
Starts the Periodic Table. It doesn’t affect the stack.
Units Usage (61), Units Type (60)
None
MOLWT, PERINFO, PTPROP
Command
Polynomial Evaluation Command: Evaluates an n-degree polynomial at x. The arguments must be an array of length n + 1 containing the polynomial’s coefficients listed from highest order to lowest, and the value x at which the polynomial is to be evaluated.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| [ array ]coefficients | x | → | p(x) |
Find the polynomial x4 + 2x3 - 25x2 - 26x + 120 at x = 8:
| Command | [ 1 2 –25 –26 120 ] 8 PEVAL |
|---|---|
| Result | 3432 |
PCOEF, PROOT
Command
Purge Directory Command: Purges the named directory (whether empty or not).
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `global` | → |
CLVAR, CRDIR, HOME, PATH, PURGE, UPDIR
RPL Command
Pick Object Command: Copies the contents of a specified stack level to level 1.
| Ln+1... | L2 | L1 | Ln+1 | L2 | L1 | |
|---|---|---|---|---|---|---|
| objn ... | obj1 | n | → | objn ... | obj1 | obji |
| L = Level | ||||||
DUP, DUPN, DUP2, OVER, ROLL, ROLLD, ROT, SWAP
RPL Command
Duplicates the object on level 3 of the stack.
| L3 | L2 | L1 | L4 | L3 | L2 | L1 | |
|---|---|---|---|---|---|---|---|
| obj1 | obj2 | obj3 | → | obj1 | obj2 | obj3 | obj1 |
| L = Level; A = Argument; I =Item | |||||||
333 22 1 PICK3 returns 333 22 1 333.
PICK, OVER, DUP
Command
PICT Command: Puts the name PICT on the stack. PICT is the name of a storage location in calculator memory containing the current graphics object. The command PICT enables access to the contents of that memory location as if it were a variable. Note, however, that PICT is not a variable as defined in the calculator: its name cannot be quoted, and only graphics objects may be stored in it. If a graphics object smaller than 131 wide × 80 pixels high is stored in PICT, it is enlarged to 131 × 80. (These values are 131 x 64 on the HP 48gII). A graphics object of unlimited pixel height and up to 2048 pixels wide can be stored in PICT.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | PICT |
PICT RCL returns the current graphics object to the stack.
GOR, GXOR, NEG, PICTURE, PVIEW, RCL, REPL, SIZE, STO, SUB
Command
Picture Environment Command: Selects the Picture environment (that is, selects the graphics display and activates the graphics cursor and Picture menu). When executed from a program, PICTURE suspends program execution until −is pressed.
None
This program: « "Press CANCEL to return to stack" 1 DISP 3 WAIT PICTURE »
displays a message for 3 seconds, then selects the Picture environment. (The character in the
program indicates a linefeed.)
PICT, PVIEW, TEXT
Command
Port Initialize Command: Initializes all currently active ports. It may affect data already stored in a port. PINIT is particularly useful when a third-party library has corrupted memory. It stores and then purges an object in each internal port. This has the effect of initializing each port without disturbing any previous-stored data, while removing any invalid objects.
None
Command
Pixel On? Command: Tests whether the specified pixel in PICT is on; returns 1 (true) if the pixel is on, and 0 (false) if the pixel is off.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| (x,y) | → | 0/1 |
| { #n #m } | → | 0/1 |
PIXON, PIXOFF
Command
Pixel Off Command: Turns off the pixel at the specified coordinate in PICT.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| (x,y) | → | |
| { #n #m } | → |
PIXON, PIX?
Command
Pixel On Command: Turns on the pixel at the specified coordinate in PICT.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| (x,y) | → | |
| { #n #m } | → |
PIXOFF, PIX?
Command
Packet Command: Used to send command “packets” (and receive requested data) to a Kermit server. To send calculator objects, use SEND. PKT allows additional commands to be sent to a Kermit server. The packet data, packet type, and the response to the packet transmission are all in string form. PKT first does an I (initialization) packet exchange with the Kermit server, then sends the server a packet constructed from the data and packet-type arguments supplied to PKT. The response to PKT will be either an acknowledging string (possibly blank) or an error packet (see KERRM). For the type argument, only the first letter is significant.
I/O Device (–33), I/O Messages (–39), I/O Device for Wire (–78). The I/O Data Format flag (– 35) can be significant if the server sends back more than one packet.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| “data” | “type” | → | “response” |
| Example 1: A PKT command to send a generic directory request is "D" "G" PKT. | |||
| Example 2: To send a host command packet, use a command from the server’s operating system for the data | |||
| string and "C" for the type string. For example, "`ABC` PURGE" "C" PKT on a local calculator would instructor a server calculator to purge variable ABC. | |||
CLOSEIO, KERRM, SERVER
Command
Stores its argument in EQ and opens the PLOT SETUP screen.
An expression.
The input expression.
Store SIN(X) in EQ and open the PLOT SETUP screen:
Command: PLOT(SIN(X))
PLOT SETUP screen is open with SIN(X) in EQ. SIN(X) is copied to history (LASTARG in RPN mode).
PLOTADD
Function
Adds a function to the existing plot function list, and opens the Plot Setup screen.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| (symb) | → |
Command
PICT Maximum Command: Specifies (x, y) as the coordinates at the upper right corner of the display. The complex number (x, y) is stored as the second element in the reserved variable PPAR.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| (x,y) | → |
PDIM, PMIN, XRNG, YRNG
Command
PICT Minimum Command: Specifies (x, y) as the coordinates at the lower left corner of the display. The complex number (x, y) is stored as the first element in the reserved variable PPAR.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| (x,y) | → |
PDIM, PMAX, XRNG, YRNG
Command
Finds the minimal polynomial of a matrix.
An nxn matrix A.
A matrix whose first zero-row contains the minimal polynomial of A. In step-by-step mode, PMINI shows the row-reduction steps.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Step-by-step mode can be set (flag –100 set). 01 10
| Find the minimal polynomial of | : |
|---|---|
| Command: | PMINI([[0,1][1,0]]) |
| 1 0 0 1 | 1 |
| 0 1 1 0 | X |
2 0 0 0 0 X –1
Result: So, the minimal polynomial is X2-1, as it is in the first row to contain entirely
zeros, except for the result.
JORDAN, PCAR
Command
Polar Plot Type Command: Sets the plot type to POLAR. When the plot type is POLAR, the DRAW command plots the current equation in polar coordinates, where the independent variable is the polar angle and the dependent variable is the radius. The current equation is specified in the reserved variable EQ. The plotting parameters are specified in the reserved variable PPAR, which has this form: { (xmin, ymin) (xmax, ymax) indep res axes ptype depend } For plot type POLAR, the elements of PPAR are used as follows:
expr = expr Each expression is plotted separately. The intersection of the
two graphs shows where the expressions are equal
name = expr Only the expression is plotted
Simultaneous Plotting (–28), Curve Filling (–31)
None
BAR, CONIC, DIFFEQ, FUNCTION, GRIDMAP, HISTOGRAM, PARAMETRIC, PARSURFACE, PCONTOUR, SCATTER, SLOPEFIELD, TRUTH, WIREFRAME, YSLICE
Command
Displays a menu or list of CAS operations with polynomials.
If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered list. If the flag is set, displays the operations as a menu of function keys.
ALGB, ARIT, CONSTANTS, DIFF, EXP&LN, INTEGER, MAIN, MATHS, MATR, MODULAR, REWRITE, TESTS, TRIGO
Command
Restores the flags and current directory saved by the most recent execution of PUSH. If no PUSH saves are left, the command has no effect.
None
In Algebraic mode the command returns NOVAL to level 1 of the stack.
PUSH, RCLF, STOF
Command
Position Command: Returns the position of a substring within a string or the position of an object within a list. If there is no match for obj or substring, POS returns zero.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| “string” | “substring” | → | n |
| { list } | obj | → | n |
CHR, NUM, REPL, SIZE, SUB
Command
Find the potential field function describing a field whose vector gradient is input. This command is the opposite of DERIV. Given a vector V it attempts to return a function U such that grad U is equal to V; ∇U = V . For this to be possible, CURL(V) must be zero, otherwise the command reports a “Bad Argument Value” error. Step-by-step mode is available with this command.
Level 2/Argument 1: A vector V of expressions. Level 1/Argument 2: A vector of the names of the variables.
Level 1/Item 1: A function U of the variables that is the potential from which V is derived. An arbitrary constant can be added, the command does not do this.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). Step-by-step mode can be set (flag –100 set).
To confirm that this command is the opposite of DERIV, use the output of the example in DERIV, and show that the result is the same as the input given in the DERIV example. Find the function of the spatial variables x, y, and z whose gradient is: (4xy+z)i + (2x2 + 6yz)j + (x+3y2)k
Command: POTENTIAL([4*X*Y+Z, 2*X^2+6*Y*Z, X+3*Y^2], [X,Y,Z])
EXPAND(ANS(1))
Result: 2*Y*X^2+Z*X+3*Z*Y^2
DERIV, VPOTENTIAL
Function
Rewrites an expression raised to a power as a product. If followed by repeated execution of DISTRIB allows an expression to be expanded fully, step by step.
An expression raised to a power.
The result from applying the distributive property of exponentiation over multiplication.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
| Example: Expand (X+1)3. | |
|---|---|
| Command | POWEXPAND((X+1)^3) |
(X+1)·(X+1)·(X+1)
Function
Raises an object (number or expression) to the specified power, and expresses the result modulo the current modulus.
Level 2/Argument 1: The object. Level 1/Argument 2: The exponent.
The result of the object raised to the exponent, modulo the current modulus.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Command
Print Level 1 Command: Prints an object in multiline printer format. All objects except strings are printed with their identifying delimiters. Strings are printed without the leading and trailing " delimiters. If flag –34 is set (printer output directed to the serial port), flag –33 must be clear. Multiline printer format is similar to multiline display format, with the following exceptions:
Row 2 1] 4 2] 5 3] 6
I/O Device (–33), Printing Device (–34), Double-spaced Printing (–37), Linefeed (–38), I/O Device for Wire (–78). If flag –34 is set, flag –33 must be clear.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| object | → | object |
CR, DELAY, OLDPRT, PRLCD, PRST, PRSTC, PRVAR
Command
Predicted y-Value Command: Returns the predicted dependent-variable value ydependent, based on the independent-variable value xindependent, the currently selected statistical model, and the current regression coefficients in the reserved variable ΣPAR. PREDV is the same as PREDY. See PREDY.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| xindependent | → | ydependent |
PREDY
Command
Predicted x-Value Command: Returns the predicted independent-variable value xindependent, based on the dependent-variable value ydependent, the currently selected statistical model, and the current regression coefficients in the reserved variable ΣPAR. The value is predicted using the regression coefficients most recently computed with LR and stored in the reserved variable ΣPAR. For the linear statistical model, the equation used is this: ydependent = (mxindependent) + b where m is the slope (the third element in ΣPAR) and b is the intercept (the fourth element in ΣPAR). For the other statistical models, the equations used by PREDX are listed in the LR entry. If PREDX is executed without having previously generated regression coefficients in ΣPAR, a default value of zero is used for both regression coefficients, and an error results.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| ydependent | → | xindependent |
Given five columns of data in ΣDAT, the command sequence: 2 XCOL 5 YCOL LOGFIT LR 23 PREDX sets column 2 as the independent variable column, sets column 5 as the dependent variable column, and sets the logarithmic statistical model. It then executes LR, generating intercept and slope regression coefficients, and storing them in ΣPAR. Then, given a dependent value of 23, it returns a predicted independent value based on the regression coefficients and the statistical model.
COLΣ, CORR, COV, EXPFIT, ΣLINE, LINFIT, LOGFIT, LR, PREDY, PWRFIT, XCOL, YCOL
Command
Predicted y-Value Command: Returns the predicted dependent-variable value ydependent, based on the independent-variable value xindependent, the currently selected statistical model, and the current regression coefficients in the reserved variable ΣPAR. The value is predicted using the regression coefficients most recently computed with LR and stored in the reserved variable ΣPAR. For the linear statistical model, the equation used is this: ydependent = (mxindependent) + b where m is the slope (the third element in ΣPAR) and b is the intercept (the fourth element in ΣPAR). For the other statistical models, the equations used by PREDY are listed in the LR entry. If PREDY is executed without having previously generated regression coefficients in ΣPAR, a default value of zero is used for both regression coefficients–in this case PREDY will return 0 for statistical models LINFIT and LOGFIT, and error for statistical models EXPFIT and PWRFIT.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| xindependent | → | ydependent |
Given four columns of data in ΣDAT, the command sequence: 2 XCOL 4 YCOL PWRFIT LR 11 PREDY sets column 2 as the independent variable column, sets column 4 as the dependent variable column, and sets the power statistical model. It then executes LR, generating intercept and slope regression coefficients, and storing them in ΣPAR. Then, given an independent value of 11, it returns a predicted dependent value based on the regression coefficients and the statistical model.
COLΣ, CORR, COV, EXPFIT, ΣLINE, LINFIT, LOGFIT, LR, PREDX, PWRFIT, XCOL, YCOL
Function
With respect to the current default variable, returns the difference between the values of a function at two specified values of the variable. PREVAL can be used in conjunction with INTVX to evaluate definite integrals. See the example below.
Level 3/Argument 1: A function. Level 2/Argument 2: The lower bound. Level 3/Argument 1: The upper bound. The bounds can be expressions.
The result of the evaluation.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Evaluate the following:
3 3
∫0 ( x + 3 x ) dx
| Command | PREVAL(INTVX(X^3+3*X),0,3) |
|---|---|
| Result | 135/4 |
Function
Given an integer, finds the closest prime number smaller than the integer. Like ISPRIME?, it uses a pseudoprime check for large numbers.
An integer or an expression that evaluates to an integer.
The closest prime number smaller than the integer.
Find the closest, smaller prime number to 145.
| Command | PREVPRIME(145) |
|---|---|
| Result | 139 |
ISPRIME?, NEXTPRIME
Command
Print LCD Command: Prints a pixel-by-pixel image of the current display (excluding the annunciators). The width of the printed image of characters in the display is narrower using PRLCD than using a print command such as PR1. The difference results from the spacing between characters. On the display there is a single blank column between characters, and PRLCD prints this spacing. Print commands such as PR1 print two blank columns between adjacent characters.
I/O Device (–33), Printing Device (–34), Double-spaced Printing (–37), Linefeed (–38). Flag –38 must be clear, I/O Device for Wire (–78). If flag –34 is set, flag –33 must be clear.
None
The command sequence ERASE DRAW PRLCD clears PICT, plots the current equation, then prints the graphics display.
CR, DELAY, OLDPRT, PRST, PRSTC, PRVAR, PR1
Command
Prompt Command: Displays the contents of “prompt” in the status area, and halts program execution. PROMPT is equivalent to 1 DISP 1 FREEZE HALT.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| “prompt” | → |
CONT, DISP, FREEZE, HALT, INFORM, INPUT, MSGBOX
Command
Prompt Command: Creates a variable with the name supplied as an argument, prompts for a value, and stores the value you enter in the variable.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| “global” | → |
PROMPT, STO
Command
Polynomial Roots Command: Returns all roots of an n-degree polynomial having real or complex coefficients. For an nth-order polynomial, the argument must be a real or complex array of length n + 1 containing the coefficients listed from highest order to lowest. The result is a real or complex vector of length n containing the computed roots. PROOT interprets leading coefficients of zero in a limiting sense. As a leading coefficient approaches zero, a root of the polynomial approaches infinity: therefore, if flag –22 is clear (the default), PROOT reports an Infinite Result error if a leading coefficient is zero. If flag –22 is set, PROOT returns a root of (MAXREAL,0) for each leading zero in an array containing real coefficients, and a root of (MAXREAL,MAXREAL) for each leading zero in an array containing complex coefficients.
Infinite Result Exception (–22)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| [ array ]coefficients | → | [ array ]roots |
Find the roots of the polynomial x4 + 2x3 - 25x2 - 26x + 120: Command: [ 1 2 –25 –26 120 ] PROOT
Result: [ 2 –3 4 –5 ]
PCOEF, PEVAL
Command
Toggles between an improper fraction and its corresponding integer and fractional part.
An improper fraction, or an object that evaluates to an improper fraction. It must not contain real numbers. Alternately, the input may be an integer part plus a proper fraction.
An integer part plus a proper fraction; or alternately, if the input was an integer part plus a proper fraction, an improper fraction.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Express the following as a proper fraction: 3 x +4 ------------- 2 x
| Command | PROPFRAC((X^3+4)/X^2)) |
|---|---|
| Result | X+(4/X^2) |
Command
Print Stack Command: Prints all objects in the stack, starting with the object on the highest level. Objects are printed in multiline printer format. See the PR1 entry for a description of multiline printer format.
I/O Device (–33), Printing Device (–34), Double-spaced Printing (–37), Linefeed (–38), I/O Device for Wire (–78). If flag –34 is set, flag –33 must be clear. Generally, flag –38 should be clear.
None
CR, DELAY, OLDPRT, PRLCD, PRSTC, PRVAR, PR1
Command
Print Stack (Compact) Command: Prints in compact form all objects in the stack, starting with the object on the highest level. If flag –34 is set (printer output directed to the serial port), flag –33 must be clear. When flag –38 is set, linefeeds are not added at the end of each print line. Generally, flag –38 should be clear for execution of PRSTC. Compact printer format is the same as compact display format. Multiline objects are truncated and appear on one line only.
I/O Device (–33), Printing Device (–34), Double-spaced Printing (–37), Linefeed (–38), I/O Device for Wire (–78)
None
CR, DELAY, OLDPRT, PRLCD, PRST, PRVAR, PR1
Command
Print Variable Command: Searches the current directory path or port for the specified variables and prints the name and contents of each variable. Objects are printed in multiline printer format. See the PR1 entry for a description of multiline printer format. If flag –34 is set (printer output directed to the serial port), flag –33 must be clear. When flag –38 is set, linefeeds are not added at the end of each print line. Generally, flag –38 should be clear for execution of PRVAR.
I/O Device (–33), Printing Device (–34), Double-spaced Printing (–37), Linefeed (–38), I/O Device for Wire (–78). If flag –34 is set, flag –33 must be clear. Generally, flag –38 should be clear.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `name` | → | |
| { name1 name2 ... } | → | |
| :nport : `global` | → |
CR, DELAY, OLDPRT, PR1, PRLCD, PRST, PRSTC
Command
Population Standard Deviation Command: Calculates the population standard deviation of each of the m columns of coordinate values in the current statistics matrix (reserved variable ΣDAT). PSDEV returns a vector of m real numbers, or a single real number if m = 1. The population standard deviation is computed using this formula: n
1 2
-- ∑ ( x k – x ) nk = 1
where xk is the kth coordinate value in a column, x is the mean of the data in this column, and n is the number of data points.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | xpsdev | |
| → | [ xpsdev1 xpsdev2 ... xpsdevm } |
MEAN, PCOV, PVAR, SDEV, TOT, VAR
Function
Calculates the polygamma function, the nth derivative of the digamma function, at a point a. PSI(a, 0) is equivalent to Psi(a).
Level 2/Argument 1: A real or complex expression specifying the point a. Level 1/Argument 2: A non-negative integer, n.
The value of the polygamma function PSI(a, n).
Exact mode must be set (flag –105 clear), and numeric mode must not be set (flag –3 clear), if symbolic results are wanted. Complex mode must be set (flag –103 set) if a complex value is used for point a.
Psi Psi
Function
Calculates the digamma function at a point a. The digamma function is the derivative of the natural logarithm (ln) of the gamma function. The function can be represented as follows: ′
d Γ (z )
Ψ ( z ) = ----- ( ln Γ ( z )) = ------------
dz Γ (z)
A real or complex expression specifying the point a.
The digamma function at the specified point.
Exact mode must be set (flag –105 clear), and numeric mode must not be set (flag –3 clear), if symbolic results are wanted. For example, with these settings, Psi(3) evaluates to the symbolic value Psi(3). Complex mode must be set (flag –103 set) if a complex value is used for point a.
PSI
Function
Returns the Taylor polynomial at x = a for a specified polynomial.
Level 2/Argument 1: A polynomial, P. Level 1/Argument 2: A number, a.
A polynomial, Q such that Q(x – a)=P(x).
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Find the polynomial Q(x) such that Q(x-2)=x2+3x+2.
| Command | PTAYL(X^2+3*X+2, 2) |
|---|---|
| Result | X^2+7*X+12 |
Function
Returns the specified property for the specified element. It takes the element’s atomic number or symbol as a name (with certain restrictions) and the property number. It returns the property, usually a value or a string. It chooses to use or not use units according to the Units Usage flag (flag 61: SI units if clear, no units if set). If you use PTPROP as an algebraic function, you must use the symbol to define the element — you can’t use its atomic number. See Appendix B for a full list of available properties.
Units Usage (61)
| Level 2 | Level 1 | Level 1 | |
|---|---|---|---|
| `symb` | x | → | “string” or x or x_unit or `name` |
| y | x | → | “string” or x or x_unit or `name` |
| Example 1: The command sequence `Hg` 6 PTPROP returns "[Xe]4f14·5d10·6s2". | |||
| Example 2: The command sequence 79 8 PTPROP returns 1337.58 when flag 61 is set. | |||
MOLWT, PERINFO, PERTBL
Command
Purge Command: Purges the named variables or empty subdirectories from the current directory. PURGE executed in a program does not save its argument for recovery by LASTARG. To empty a named directory before purging it, use PGDIR. To help prepare a list of variables for purging, use VARS. Purging PICT replaces the current graphics object with a 0 × 0 graphics object. If a list of objects (with global names, backup objects, library objects, or PICT) for purging contains an invalid object, then the objects preceding the invalid object are purged, and the error Bad Argument Type occurs. To purge a library or backup object, tag the library number or backup name with the appropriate port number (:nport), which must be in the range from 0 to 3. For a backup object, the port
number can be replaced with the wildcard character &, in which case the calculator will search ports 0 through 2, and then main memory for the named backup object. A library object must be detached before it can be purged from the HOME directory. Neither a library object nor a backup object can be purged if it is currently “referenced” internally by stack pointers (such as an object on the stack, in a local variable, on the LAST stack, or on an internal return stack). This produces the error Object in Use. To avoid these restrictions, use NEWOB before purging. (See NEWOB.)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `global` | → | |
| { global1 ... globaln } | → | |
| PICT | → | |
| :nport :namebackup | → | |
| :nport :nlibrary | → |
CLEAR, CLVAR, NEWOB, PGDIR
Command
Saves the current status of the flags, and the current directory path. This allows the user to change the flags or the directory path, then restore them all with the command POP. PUSH is equivalent to saving the results of the commands RCLF and PATH, but it saves them in a stack from which the most recently saved values are recovered by POP, with no need to use named variables. The flags and the path are stored in the CASDIR directory, as a list of lists, in the variable ENVSTACK.
None.
Item 1: In Algebraic mode the command returns NOVAL.
POP, RCLF, STOF
Command
Put Element Command: Replaces the object at a specified position (second input) in a specified array or list (first input) with a specified object (third input). If the array or list is unnamed, returns the new array or list. For matrices, nposition counts in row order.
| Level 3/Argument 1 | Level 2/Argument 2 | Level 1/Argument 3 | Level 1/Item 1 | |
|---|---|---|---|---|
| [[ matrix ]]1 | nposition | zput | → | [[ matrix ]]2 |
| [[ matrix ]]1 | { nrow mcol } | zput | → | [[ matrix ]]2 |
| `namematrix` | nposition | zput | → | |
| `namematrix` | { nrow mcol } | zput | → | |
| [ vector ]1 | nposition | zput | → | [ vector ]2 |
| [ vector ]1 | { nposition } | zput | → | [ vector ]2 |
| `namevector` | nposition | zput | → | |
| `namevector` | { nposition } | zput | → | |
| { list }1 | nposition | objput | → | { list }2 |
| { list }1 | { nposition } | objput | → | { list }2 |
| `namelist` | nposition | objput | → | |
| `namelist` { nposition } objput → | ||||
Example 1: This command sequence: | ||||
| [[ 2 3 4 ][ 4 1 2 ]] { 1 3 } 96 PUT returns [[ 2 3 96 ][ 4 1 2 ]]. | ||||
Example 2: The command sequence: | ||||
| [[ 2 3 4 ][ 4 1 2 ]] 5 96 PUT returns [[ 2 3 4 ][ 4 96 2 ]]. | ||||
Example 3: The command sequence: | ||||
| { A B C D E } { 3 } `Z` PUT returns { A B Z D E }. | ||||
GET, GETI, PUTI
Command
Put and Increment Index Command: Replaces the object at a specified position (second input) in a specified array or list (first input) with a specified object (third input), returning a new array or list together with the next position in the array or list. For matrices, the position is incremented in row order. Unlike PUT, PUTI returns a named array or list. This enables a subsequent execution of PUTI at the next position of a named array or list.
Index Wrap Indicator (–64)
| L3/A1 | L2/A2 | L1/A3 | L2/I1 | L1/I2 | |
|---|---|---|---|---|---|
| [[ matrix ]]1 | nposition1 | zput | → | [[ matrix ]]2 | nposition2 |
| [[ matrix ]]1 | { nrow mcol }1 | zput | → | [[ matrix ]]2 | { nrow mcol }2 |
| `namematrix` | nposition1 | zput | → | `namematrix` | nposition2 |
| `namematrix` | { nrow mcol }1 | zput | → | `namematrix` | { nrow mcol }2 |
| [ vector ]1 | nposition1 | zput | → | [ vector ]2 | nposition2 |
| [ vector ]1 | { nposition1 } | zput | → | [ vector ]2 | { nposition2 } |
| `namevector` | nposition1 | zput | → | `namevector` | nposition2 |
| `namevector` | { nposition1 } | zput | → | `namevector` | { nposition2 } |
| { list }1 | nposition1 | objput | → | { list }2 | nposition2 |
| { list }1 | { nposition1 } | objput | → | { list }2 | { nposition2 } |
| `namelist` | nposition1 | objput | → | `namelist` | nposition2 |
| `namelist` | { nposition1 } | objput | → | `namelist` | { nposition2 } |
| L = Level; A = Argument; I = item | |||||
The following program uses PUTI and flag –64 to replace A, B, and C in the list with X. « { A B C } DO `X` PUTI UNTIL -64 FS? END »
GET, GETI, PUT
Command
Population Variance Command: Calculates the population variance of the coordinate values in each of the m columns in the current statistics matrix (ΣDAT). The population variance (equal to the square of the population standard deviation) is returned as a vector of m real numbers, or as a single real number if m = 1. The population variances are computed using this formula: n
1 2
-- ∑ ( x k – x ) nk = 1
where xk is the kth coordinate value in a column, x is the mean of the data in this column, and n is the number of data points.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | xpvariance | |
| → | [ xpvariance1, ...,xpvariancem ] |
MEAN, PCOV, PSDEV, SDEV, VAR
Command
Port-Variables Command: Returns a list of the backup objects (:nport:name) and the library objects (:nport:nlibrary) in the specified port. Also returns the available memory size (RAM). The port number, nport, must be in the range from 0 to 2.
If nport = 0, then memory is bytes of available main RAM; otherwise memory is bytes of available RAM in the specified port.
| Level 1/Argument 1 | Level 2/Item 1 | Level 1/Item 2 | |
|---|---|---|---|
| nport | → | { :nport :namebackup ... } | memory |
| nport | → | { :nport :nlibrary ... } | memory |
PVARS, VARS
Command
PICT View Command: Displays PICT with the specified coordinate at the upper left corner of the graphics display. PICT must fill the entire display on execution of PVIEW. Thus, if a position other than the upper left corner of PICT is specified, PICT must be large enough to fill a rectangle that extends 131 pixels to the right and 80 pixels down on the HP 50g and 49g+ (64 pixels down on the HP 48gII). If PVIEW is executed from a program with a coordinate argument (versus an empty list), the graphics display persists only until the keyboard is ready for input (for example, until the end of program execution). However, the FREEZE command freezes the display until a key is pressed. If PVIEW is executed with an empty list argument, PICT is centered in the graphics display with scrolling mode activated. In this case, the graphics display persists until −is pressed. PVIEW does not activate the graphics cursor or the Picture menu. To activate the graphics cursor and Picture menu, execute PICTURE.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| (x,y) | → | |
| { #n, #m } | → | |
| {} | → |
The program « { # 0d # 0d } PVIEW 7 FREEZE » displays PICT in the graphics display with coordinates { # 0d # 0d } in the upper left corner of the display, then freezes the full display until a key is pressed.
FREEZE, PICTURE, TEXT
Command
Power Curve Fit Command: Stores PWRFIT as the fifth parameter in the reserved variable ΣPAR, indicating that subsequent executions of LR are to use the power curve fitting model. LINFIT is the default specification in ΣPAR.
None
BESTFIT, EXPFIT, LINFIT, LOGFIT, LR
Command
Pixel to Complex Command: Converts the specified pixel coordinates to user-unit coordinates. The user-unit coordinates are derived from the (xmin, ymin) and (xmax, ymax) parameters in the reserved variable PPAR. The coordinates correspond to the geometrical center of the pixel.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| { #n #m } | → | (x,y) |
C→PX
Command
To Quotient Command: Returns a rational form of the argument. The rational result is a “best guess”, since there might be more than one rational expression consistent with the argument. →Q finds a quotient of integers that agrees with the argument to within the number of decimal places specified by the display format mode. →Q also acts on numbers that are part of algebraic expressions or equations.
Number Display Format (–45 to –50)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | `a/b` |
| (x,y) | → | `a/b + c/d*i` |
| `symb1` | → | `symb2` |
`Y+2.5` →Q returns `Y+5/2`
→Qπ, /, XQ
Command
To Quotient Times π Command: Returns a rational form of the argument, or a rational form of the argument with π, square roots, natural logs, and exponentials factored out, whichever yields the smaller denominator. The rational result is a “best guess”, since there might be more than one rational expression consistent with the argument. →Qπ finds a quotient of integers that agrees with the argument to the number of decimal places specified by the display format mode. →Qπ also acts on numbers that are part of algebraic expressions or equations. For a complex argument, the real or imaginary part (or both) can have π as a factor.
Number Display Format (–45 to –50)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | `a/b*π` |
| x | → | `a/b` |
| `symb1` | → | `symb2` |
| (x,y) | → | `a/b*π + c/d*π*i` |
| (x,y) | → | `a/b + c/d*i` |
In Fix mode to three decimal places, 6.2832 →Qπ returns `44/7`. In Standard mode, however, 6.2832 →Qπ returns `3927/625`.
→Q, /, XQ, π
Command
qr Factorization of a square Matrix Command: Returns the qr factorization of an n × n matrix. qr factors an n × n matrix A into two matrices:
| Level 1/Argument 1 | Level 2/Item 1 | Level 1/Item 2 | |
|---|---|---|---|
| [[ matrix ]]A | → | [[ matrix ]]Q | [[ matrix ]]R |
LQ, LSQ QR
Command
QR Factorization of a Matrix Command: Returns the QR factorization of an m × n matrix. QR factors an m × n matrix A into three matrices:
| Level 1/Argument 1 | Level 3/Item 1 | Level 2/Item 2 | Level 1/Item 3 | |
|---|---|---|---|---|
| [[ matrix ]]A | → | [[ matrix ]]Q | [[ matrix ]]R | [[ matrix ]]P |
LQ, LSQ
Command
Solve Quadratic Equation Command: This command is identical to the computer algebra command SOLVE, and is included for backward compatibility with the HP 48G series.
Principal Solution (–1)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| `symb1` | `global` | → | `symb2` |
COLCT, EXPAN, ISOL, SHOW, SOLVE
Function
Returns the quotient part of the Euclidean division of two polynomials.
Level 2/Argument 1: The numerator polynomial. Level 1/Argument 2: The denominator polynomial.
The quotient of the Euclidean division.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
3 2 2
Find the quotient of the division of x + 6 x + 11 x + 6 by x + 5 x + 6 .
Command: QUOT(X^3+6*X^2+11*X+6, X^2+5*X+6)
X+1
REMAINDER, DIV2, IQUOT
Function
Quote Argument Function: Returns its argument unevaluated. When an algebraic expression is evaluated, the arguments to a function in the expression are evaluated before the function. For example, when SIN(X) is evaluated, the name X is evaluated first, and the result is placed on the stack as the argument for SIN. This process creates a problem for functions that require symbolic arguments. For example, the integration function requires as one of its arguments a name specifying the variable of integration. If evaluating an integral expression caused the name to be evaluated, the result of evaluation would be left on the stack for the integral, rather than the name itself. To avoid this problem, the calculator automatically (and invisibly) quotes such arguments. When the quoted argument is evaluated, the unquoted argument is returned. If a user-defined function takes symbolic arguments, quote the arguments using QUOTE.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| obj | → | obj |
The following user-defined function ArcLen calculates the arc length of a function:
« → start end expr var
« start end expr var ˆ SQ 1 + ƒ var » » `OArcLen K To use this user-defined function in an algebraic expression, the symbolic arguments must be quoted: `ArcLen(0,π,QUOTE(SIN(X)),QUOTE(X))`
APPLY, | (Where)
Command
Expresses a quadratic form in matrix form.
Level 2/Argument 1: A quadratic form. Level 1/Argument 2: A vector containing the variables.
Level 2/Item 1: The quadratic form expressed in matrix form. Level 1/Item 2: The vector containing the variables.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Express the following quadratic form in matrix form:
2 2
x + xy + y
Command: QXA(X^2+X*Y+Y^2, [X,Y])
{[[1,1/2][1/2,1]],[X,Y]}
AXQ, GAUSS, SYLVESTER
Command
Radians Mode Command: Sets Radians angle mode. RAD sets flag –17 and clears flag –18, and displays the RAD annunciator. In Radians angle mode, real-number arguments that represent angles are interpreted as radians, and real-number results that represent angles are expressed in radians.
None
DEG, GRAD
Command
Random Number Command: Returns a pseudo-random number generated using a seed value, and updates the seed value. The calculator uses a linear congruential method and a seed value to generate a random number xrandom in the range 0 ≤ x < 1. Each succeeding execution of RAND returns a value computed from a seed value based upon the previous RAND value. (Use RDZ to change the seed.)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | xrandom |
COMB, PERM RDZ, !
Command
Matrix Rank Command: Returns the rank of a rectangular matrix.
Rank is computed by calculating the singular values of the matrix and counting the number of non-negligible values. If all computed singular values are zero, RANK returns zero. Otherwise RANK consults flag –54 as follows:
Singular Value (–54)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| [[ matrix ]] | → | Nrank |
LQ, LSQ, QR
Command
Random Matrix Command: Returns a matrix of specified dimensions that contains random integers in the range –9 through 9. The probability of a particular nonzero digit occurring is 0.05; the probability of 0 occurring is 0.1.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| {mn} | → | [[ random matrix ]]m×n |
| [[ matrix ]]m×n | → | [[ random matrix ]]m×n |
RAND, RDZ
Function
Prefix Divide Function: Prefix form of / (divide). RATIO is identical to / (divide), except that, in algebraic syntax, RATIO is a prefix function, while / is an infix function. For example, RATIO(A,2) is equivalent to A/2.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| z1 | z2 | → | z1/z2 |
| [ array ] | {[ matrix ]] | → | [[ array × matrix–1]] |
| [ array ] | z | → | [ array/z ] |
| z | `symb` | → | `z/symb` |
| `symb` | z | → | `symb/z` |
| `symb1` | `symb2` | → | `symb1/symb2` |
| #n1 | n2 | → | #n3 |
| n1 | #n2 | → | #n3 |
| #n1 | #n2 | → | #n3 |
| x_unit1 | y_unit2 | → | (x/y)_unit1/unit2 |
| x | y_unit | → | (x/y)_1/unit |
| x_unit | y | → | (x/y)_unit |
| `symb` | x_unit | → | `symb/x_unit` |
| x_unit | `symb` | → | `x_unit/symb` |
/
Command
Recall from EQ Command: Returns the unevaluated contents of the reserved variable EQ from the current directory. To recall the contents of EQ from a parent directory (when EQ doesn’t exist in the current directory) evaluate the name EQ.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | objEQ |
STEQ
Command
Multiply Row by Constant Command: Multiplies row n of a matrix (or element n of a vector) by a constant xfactor, and returns the modified matrix. RCI rounds the row number to the nearest integer, and treats vector arguments as column vectors.
| Level 3/Argument 1 | Level 2/Argument 2 | Level 1/Argument 3 | Level 1/Item 1 | |
|---|---|---|---|---|
| [[ matrix ]]1 | xfactor | nrow number | → | [[ matrix ]]3 |
| [ vector ]1 | xfactor | nelement number | → | [ vector ]2 |
RCIJ
Command
Add Multiplied Row Command: Multiplies row i of a matrix by a constant xfactor, adds this product to row j of the matrix, and returns the modified matrix; or multiplies element i of a vector
by a constant xfactor, adds this product to element j of the vector, and returns the modified vector. RCIJ rounds the row numbers to the nearest integer, and treats vector arguments as column vectors.
| Level 4/Argument 1 Level 3/Argument 2 Level 2/Argument 3 Level 1/Argument 4 | Level 1/Item 1 | ||||
|---|---|---|---|---|---|
| [[ matrix ]]1 | xfactor | nrow i | nrow j | → [[ matrix ]]2 | |
| [ vector ]1 | xfactor | nelement i | nelement j | → | [ vector ]2 |
RCI
Command Operation
Recall Command: Returns the unevaluated contents of a specified variable. RCL searches the entire current path, starting with the current directory. To search a different path, specify { path name }, where path is the new path to the variable name. The path subdirectory does not become the current subdirectory (unlike EVAL). To recall a library or backup object, tag the library number or backup name with the appropriate port number (nport), which must be an integer in the range 0 to 3. Recalling a backup object brings a copy of its contents to the stack, not the entire backup object. To search for a backup object, replace the port number with the wildcard character &, in which case the calculator will search (in order) ports 0 through 3, and the main memory for the named backup object. You can specify a port (that is, nport) in one of two ways:
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `obj` | → | obj |
| PICT | → | grob |
| :nport :nlibrary | → | obj |
| :nport :namebackup | → | obj |
| :nport :{ path } | → | obj |
STO
Command
Recall Alarm Command: Recalls a specified alarm. objaction is the alarm execution action. If an execution action was not specified, objaction defaults to an empty string. xrepeat is the repeat interval in clock ticks, where 1 clock tick equals 1/8192 second. If a repeat interval was not specified, the default is 0.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| nindex | → | { date time objaction xrepeat } |
DELALARM, FINDALARM, STOALARM
Command
Recall Flags Command: Returns a list of integers representing the states of the system and user flags, respectively. A bit with value 1 indicates that the corresponding flag is set; a bit with value 0 indicates that the corresponding flag is clear. The rightmost (least significant) bit of #nsystem and #nuser indicate the states of system flag –1 and user flag +1, respectively. Used with STOF, RCLF lets a program that alters the state of a flag or flags during program execution preserve the pre-program-execution flag status.
Binary Integer Wordsize (–5 through –10)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | { #nsystem #nuser #nsystem2 #nuser2 } |
STOF, PUSH, POP
Command
Recall Key Assignments Command: Returns the current user key assignments. This includes an S if the standard definitions are active (not suppressed) for those keys without user key assignments. The argument xkey is a real number of the form rc.p specifying the key by its row number r, its column number c, and its plane (shift) p. (For a definition of plane, see the entry for ASN.)
User-Mode Lock (–61) and User Mode (–62) affect the status of the user keyboard
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | { obj1, xkey 1, ... ,objn, xkey n } | |
| → | { S, obj1, xkey 1, ... objn, xkey n } |
ASN, DELKEYS, STOKEYS
Command
Recall Menu Number Command: Returns the menu number of the currently displayed menu. xmenu has the form mm.pp, where mm is the menu number and pp is the page of the menu.
Executing RCLMENU when the current menu is a user-defined menu (build by TMENU) returns 0.01 (in 2 Fix mode), indicating “Last menu”.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | xmenu |
If the third page of the PRG STACK menu is currently active, RCLMENU returns 73.03.
MENU, TMENU
Command
Returns the name or list of names stored in the current CAS variable. This is the same action as recalling the contents of the variable VX in the CASDIR directory.
None.
Level 1/Item 1: The name of the current CAS variable.
STOVX
Command
Recall Sigma Command: Returns the current statistical matrix (the contents of reserved variable ΣDAT) from the current directory. To recall ΣDAT from the parent directory (when ΣDAT doesn’t exist in the current directory), evaluate the name ΣDAT.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | obj |
CLΣ, STOΣ, Σ+, Σ–
Command
Recall Wordsize Command: Returns the current wordsize in bits (1 through 64).
Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | n |
BIN, DEC, HEX, OCT, STWS
Command
Redimension Array Command: Rearranges the elements of the argument according to specified dimensions.
If the list contains a single number nelements, the result is an n-element vector. If the list contains two numbers nrows and mcols, the result is an n × m matrix. Elements taken from the argument vector or matrix preserve the same row order in the resulting vector or matrix. If the result is dimensioned to contain fewer elements than the argument vector or matrix, excess elements from the argument vector or matrix at the end of the row order are discarded. If the result is dimensioned to contain more elements than the argument vector or matrix, the additional elements in the result at the end of the row order are filled with zeros. If the argument vector or matrix is specified by global, the result replaces the argument as the contents of the variable.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |||||
|---|---|---|---|---|---|---|---|
| [ vector ]1 | { nelements } | → | [ vector ]2 | ||||
| [ vector ] | { nrows, mcols } | → | [[ matrix ]] | ||||
| [[ matrix ]] | { nelements } | → | [ vector ] | ||||
| [[ matrix ]]1 | { nrows, mcols } | → | [[ matrix ]]2 | ||||
| `global` | { nelements } | → | |||||
| `global` { nrows, mcols } → | |||||||
| |||||||
TRN
Command
Randomize Command: Uses a real number xseed as a seed for the RAND command. If the argument is 0, a random value based on the system clock is used as the seed.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| xseed | → |
COMB, PERM, RAND, !
Function
Real Part Function: Returns the real part of the argument. If the argument is a vector or matrix, RE returns a real array, the elements of which are equal to the real parts of the corresponding elements of the argument array.
Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | x |
| x_unit | → | x |
| (x,y) | → | x |
| [ R-array ] | → | [ R-array ] |
| [ C-array ] | → | [ R-array ] |
| `symb` | → | `RE(symb`) |
C→R, IM, R→C
Command
Receive Renamed Object Command: Prepares the calculator to receive a file from another Kermit server device, and to store the file in a specified variable. RECN is identical to RECV except that the name under which the received data is stored is specified.
I/O Device flag (–33), I/O Data Format (–35), RECV Overwrite (–36), I/O Messages (–39), I/O Device for Wire (–78)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `name` | → | |
| “name” | → |
BAUD, CKSM, CLOSEIO, FINISH, KERRM, KGET, PARITY, RECV, SEND, SERVER, TRANSIO
Command
Rectangular Mode Command: Sets Rectangular coordinate mode. RECT clears flags –15 and –16. In Rectangular mode, vectors are displayed as rectangular components. Therefore, a 3D vector would appear as [X Y Z].
None
CYLIN, SPHERE
Command
Receive Object Command: Instructs the calculator to look for a named file from another Kermit server device. The received file is stored in a variable named by the sender. Since the calculator does not normally look for incoming Kermit files, you must use RECV to tell it to do so.
I/O Device flag (–33), I/O Data Format (–35), RECV Overwrite (–36), I/O Messages (–39), I/O Device for Wire (–78)
None
BAUD, CKSM, FINISH, KGET, PARITY, RECN, SEND, SERVER, TRANSIO
Command
Reduces a matrix to echelon form. This is a subdiagonal reduction (Gauss, not Gauss-Jordan).
A real or complex matrix.
The equivalent matrix in echelon form.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Complex mode must be set (flag –103 set) if the input is complex.
rref, RREFMOD
Function
Returns the remainder of the Euclidean division of two polynomials.
Level 2/Argument 1: The numerator polynomial. Level 1/Argument 2: The denominator polynomial.
The remainder resulting from the Euclidean division.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). Complex mode must be set (flag –103 set) if either input is complex.
3 2 2
Find the remainder of the division of x + 6 x + 11 x + 6 by x + 5 x + 6 .
| Command | REMAINDER(X^3+6*X^2+11*X+6, X^2+5*X+6) |
|---|---|
| Result | 0 |
QUOT
Command
Rename Object Command: Renames an object to the name that you specify.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| new `name` | old `name` | → |
COPY
Function
Given a polynomial expression and a variable, reorders the variables in the expression in the order of powers set on the CAS Modes screen, that is, either in increasing or decreasing order.
Level 2/Argument 1: The polynomial expression. Level 1/Argument 2: The variable with respect to which the reordering is performed.
The reordered expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). Complex mode must be set (flag –103 set) if the polynomial contains complex terms. The polynomial terms order flag (flag –114) must be set for increasing power order, or clear (the default) for decreasing power order.
Reorder the polynomial x2 + 2y2 +2x +3y in order of powers of y. Assume that increasing power mode has been set in the CAS modes.
| Command | REORDER(X^2+2*Y^2+2*X+6+3*Y, Y) |
|---|---|
| Result | 2*Y^2+3*Y+(X^2+2*X) |
Command
REPEAT Command: Starts loop clause in WHILE … REPEAT … END indefinite loop structure. See the WHILE entry for more information.
None
END, WHILE
Command
Replace Command: Replaces a portion of the target object (first input) with a specified object (third input), beginning at a specified position (second input). For arrays, nposition counts in row order. For matrices, nposition specifies the new location of the upper left-hand element of the replacement matrix. For graphics objects, the upper left corner of grob1 is positioned at the user-unit or pixel coordinates (x,y) or { #n #m }. From there, it overwrites a rectangular portion of grobtarget or PICT. If grob1 extends past grobtarget or PICT in either direction, it is truncated in that direction. If the specified coordinate is not on the target graphics object, the target graphics object does not change.
| Level 3/Argument 1 | Level 2/Argument 2 | Level 1/Argument 3 | Level 1/Item 1 | |||||
|---|---|---|---|---|---|---|---|---|
| [[ matrix ]]1 | nposition | [[ matrix ]]2 | → | [[ matrix ]]3 | ||||
| [[ matrix ]]1 | { nrow, ncolumn } | [[ matrix ]]2 | → | [[ matrix ]]3 | ||||
| [ vector ]1 | nposition | [ vector ]2 | → | [ vector ]3 | ||||
| { listtarget } | nposition | { list1 } | → | { listresult } | ||||
| “stringtarget” | nposition | “string1” | → | “stringresult” | ||||
| grobtarget | (#n, #m) | grob1 | → | grobresult | ||||
| grobtarget | (x,y) | grob1 | → | grobresult | ||||
| PICT | (#n, #m) | grob1 | → | |||||
| PICT | (x,y) | grob1 | → | |||||
| Example 1: [[ 1 1 1 1 ][ 1 1 1 1 ][ 1 1 1 1 ]] 6 [[ 2 2 ][ 2 2 ]] | ||||||||
| REPL returns [[ 1 1 1 1 ][ 1 2 2 1 ][ 1 2 2 1 ]]. | ||||||||
| ||||||||
| PICT with a 5 x 5 graphics object, each of whose pixels is on (dark), and whose upper left corner is positioned at (0,0) in PICT. | ||||||||
CHR, GOR, GXOR, NUM, POS, SIZE, SUB
Command
Resolution Command: Specifies the resolution of mathematical and statistical plots, where the resolution is the interval between values of the independent variable used to generate the plot. A real number ninterval specifies the interval in user units. A binary integer #ninterval specifies the interval in pixels. The resolution is stored as the fourth item in PPAR, with default value 0. The interpretation of the default value is summarized in the following table.
| Plot Type | Default Interval |
|---|---|
| BAR | 10 pixels (bar width = 10 pixel columns) |
| DIFFEQ | unlimited: step size is not constrained |
| FUNCTION | 2 pixels (plots a point in every other column of pixels) |
| CONIC | 2 pixels (plots a point in every other column of pixels) |
| TRUTH | 2 pixels (plots a point in every other column of pixels) |
| GRIDMAP | RES does not apply |
| HISTOGRAM | 10 pixels (bin width = 10 pixel columns) |
| PARAMETRIC | [independent variable range in user units]/130 |
| PARSURFACE | RES does not apply |
| Plot Type | Default Interval |
| PCONTOUR | RES does not apply |
| POLAR | 2°, 2 grads, or π/90 radians |
| SCATTER | RES does not apply |
| SLOPEFIELD | RES does not apply |
| WIREFRAME | RES does not apply |
| YSLICE | 2 pixels (plots a point in every other column of pixels) |
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| ninterval | → | |
| #ninterval | → |
BAR, CONIC, DIFFEQ, FUNCTION, GRIDMAP, HISTOGRAM, PARAMETRIC, PARSURFACE, PCONTOUR, POLAR, SCATTER, SLOPEFIELD, TRUTH, WIREFRAME, YSLICE
Command
Restore HOME Command: Replaces the current HOME directory with the specified backup copy (:nport:namebackup) previously created by ARCHIVE. The specified port number must be in the range 0 to 3. To restore a HOME directory that was saved on a remote system using :IO:name ARCHIVE, put the backup object itself on the stack, execute RESTORE and then execute a warm start.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| :nport :namebackup | → | |
| backup | → |
To restore a HOME directory that was saved as the file AUG1 on a remote system, execute `AUG1` SEND on the remote system, then execute the following on the local calculator: RECV `AUG1` RCL RESTORE
ARCHIVE
Function
Returns the resultant of two polynomials of the current variable. That is, it returns the determinant of the Sylvester matrix of the two polynomials.
Level 2/Argument 1: The first polynomial. Level 1/Argument 2: The second polynomial.
The determinant of the two matrices that correspond to the polynomials.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Complex mode must be set (flag –103 set) if either input contains complex terms.
Obtain the resultant of the two polynomials x3-px+q and 3x2-p.
| Command | RESULTANT(X^3-P*X+Q, 3*X^2-P) |
|---|---|
| Result | 27*Q^2-4*P^3 |
Command
Reverse List Command: Reverses the order of the elements in a list.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| { objn ... obj1 } | → | { obj1 ... objn } |
SORT
Command
Displays a menu or list of CAS operations that rewrite expressions.
If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered list. If the flag is set, displays the operations as a menu of function keys.
ALGB, ARIT, CONSTANTS, DIFF, EXP&LN, INTEGER, MAIN, MATHS, MATR, MODULAR, POLYNOMIAL, TESTS, TRIGO
Function
Performs symbolic integration on a function using the Risch algorithm. RISCH is similar to the INTVX command, except that it allows you to specify the variable of integration.
Level 2/Argument 1: The function to integrate. Level 1/Argument 2: The variable of integration.
The antiderivative of the function with respect to the variable.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Find the antiderivative of the following function, with respect to y: 2 y + 3y + 2
| Command | RISCH(Y^2-3*Y+2,Y) |
|---|---|
| Result | 1/3*Y^3-3*(1/2*Y^2)+2*Y |
IBP, INT, INTVX
Command
Solve for Initial Values (Runge–Kutta–Fehlberg) Command: Computes the solution to an initial value problem for a differential equation, using the Runge-Kutta-Fehlberg (4,5) method. RKF solves y`(t) = f(t,y), where y(t0) = y0. The arguments and results are as follows:
| L3/A1 | L2/A2 | L1/A3 | L2/I1 | L1/I2 | |
|---|---|---|---|---|---|
| { list } | xtol | xT final | → | { list } | xtol |
| { list } | { xtol xhstep } | xT final | → | { list } | xtol |
| L = Level; A = Argument; I = item | |||||
Solve the following initial value problem for y(8), given that y(0) = 0: 1
y′ = − 2 y 2 = f (t , y )
1+ t 2 1. Store the independent variable’s initial value, 0, in T. 2. Store the dependent variable’s initial value, 0, in Y. 1
3. Store the expression, − 2 y 2 , in F.
1+ t 2
4. Enter a list containing these three items: { T Y F }. 5. Enter the tolerance. Use estimated decimal place accuracy as a guideline for choosing a tolerance: 0.00001. 6. Enter the final value for the independent variable: 8. The stack should look like this: { T Y F } .00001 8 7. Press RKF. The variable T now contains 8, and Y now contains the value .123077277659. The actual answer is .123076923077, so the calculated answer has an error of approximately .00000035, well within the specified tolerance.
RKFERR, RKFSTEP, RRK, RRKSTEP, RSBERR
Command
Error Estimate for Runge–Kutta–Fehlberg Method Command: Returns the absolute error estimate for a given step h when solving an initial value problem for a differential equation. The arguments and results are as follows:
| L2/A1 | L1/A2 | L4/I1 | L3/I2 | L2/I3 | L1/I4 | |
|---|---|---|---|---|---|---|
| { list } | h | → | { list } | h | ydelta | error |
| L = Level; A = Argument; I = item | ||||||
RKF, RKFSTEP, RRK, RRKSTEP, RSBERR
Command
Next Solution Step for RKF Command: Computes the next solution step (hnext) to an initial value problem for a differential equation. The arguments and results are as follows:
| L3/A1 | L2/An | L1/An+1 | L3/I1 | L2/I2 | L1/I3 | |
|---|---|---|---|---|---|---|
| { list } | xtol | h | → | { list } | xtol | hnext |
| L = Level; A = Argument; I = item | ||||||
RKF, RKFERR, RRK, RRKSTEP, RSBERR
Command
Rotate Left Command: Rotates a binary integer one bit to the left. The leftmost bit of #n1 becomes the rightmost bit of #n2.
Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| #n1 | → | #n2 |
RLB, RR, RRB
Command
Rotate Left Byte Command: Rotates a binary integer one byte to the left. The leftmost byte of #n1 becomes the rightmost byte of #n2. RLB is equivalent to executing RL eight times.
Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| #n1 | → | #n2 |
RL, RR, RRB
Function
Round Function: Rounds an object to a specified number of decimal places or significant digits, or to fit the current display format. nround (or symbround if flag –3 is set) controls how the level 2 argument is rounded, as follows:
| nround or symbround | Effect on Level 2 Argument |
|---|---|
| 0 through 11 | Rounded to n decimal places. |
| –1 through –11 | Rounded to n significant digits. |
| 12 | Rounded to the current display format. |
For complex numbers and arrays, each real number element is rounded. For unit objects, the numerical part of the object is rounded.
Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| z1 | nround | → | z2 |
| z | `symbround` | → | `RND(symbround)` |
| `symb` | nround | → | `RND(symb,nround)` |
| `symb1` | `symbround` | → | `RND(`symb1, symbround)` |
| [ array1 ] | nround | → | [ array2 ] |
| x_unit | nround | → | y_unit |
| x_unit | `symbround` → | `RND(x_unit, symbround)` | |
| Example 1: (4.5792,8.1275) 2 RND returns (4.58,8.13). | |||
| Example 2: [ 2.34907 3.96351 2.73453 ] -2 RND returns [ 2.3 4 2.7 ]. | |||
TRNC
Command
Row Norm Command: Returns the row norm (infinity norm) of its argument array. The row norm is the maximum (over all rows) of the sums of the absolute values of all elements in each row. For a vector, the row norm is the largest absolute value of any of its elements.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| [ array ] | → | xrow norm |
CNRM, CROSS, DET, DOT
RPL command
Roll Objects Command: Moves the contents of a specified level to level 1, and rolls upwards the portion of the stack beneath the specified level. In RPN mode, 3 ROLL is equivalent to ROT.
| Ln+1... L2 | L1 | Ln ... | L2 | L1 | |
|---|---|---|---|---|---|
| objn ... obj1 | n | → | objn–1 ... | obj1 | objn |
| L = Level | |||||
OVER, PICK, ROLLD, ROT, SWAP
RPL command
Roll Down Command: Moves the contents of level 2 to a specified level, n, and rolls downward the portion of the stack beneath the specified level.
| Ln+1... L2 | L1 | Ln | Ln–1 ... | L1 | |
|---|---|---|---|---|---|
| objn ... obj2 | n (obj1) | → | obj1 | objn ... | obj2 |
| L = Level | |||||
OVER, PICK, ROLL, ROT, SWAP
Command
This command remains from earlier HP graphing calculators and should not be used. It was used to transfer the ROM from one HP 49G to another.
Command
Root-Finder Command: Returns a real number xroot that is a value of the specified variable global for which the specified program or algebraic object most nearly evaluates to zero or a local extremum. ROOT is the programmable form of the HP Solve application. guess is an initial estimate of the solution. ROOT produces an error if it cannot find a solution, returning the message Bad Guess(es) if one or more of the guesses lie outside the domain of the equation, or returns the message Constant? if the equation returns the same value at every sample point. ROOT does not return interpretive messages when a root is found.
| Level 3/Argument 1 | Level 2/Argument 2 | Level 1/Argument 3 | Level 1/Item 1 | |
|---|---|---|---|---|
| «program» | `global` | guess | → | xroot |
| «program» | `global` | { guesses } | → | xroot |
| `symb` | `global` | guess | → | xroot |
| `symb` | `global` | { guesses } | → | xroot |
RPL Command
Rotate Objects Command: Rotates the first three objects on the stack, moving the object on level 3 to level 1. In RPN mode, ROT is equivalent to 3 ROLL.
| L3 | L2 | L1 | L3 | L2 | L1 | |
|---|---|---|---|---|---|---|
| obj3 | obj2 | obj1 | → | obj2 | obj1 | obj3 |
| L = Level | ||||||
OVER, PICK, ROLL, ROLLD, SWAP, UNROT
Command
Delete Row Command: Deletes row n of a matrix (or element n of a vector), and returns the modified matrix (or vector) and the deleted row (or element). nrow or nelement is rounded to the nearest integer.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 2/Item 1 | Level 1/Item 2 | |
|---|---|---|---|---|
| [[ matrix ]]1 | nrow | → | [[ matrix ]]2 | [ vector ]row |
| [ vector ]1 | nelement | → | [ vector ]2 | elementn |
COL–, COL+, ROW+, RSWP
Command
Insert Row Command: Inserts an array into a matrix (or one or more numbers into a vector) at the position indicated by nindex, and returns the modified matrix (or vector). The inserted array must have the same number of columns as the target array. nindex is rounded to the nearest integer. The original array is redimensioned to include the new columns or elements, and the elements at and below the insertion point are shifted down.
| Level 3/Argument 1 | Level 2/Argument 2 | Level 1/Argument 3 | Level 1/Item 1 | |
|---|---|---|---|---|
| [[ matrix ]]1 | [[ matrix ]]2 | nindex | → | [[ matrix ]]3 |
| [[ matrix ]]1 | [ vector ]row | nindex | → | [[ matrix ]]2 |
| [ vector ]1 | nelement | nindex | → | [ vector ]2 |
COL–, COL+, ROW–, RSWP
Command
Rows to Matrix Command: Transforms a series of row vectors and a row count into a matrix containing those rows, or transforms a sequence of numbers and an element count into a vector with those numbers as elements.
| Ln+1/A1 7 | L2/An | L1/An+1 | Level 1/Item 1 | |
|---|---|---|---|---|
| [ vector ]row 1 + | [ vector ]row n | nrow count | → | [[ matrix ]] |
| element1 + | elementn | nelement count | → | [ vector ]column |
| L = Level; A = Argument; I = item | ||||
→COL, COL→, →ROW
Command
Matrix to Rows Command: Transforms a matrix into a series of row vectors, returning the vectors and row count, or transforms a vector into its elements, returning the elements and element count.
| L1/Argument1 | Ln+1/I1 7 L2/In | L1/In+1 | |
|---|---|---|---|
| [[ matrix ]] | → | [ vector ]row n … [ vector ]row n | nrowcount |
| [ vector ] | → | element1 … elementn | nelementcount |
| L =Level; A = Argument; I = Item | |||
→COL, COL→, ROW→
Command
User RPL program function. This function allows for the entry and execution of User RPL programs while in algebraic mode. While RPL programs can be written in algebraic mode without the use of this function, some RPL constructs, such as FOR…NEXT loops, will produce an error message if not preceded by the RPL> function. As an algebraic function, it will be placed on the command line with a pair of parentheses attached, which must be removed before its use. For example, to enter the user RPL program of « 1 5 + » in algebraic mode, choose the RPL> function from the catalog and press `. Remove the parentheses by pressing ™ƒƒ. Then enter the program by pressing …å1#5#+`. The program object will now be on the first command line. It can be evaluated by pressing N!î`.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | obj |
Command
Rotate Right Command: Rotates a binary integer one bit to the right. The rightmost bit of #n1 becomes the leftmost bit of #n2.
Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| #n1 | → | #n2 |
RL, RLB, RRB
Command
Rotate Right Byte Command: Rotates a binary integer one byte to the right. The rightmost byte of #n1 becomes the leftmost byte of #n2. RRB is equivalent to doing RR eight times.
Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| #n1 | → | #n2 |
RL, RLB, RR
Command
Reduces a matrix to row-reduced echelon form, and provides a list of pivot points.
A matrix.
Level 2/Item 1: The pivot points. Level 1/Item 2: An equivalent matrix in row reduced echelon form.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear) If flag –126 is clear (the default), row reduction is done with the last column. If the flag is set, row reduction is done without reducing the last column, but the last column will be modified by the reduction of the rest of the matrix.
Reduce to row-reduced echelon form, and find the pivot points, for the matrix: 2 1 3 4
| Command | rref([[2,1][3,4]]) |
|---|---|
| Result | {Pivots: {5,1.,2,1.},[[10,0][0,5]]} |
RREFMOD RREF
Command
Reduces a matrix to row-reduced echelon form. The reduction is carried out completely, so a square matrix is reduced to an identity matrix. Step-by-step mode can be used to show how the reduction proceeds.
A matrix.
An equivalent matrix in row reduced echelon form.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Step-by-step mode can be set (flag –100 set).
Solve the system of linear equations: 3x + 4y = 5 5x + 6y = 7 by reducing the augmented matrix that represents this system.
| Command | RREF([[3, 4, 5] [ 5, 6, 7]]) |
|---|---|
| Result | [[1, 0, -1] [0, 1, 2]] |
This reduced matrix represents the system: 1x + 0y = –1 0x + 1y = 2 so that the solution is x = –1, y = 2 .
rref, RREFMOD
Command
Performs modular row-reduction to echelon form on a matrix, modulo the current modulus.
A matrix.
The modular row-reduced matrix. The modulo value is set using the Modes CAS input form.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). If flag –126 is clear (the default), row reduction is done with the last column. If the flag is set, row reduction is done without reducing the last column, but the last column will be modified by the reduction of the rest of the matrix.
Reduce to row-reduced echelon form, modulo 3, the matrix: 2 1 3 4
| Command | rref[[2,1][3,4]] |
|---|---|
| Result | [[-1,0][0,1]] |
rref
Command
Solve for Initial Values (Rosenbrock, Runge–Kutta) Command: Computes the solution to an initial value problem for a differential equation with known partial derivatives. RRK solves y`(t) = f(t,y), where y(t0) = y0. The arguments and results are as follows:
| L3/A1 | L2/A2 | L1/A3 | L2/I1 | L1/I2 | |
|---|---|---|---|---|---|
| { list } | xtol | xT final | → | { list } | xtol |
| { list } | { xtol xhstep } | xT final | { list } | xtol | |
| L = Level; A = Argument; I = item | |||||
Solve the following initial value problem for y(8), given that y(0) = 0: 1
y′ = − 2 y 2 = f (t , y )
1+ t 2
The derivative of the function with respect to y (∂f/∂y) is –4y, and the derivative of the function − 2t
with respect to t (∂f/∂t) is .
(1 + t 2 ) 2 1. Store the independent variable’s initial value, 0, in T. 2. Store the dependent variable’s initial value, 0, in Y. 1
3. Store the expression, − 2 y 2 , in F.
1+ t 2
4. Store ∂f/∂y, –4y, in FY. − 2t
5. Store ∂f/∂t, , in FT.
(1 + t 2 ) 2 6. Enter these five items in a list: { T Y F FY FT }. 7. Enter the tolerance. Use estimated decimal place accuracy as a guideline for choosing a tolerance: 0.00001. 8. Enter the final value for the independent variable: 8. The stack should look like this: { T Y F FY FT } .00001 8 9. Press RRK. The variable T now contains 8, and Y now contains the value .123077277659. The actual answer is .123076923077, so the calculated answer has an error of approximately .00000035, well within the specified tolerance.
RKF, RKFERR, RKFSTEP, RRKSTEP, RSBERR
Command
Next Solution Step and Method (RKF or RRK) Command: Computes the next solution step (hnext) to an initial value problem for a differential equation, and displays the method used to arrive at that result. The arguments and results are as follows:
RRKSTEP will use the Euler method to compute the next solution step and will consider the error tolerance satisfied. The Rosenbrock method will fail if the current independent variable is zero and the stepsize ≤ 2.5 × 10-499 or if the variable is nonzero and the stepsize is 2.5 × 10-11 times its magnitude. The Runge–Kutta–Fehlberg method will fail if the current independent variable is zero and the stepsize ≤ 1.3 × 10-498 or if the variable is nonzero and the stepsize is 1.3 × 10-10 times its magnitude.
L4/A1 L3/A2 L2/A3 L1/A4 L4/I1 L3/I2 L2/I3 L1/I4
{ list } xtol h last → { list } xtol hnext current
L = Level; A = Argument; I = item
RKF, RKFERR, RKFSTEP, RRK, RSBERR
Command
Error Estimate for Rosenbrock Method Command: Returns an error estimate for a given step h when solving an initial values problem for a differential equation. The arguments and results are as follows:
| L2/A1 | L1/A2 | L4/I1 | L3/I2 | L2/I3 | L1/I4 | |
|---|---|---|---|---|---|---|
| { list } | h | → | { list } | h | ydelta | error |
| L = Level; A = Argument; I = item | ||||||
RKF, RKFERR, RKFSTEP, RRK, RRKSTEP
Command
Residual Command: Computes the residual B – AZ of the arrays B, A, and Z. A, B, and Z are restricted as follows:
| Level 3/Argument 1 | Level 2/Argument 2 | Level 1/Argument 3 | Level 1/Item 1 | |
|---|---|---|---|---|
| [ vector ]B | [[ matrix ]]A | [ vector ]Z | → | [ vector ]B–AZ |
| [[ matrix ]]B | [[ matrix ]]A | [[ matrix ]]Z | → | [[ matrix ]]B–AZ |
DET, IDN
Command
Row Swap Command: Swaps rows i and j of a matrix and returns the modified matrix, or swaps elements i and j of a vector and returns the modified vector. Row numbers are rounded to the nearest integer. Vector arguments are treated as column vectors.
| Level 3/Argument 1 | Level 2/Argument 2 | Level 1/Argument 3 | Level 1/Item 1 | |
|---|---|---|---|---|
| [[ matrix ]]1 | nrow i | nrow j | → | [[ matrix ]]2 |
| [ vector ]1 | nelement i | nelement j | → | [ vector ]2 |
CSWP, ROW+, ROW–
Command
Displays a list of names of individuals involved with the HP 49G calculator project.
None
Command
Real to Binary Command: Converts a positive real to its binary integer equivalent. For any value of n ≤ 0, the result is # 0. For any value of n ≥ 1.84467440738E19 (base 10), the result is # FFFFFFFFFFFFFFFF (base 16).
Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| n | → | #n |
B→R
Command
Real to Complex Command: Combines two real numbers or real arrays into a single complex number or complex array. The first input represents the real element(s) of the complex result. The second input represents the imaginary element(s) of the complex result. Array arguments must have the same dimensions.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| x | y | → | (x,y) |
| [ R-array1 ] | [ R-array2 ] | → | [ C-array ] |
C→R, IM, RE
Function
Radians to Degrees Function: Converts a real number expressed in radians to its equivalent in degrees. This function operates independently of the angle mode.
Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | (180/π)x |
| `symb` | → | `R→D(symb)` |
D→R
Function
Converts a real number to an integer.
Numeric mode must not be set (flag –3 clear).
Level 1/Argument 1: An integral real number or an expression that evaluates to an integral real.
Level 1/Item 1: The real value converted to an integer.
I→R
Command
Same Object Command: Compares two objects, and returns a true result (1) if they are identical, and a false result (0) if they are not. SAME is identical in effect to == for all object types except algebraics, names, and some units. (For algebraics and names, == returns an expression that can be evaluated to produce a test result based on numerical values.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| obj1 | obj2 | → | 0/1 |
| Example 1: { A B } (4,5) SAME returns 0. | |||
| Example 2: { A B } { B A } SAME returns 0. | |||
| Example 3: "CATS" "CATS" SAME returns 1. | |||
TYPE, ==
Command
Serial Break Command: Interrupts serial transmission or reception. SBRK is typically used when a problem occurs in a serial data transmission.
I/O Device (–33), I/O Device for Wire (–78)
None
BUFLEN, SRECV, STIME, XMIT
Command
Scale Plot Command: Adjusts the first two parameters in PPAR, (xmin, ymin) and (xmax, ymax), so that xscale and yscale are the new plot horizontal and vertical scales, and the center point doesn’t change. The scale in either direction is the number of user units per tick mark. The default scale in both directions is 1 user-unit per tick mark.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| xscale | yscale | → |
AUTO, CENTR, SCALEH, SCALEW
Command
Multiply Height Command: Multiplies the vertical plot scale by xfactor. Executing SCALEH changes the y-axis display range — the ymin and ymax components of the first two complex numbers in the reserved variable PPAR. The plot origin (the user-unit coordinate of the center pixel) is not changed.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| xfactor | → |
AUTO, SCALEW, YRNG
Command
Multiply Width Command: Multiplies the horizontal plot scale by xfactor.
Executing SCALEW changes the x-axis display range—the xmin and xmax components of the first two complex numbers in the reserved variable PPAR. The plot origin (the user-unit coordinate of the center pixel) is not changed.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| xfactor | → |
AUTO, SCALEH, XRNG
Command
Draw Scatter Plot Command: Draws a scatterplot of (x, y) data points from the specified columns of the current statistics matrix (reserved variable ΣDAT ). The data columns plotted are specified by XCOL and YCOL, and are stored as the first two parameters in the reserved variable ΣPAR. If no data columns are specified, columns 1 (independent) and 2 (dependent) are selected by default. The y-axis is autoscaled and the plot type is set to SCATTER. When SCATRPLOT is executed from a program, the resulting display does not persist unless PICTURE or PVIEW is subsequently executed.
None
The following program plots a scatter plot of the data in columns 3 and 4 of ΣDAT, draws a best fit line, and displays the plot: « 3 XCOL 4 YCOL SCATRPLOT BESTFIT ΣLINE STEQ FUNCTION DRAW { # 0d # 0d } PVIEW 7 FREEZE »
BARPLOT, PICTURE, HISTPLOT, PVIEW, SCLΣ, XCOL, YCOL
Command
Scatter Plot Type Command: Sets the plot type to SCATTER. When the plot type is SCATTER, the DRAW command plots points by obtaining x and y coordinates from two columns of the current statistics matrix (reserved variable ΣDAT). The columns are specified by the first and second parameters in the reserved variable ΣPAR (using the XCOL and YCOL commands). The plotting parameters are specified in the reserved variable PPAR, which has this form: { (xmin, ymin), (xmax, ymax), indep, res, axes, ptype, depend } For plot type SCATTER, the elements of PPAR are used as follows:
None
BAR, CONIC, DIFFEQ, FUNCTION, GRIDMAP, HISTOGRAM, PARAMETRIC, PARSURFACE, PCONTOUR, POLAR, SLOPEFIELD, TRUTH, WIREFRAME, YSLICE
Command
Schur Decomposition of a Square Matrix Command: Returns the Schur decomposition of a square matrix. SCHUR decomposes A into two matrices Q and T:
| Level 1/Argument 1 | Level 2/Item 1 | Level 1/Item 2 | |
|---|---|---|---|
| [[ matrix ]]A | → | [[ matrix ]]Q | [[ matrix ]]T |
LQ, LU, QR, SVD, SVL, TRN
Command
Scientific Mode Command: Sets the number display format to scientific mode, which displays one digit to the left of the fraction mark and n significant digits to the right. Scientific mode is equivalent to scientific notation using n + 1 significant digits, where 0 ≤ n ≤ 11. (Values for n outside this range are rounded to the nearest integer.) In scientific mode, numbers are displayed and printed like this: (sign) mantissa E (sign) exponent where the mantissa has the form n.(n … ) and has zero to 11 decimal places, and the exponent has one to three digits.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| n | → |
The number 103.6 in Scientific mode to four decimal places appears as 1.0360E2.
ENG, FIX, STD
Command
Scale Sigma Command: Adjusts (xmin, y min) and (xmax, ymax) in PPAR so that a subsequent scatter plot exactly fills PICT. When the plot type is SCATTER, the command AUTO incorporates the functions of SCLΣ. In addition, the command SCATRPLOT automatically executes AUTO to achieve the same result. SCLΣ is included for compatibility with the HP 28.
None
AUTO, SCATRPLOT
Command
Store Conjugate Command: Conjugates the contents of a named object. The named object must be a number, an array, or an algebraic object. For information on conjugation, see CONJ.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `name` | → |
CONJ, SINV, SNEG
Command
Displays any object. This is the programmable equivalent of pressing I%VIEW% and is the best way to view any object larger than the screen, such as complicated algebraic expressions.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| Grob | → |
Command
Standard Deviation Command: Calculates the sample standard deviation of each of the m columns of coordinate values in the current statistics matrix (reserved variable ΣDAT). SDEV returns a vector of m real numbers, or a single real number if m = 1. The standard deviation (the square root of the variances) is computed using this formula:
1 n 2
----------- ∑ ( x i – x ) n – 1i = 1
where xi is the ith coordinate value in a column, x is the mean of the data in this column, and n is the number of data points.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | xsdev | |
| → | [ xsdev 1 xsdev 2 ... xsdev m ] |
MAXΣ, MEAN, MINΣ, PSDEV, PVAR, TOT, VAR
Command
Send Object Command: Sends a copy of the named objects to a Kermit device.
Data is always sent from a local Kermit, but can be sent either to another local Kermit (which must execute RECV or RECN) or to a server Kermit. To rename an object when sending it, include the old and new names in an embedded list.
I/O Device flag (–33), I/O Data Format (–35), I/O Messages (–39), I/O Device for Wire (–78) If flag –35 is clear (ASCII transfer), the translation setting also has an effect.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `name` | → | |
| { name1 ... namen } | → | |
| {{ nameold namenew } name ... } | → | |
| Example 1: | Executing {{ AAA BBB }} SEND sends the variable named AAA but changes its name | |
| to BBB. | ||
Example 2: Executing {{ AAA BBB } CCC } SEND sends AAA as BBB and sends CCC under its | ||
| own name. (If the new name is not legal on the calculator, just enter it as a string.) | ||
BAUD, CLOSEIO, CKSM, FINISH, KERRM, KGET, PARITY, RECN, RECV, SERVER, TRANSIO
Command
Sequential Calculation Command: Returns a list of results generated by repeatedly executing objexec using index over the range xstart to xend, in increments of xincr. objexec is a program or algebraic object that is a function of index. index must be a global or local name. The remaining objects can be anything that will evaluate to real numbers. The action of SEQ for arbitrary inputs can be predicted exactly from this equivalent program.
xstart xend FOR index objexec EVAL xincr STEP n → LIST
where n is the number of new objects left on the stack by the FOR … STEP loop. Notice that index becomes a local variable regardless of its original type.
| L5/A1 | L4/A2 | L3/A3 | L2/A4 | L1/A5 | Li/I1 | |
|---|---|---|---|---|---|---|
| objexec | index | xstart | xend | xincr | → | { list } |
| L = Level; A = Argument; I = item | ||||||
Example 1: `n^2` `n` 1 4 1 returns { 1 4 9 16 }.
Example 2: « n SQ » `n` 2 4 1 returns { 4 9 16 }. | ||||||
DOSUBS, STREAM
Command
For a given function, computes Taylor series, asymptotic development and limit at finite or infinite points.
Level 3/Argument 1: The function f(x) Level 2/Argument 2: The variable if the limit point is 0, or an equation x = a if the limit point is a. If the function is in terms of the current variable, this can be given as just the value a.
Level 1/Argument 3: The order for the series expansion. The minimum value is 2, and the maximum value is 20.
Level 2/Item 1: A list containing the limit as a value and as the equivalent expression, an expression approximating the function near the limit point, and the order of the remainder. These are expressed in terms of a small parameter h. Level 1/Item 2: An expression for h in terms of the original variable.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Obtain the second order Taylor series expansion of ln(x) at x=1.
| Command | SERIES(LN(X),1,2) |
|---|---|
| Result | {{Limit: 0, Equiv: h, Expans: -1/2*h^2+h, Remain: h^3}, h=X- 1} |
TAYLOR0
Command
Server Mode Command: Selects Kermit Server mode. A Kermit server (a Kermit device in Server mode) passively processes requests sent to it by the local Kermit. The server receives data in response to SEND, transmits data in response to KGET, terminates Server mode in response to FINISH or LOGOUT, and transmits a directory listing in response to a generic directory request.
I/O Device (–33), I/O Data Format (–35), RECV Overwrite (–36), I/O Messages (–39), I/O Device for Wire (–78)
None
BAUD, CKSM, FINISH, KERRM, KGET, PARITY, PKT, RECN, RECV, SEND, TRANSIO
Function
Simplifies the given expression. Simplifies the expression except at the highest level, and also evaluates any existing variables that the expression contains and substitutes these back into the expression.
Level 1/Argument 1: An algebraic expression.
The expression simplified and with existing variables evaluated.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
With π stored in the variable Y, and the variables X and Z not in the current path, simplify the following expression. Note that the top-level simplification is not carried out. Sin(3x – y + 2z – (2x – z)) – Sin(x – 2y + (y + 3z))
Command: SEVAL(SIN(3*X-Y+2*Z-(2*X-Z)) - SIN(X-2*Y+(Y+3*Z))
-SIN(π –(X+3*Z)) -SIN(π –(X+3*Z))
EXPAND, SIMPLIFY
Command
Set Flag Command: Sets a specified user or system flag.
User flags are numbered 1 through 128. System flags are numbered –1 through –128. See Appendix C for a listing of system flags and their flag numbers.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| nflagnumber | → |
CF, FC?, FC?C, FS?, FS?C
Command
Show Variable Command: Returns symb2, which is equivalent to symb1 except that all implicit references to a variable name are made explicit. If the level 1 argument is a list, SHOW evaluates all global variables in symb1 not contained in the list.
Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| `symb1` | `name` | → | `symb2` |
| `symb1` | { name1 name2 ... } → | `symb2` |
If 7 is stored in C and 5 is stored in D:
Command: `X-Y+2*C+3*D` { X Y } SHOW
Result: `X-Y+14+15`
COLCT, EXPAN, ISOL, QUAD
Function
Silicon Intrinsic Density Command: Calculates the intrinsic density of silicon as a function of temperature, xT. If xT is a unit object, it must reduce to a pure temperature, and the density is returned as a unit object with units of 1/cm3. If xT is a real number, its units are assumed to be K, and the density is returned as a real number with implied units of 1/cm3. xT must be between 0 and 1685 K.
Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| xT | → | xdensity |
| x_unit | → | x_1/cm3 |
| `symb` | → | `SIDENS(symb)` |
Function
Calculates the discrete antiderivative of a function f with respect to a specified variable. This is a function G such that:
G(x + 1) – G(x) = f(x) where x is the specified variable.
Level 2/Argument 1: A function Level 1/Argument 2: The variable to calculate the antiderivative with respect to.
The discrete antiderivative of the function.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Obtain the discrete antiderivative with respect to the variable y of the expression: 2x-2y
| Command | SIGMA(2*X-2*Y,Y) |
|---|---|
| Result | -(Y^2 –(2*X+1)*Y) |
SIGMAVX, RISCH
Function
Calculates the discrete antiderivative of a function f with respect to the current variable. This is a function G such that: G(x + 1) – G(x) = f(x) where x is the current variable.
Level 1/Argument 1: A function.
The discrete antiderivative of the function.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Obtain the discrete antiderivative with respect to the current variable x of the expression: 2x-2y
| Command | SIGMAVX(2*X-2*Y) |
|---|---|
| Result | X^2 –(2*Y+1)*X |
SIGMA, RISCH
Function
Sign Function: Returns the sign of a real number argument, the sign of the numerical part of a unit object argument, or the unit vector in the direction of a complex number argument. For real number and unit object arguments, the sign is defined as +1 for positive arguments, –1 for negative arguments. In exact mode, the sign for argument 0 is undefined (?). In approximate mode, the sign for argument 0 is 0. SIGN in the !´menu returns the sign of a number, while SIGN in the …ß menu returns the unit vector of a complex number. For a complex argument:
x iy
SIGN ( x + iy ) = -------------------- + --------------------
2 2 2 2
x +y x +y
Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |||||
|---|---|---|---|---|---|---|
| z1 | → | z2 | ||||
| x_unit | → | xsign | ||||
| `symb` | → | |||||
| `SIGN(symb)` | ||||||
| ||||||
ABS, MANT, XPON
Command
Tabulates the sign of a rational function of the current CAS variable.
An algebraic expression.
A list containing, the points where the expression changes sign, and between each pair of points, the sign of the expression between those points.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Show the ranges of values of x for which the expression 2-x2 is positive and negative.
Command: SIGNTAB(2 – X^2)
Result: { `-∞` – `-√2` + `√2` – `+∞` }
TABVAR
Command
Simplifies two objects by dividing them by their greatest common divisor.
Level 2/Argument 1: The first object. Level 1/Argument 2: The second object.
Level 2/Item 1: The first object divided by the greatest common divisor. Level 1/Item 2: The second object divided by the greatest common divisor.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Divide the following expressions by their greatest common divisor:
3 2
x + 6 x + 11 x + 6 3 x – 7x – 6
| Command | SIMP2(X^3+6*X^2+11*X+6, X^3-7*X-6) |
|---|---|
| Result | {X+3,X-3} |
EGCD
Command
Simplifies an expression.
An expression
An equivalent simplified expression. SIMPLIFY follows an extensive built-in set of rules, but these might not give exactly the simplification the user expects.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). SI ( 3 ⋅ X ) + SI ( 7 ⋅ X ) ---------------------------------------------------------
Simplify SI
( 5 ⋅ X )
| Command | SIMPLIFY((SIN(3*X)+SIN(7*X))/SIN(5*X)) |
|---|---|
| Result | 4*COS(X)^2 - 2 |
COLLECT, EXPAND
Analytic function
Sine Analytic Function: Returns the sine of the argument. For real arguments, the current angle mode determines the number’s units, unless angular units are specified. For complex arguments, sin(x + iy) = sinx coshy + i cosx sinhy. If the argument for SIN is a unit object, then the specified angular unit overrides the angle mode to determine the result. Integration and differentiation, on the other hand, always observe the angle mode. Therefore, to correctly integrate or differentiate expressions containing SIN with a unit object, the angle mode must be set to radians (since this is a “neutral” mode).
Numerical Results (–3), Angle Mode (–17, –18)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| z | → | sin z |
| x_unitangular | → | sin(x_unitangular) |
| `symb` | → | `SIN(symb)` |
ASIN, COS, TAN
Command
Converts complex logarithmic and exponential expressions to expressions with trigonometric terms.
An expression with complex linear and exponential terms.
The expression with logarithmic and exponential subexpressions converted to trigonometric and inverse trigonometric expressions.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Radians mode must be set (flag –17 set). Must be in complex mode (flag –103 set).
Express eix in trigonometric terms.
| Command | SINCOS(EXP(i*X)) |
|---|---|
| Result | COS(X)+iSIN(X) |
EXPLN
Analytic function
Hyperbolic Sine Analytic Function: Returns the hyperbolic sine of the argument. For complex arguments, sinh(x + iy) = sinhx cosy + i coshx siny.
Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| z | → | sinh z |
| `symb` | → | `SINH(symb)` |
ASINH, COSH, TANH
Command
Store Inverse Command: Replaces the contents of the named variable with its inverse. The named object must be a number, a matrix, an algebraic object, or a unit object. For information on reciprocals, see INV.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `name` | → |
INV, SCONJ, SNEG
Command Operation
Size Command: Returns the number of characters in a string, the number of digits in an integer, the number of elements in a list, the dimensions of an array, the number of objects in a unit object or algebraic object, or the dimensions of a graphics object. The size of a unit is computed as follows: the scalar (+1), the underscore (+1), each unit name (+1), operator or exponent (+1), and each prefix (+2). Any object type not listed above returns a value of 1.
| Level 1/Argument 1 | Level 2/Item 1 | Level 1/Item 2 | |
|---|---|---|---|
| “string” | → | n | |
| integer | → | n | |
| { list } | → | n | |
| [ vector ] | → | {n} | |
| [[ matrix ]] | → | { n m} | |
| `symb` | → | n | |
| grob | → | #nwidth | #mheight |
| PICT | → | #nwidth | #mheight |
| x_unit | → | n |
CHR, NUM, POS, REPL, SUB
Command
Shift Left Command: Shift a binary integer one bit to the left. The most significant bit is shifted out to the left and lost, while the least significant bit is regenerated as a zero. SL is equivalent to binary multiplication by 2, truncated to the current wordsize.
Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| #n1 | → | #n2 |
ASR, SLB, SR, SRB
Command
Shift Left Byte Command: Shifts a binary integer one byte to the left. The most significant byte is shifted out to the left and lost, while the least significant byte is regenerated as zero. SLB is equivalent to binary multiplication by 28 (256) (or executing SL eight times), truncated to the current wordsize.
Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| #n1 | → | #n2 |
ASR, SL, SR, SRB
Command
SLOPEFIELD Plot Type Command: Sets the plot type to SLOPEFIELD.
When plot type is set to SLOPEFIELD, the DRAW command plots a slope representation of a scalar function with two variables. SLOPEFIELD requires values in the reserved variables EQ, VPAR, and PPAR. VPAR has the following form: { xleft xright ynear yfar zlow zhigh xmin xmax ymin ymax xeye yeye zeye xstep ystep } For plot type SLOPEFIELD, the elements of VPAR are used as follows:
None
BAR, CONIC, DIFFEQ, FUNCTION, GRIDMAP, HISTOGRAM, PARAMETRIC, PARSURFACE, PCONTOUR, POLAR, SCATTER, TRUTH, WIREFRAME, YSLICE
Command
Store Negate Command: Replaces the contents of a variable with its negative. The named object must be a number, an array, an algebraic object, a unit object, or a graphics object. For information on negation, see NEG.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `name` | → |
NEG, SCONJ, SINV
Command
Spectral Norm Command: Returns the spectral norm of an array. The spectral norm of a vector is its Euclidean length, and is equal to the largest singular value of a matrix.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| [ array ] | → | xspectralnorm |
ABS, CNRM, COND, RNRM, SRAD, TRACE
Command
Finds zeros of an expression equated to 0, or solves an equation.
Level 2/Argument 1: The expression or equation. A list of equations and expressions can be given too, each will be solved for the same variable. Level 1/Argument 2: The variable to solve for.
A zero or solution, or a list of zeros or solutions.
Radians mode must be set (flag –17 set). If exact mode is set (flag –105 clear) and there are no exact solutions, the command returns a null list even when there are approximate solutions. Radians mode must be set (flag –17 set). If complex mode is set (flag –103 set) then SOLVE will search for complex roots as well as real ones. Complex roots are displayed according to the coordinate system selected.
Example 1: Find the zeros of the following expression:
3 x –x–9
| Command | SOLVE(X^3-X-9,X) |
|---|---|
| Result | X=2.24004098747 Example 2: Find the real and complex roots of the two equations: |
x – 1=3 ,
4 2
x – A= 0
Command: Clear numeric mode, clear approximate mode, set complex mode, set rectangular mode, enter:
SOLVE({X^4-1=3,X^2-A=0},X)
Result: {{X=√2×i,X=√2×-1,X=-(√2×i),X=√2},
{X=√A×-1,X=√A}} Note that in this case, imaginary solutions for X are returned, even if X is in REALASSUME.
DESOLVE, LDEC, LINSOLVE, MSLV, QUAD, SOLVEVX
Command
Starts the appropriate solver for a specified set of equations. SOLVEQN sets up and starts the appropriate solver for the specified set of equations, bypassing the Equation Library catalogs. It sets EQ (and Mpar if more than one equation is being solved), sets the unit options according to flags 60 and 61, and starts the appropriate solver. SOLVEQN uses subject and title numbers (levels 3 and 2) and a “PICT” option (level 1) and returns nothing. Subject and title numbers are listed in chapter 5. For example, a 2 in level 3 and a 9 in level 2 would specify the Electricity category and Capacitive Energy set of equations. If the “PICT” option is 0, PICT is not affected; otherwise, the equation picture (if any) is copied into PICT.
Unit Type (60), Units Usage (61)
Units Type (60), Units Usage (61)
| Level 3/Argument 1 | Level 2/Argument 2 | Level 1/Argument 3 | Level 1/Item 1 | |
|---|---|---|---|---|
| n | m | 0/1 | → |
EQNLIB, MSOLVR
Command
Displays a menu of commands used in solving equations.
If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered list. If the flag is set, displays the operations as a menu of function keys.
None
Command
Finds zeros of an expression with respect to the current variable, or solves an equation with respect to the current variable. (You use the CAS modes input form to set the current variable.)
An expression or equation in the current variable. A list of equations and expressions can be given too, each will be solved for the current variable.
A zero or solution, or a list of zeros or solutions.
Radians mode must be set (flag –17 set). For a symbolic result, clear the CAS modes numeric option (flag –3 clear). If Exact mode is set (flag –105 clear) and there are no exact solutions, the command returns a null list even when there are approximate solutions. If complex mode is set (flag –103 set) then SOLVE will search for complex roots as well as real ones. Complex roots are displayed according to the coordinate system selected.
Solve the following expression for 0, where X is the default variable on the calculator: 3 x –x–9
| Command | SOLVEVX(X^3-X-9) |
|---|---|
| Result | X=2.24004098747 |
Note that if exact mode is set, this example returns a null list as there are no exact solutions to the equation.
LINSOLVE, SOLVE
Command
Ascending Order Sort Command: Sorts the elements in a list in ascending order. The elements in the list can be real numbers, strings, lists, names, binary integers, or unit objects. However, all elements in the list must all be of the same type. Strings and names are sorted by character code number. Lists of lists are sorted by the first element in each list. To sort in reverse order, use SORT REVLIST.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| { list }1 | → | { list }2 |
REVLIST
Command
Spherical Mode Command: Sets spherical coordinate mode. SPHERE sets flags –15 and –16. In spherical mode, vectors are displayed as polar components.
None
CYLIN, RECT
Analytic function
Square Analytic Function: Returns the square of the argument. The square of a complex argument (x, y) is the complex number (x2 – y2, 2xy). Matrix arguments must be square.
Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| z | → | z2 |
| x_unit | → | x2_unit2 |
| [[ matrix ]] | → | [[ matrix × matrix ]] |
| `symb` | → | `SQ(symb)` |
√, ^
Function
Square Root Analytic Function: Returns the (positive) square root of the argument. For a complex number (x1, y1), the square root is this complex number:
θ θ
( x 2, y 2 ) = -- r cos -- , r sin ----
2 2
where r = ABS (x1, y1), and θ = ARG (x1, y1). If (x1, y1) = (0,0), then the square root is (0, 0). The inverse of SQ is a relation, not a function, since SQ sends more than one argument to the same result. The inverse relation for SQ is expressed by ISOL as this general solution: `s1*√Z` The function √ is the inverse of a part of SQ, a part defined by restricting the domain of SQ such that: 1. each argument is sent to a distinct result, and 2. each possible result is achieved. The points in this restricted domain of SQ are called the principal values of the inverse relation. The √ function in its entirety is called the principal branch of the inverse relation, and the points sent by √ to the boundary of the restricted domain of SQ form the branch cuts of √.
The principal branch used by the calculator for √ was chosen because it is analytic in the regions where the arguments of the real-valued inverse function are defined. The branch cut for the complex-valued square root function occurs where the corresponding real-valued function is undefined. The principal branch also preserves most of the important symmetries. The graphs below show the domain and range of √. The graph of the domain shows where the branch cut occurs: the heavy solid line marks one side of the cut, while the feathered lines mark the other side of the cut. The graph of the range shows where each side of the cut is mapped under the function.
These graphs show the inverse relation `s1*√Z` for the case s1=1. For the other value of s1, the half-plane in the lower graph is rotated. Taken together, the half-planes cover the whole complex plane, which is the domain of SQ. View these graphs with domain and range reversed to see how the domain of SQ is restricted to make an inverse function possible. Consider the half-plane in the lower graph as the restricted domain Z = (x, y). SQ sends this domain onto the whole complex plane in the range W = (u, v) = SQ(x, y) in the upper graph.
Principal Solution (–1), Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| z | → | z |
| x_unit | → | x unit |
| 1⁄2 | ||
| `symb` | → | ` ( symb ) ` |
SQ, ^, ISOL
Command
Shift Right Command: Shifts a binary integer one bit to the right. The least significant bit is shifted out to the right and lost, while the most significant bit is regenerated as a zero. SR is equivalent to binary division by 2.
Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| #n1 | → | #n2 |
ASR, SL, SLB, SRB
Command
Spectral Radius Command: Returns the spectral radius of a square matrix.
The spectral radius of a matrix is a measure of the size of the matrix, and is equal to the absolute value of the largest eigenvalue of the matrix.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| [[ matrix ]]n×n | → | xspectralradius |
COND, SNRM, TRACE
Command
Shift Right Byte Command: Shifts a binary integer one byte to the right. The least significant byte is shifted out to the right and lost, while the most significant byte is regenerated as zero. SRB is equivalent to binary division by 28 (or executing SR eight times).
Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| #n1 | → | #n2 |
ASR, SL, SLB, SR
Command
Serial Receive Command: Reads up to n characters from the serial input buffer and returns them as a string, along with a digit indicating whether errors occurred. SRECV does not use Kermit protocol. If n characters are not received within the time specified by STIME (default is 10 seconds), SRECV “times out”, returning a 0 to level 1 and as many characters as were received to level 2. If the level 2 output from BUFLEN is used as the input for SRECV, SRECV will not have to wait for more characters to be received. Instead, it returns the characters already in the input buffer. If you want to accumulate bytes in the input buffer before executing SRECV, you must first open the port using OPENIO (if the port isn’t already open). SRECV can detect three types of error when reading the input buffer:
Note that BUFLEN also clears the above-mentioned framing, overrun, and overflow errors. Therefore, SRECV cannot detect an input-buffer overflow after BUFLEN is executed, unless more characters were received after BUFLEN was executed (causing the input buffer to overflow again). SRECV also cannot detect framing and UART overrun errors cleared by BUFLEN. To find where the data error occurred, save the number of characters returned by BUFLEN (which gives the number of “good” characters received), because as soon as the error is cleared, new characters can enter the input buffer.
I/O Device (–33), I/O Device for Wire (–78)
| Level 1/Argument 1 | Level 2/Item 1 | Level 1/Item 2 | |
|---|---|---|---|
| n | → | `string` | 0/1 |
If 10 good bytes were received followed by a framing error, then an SRECV command told to read 10 bytes would not indicate an error. Only when SRECV tries to read the byte that caused the framing error does it return a 0. Similarly, if the input buffer overflowed, SRECV would not indicate an error until it tried to read the first byte that was lost due to the overflow.
BUFLEN, CLOSEIO, OPENIO, SBRK, STIME, XMIT
Command
Find and replace: Finds and replaces a string in a given text object. You supply the following inputs: Level 3/argument 1: the string to search. Level 2/argument 2: the string to find. Level 1/argument 3: the string to replace it with.
| Level 3/Argument 1 | Level 2/Argument 2 | Level 1/Argument 3 | Level 1/Item 1 | |
|---|---|---|---|---|
| `string` | `string` | `string` | → | `string` |
REPL
Operation
Execute Program Step Operation: Returns and executes the next step of a program. If the next step is a subroutine, executes the subroutine in a single step. SST is not programmable.
None
NEXT, SST↓
Operation
Execute Subroutine Step Operation: Returns and executes the next step of a program or subroutine. If the next step is a subroutine, returns and executes the first step of the subroutine. SST↓ is not programmable.
None
NEXT, SST
Command Operation
START Definite Loop Structure Command: Begins START … NEXT and START … STEP definite loop structures. Definite loop structures execute a command or sequence of commands a specified number of times.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| START xstart | xfinish | → | |
| NEXT → | |||
| STEP | xincrement | → | |
| STEP | `symbincrement` | → | |
FOR, NEXT, STEP
Command
Standard Mode Command: Sets the number display format to standard mode. Executing STD has the same effect as clearing flags –49 and –50. Standard format (ANSI Minimal BASIC Standard X3J2) produces the following results when displaying or printing a number.
None
The following table provides examples of numbers displayed in Standard mode:
Representable With
Number Displayed As
12 Digits?
| 1011 | 100000000000 | Yes (integer) |
|---|---|---|
| 1012 | 1.E12 | No |
| 10-11 | .000000000001 | Yes |
| 1.2 x 10-11 | 1.23E-11 | No |
| 12.345 | 12.345 | Yes |
ENG, FIX, SCI
Command Operation
STEP Command: Defines the increment (step) value, and ends definite loop structure. See the FOR and START keyword entries for more information.
None
FOR, NEXT, START
Command
Store in EQ Command: Stores an object into the reserved variable EQ in the current directory.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| obj | → |
RCEQ
Command
Serial Time-Out Command: Specifies the period that SRECV (serial reception) and XMIT (serial transmission) wait before timing out. The value for x is interpreted as a positive value from 0 to 25.4 seconds. If no value is given, the default is 10 seconds. If x is 0, there is no time-out; that is, the device waits indefinitely, which can drain the batteries. STIME is not used for Kermit time-out.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| xseconds | → | |
| 0 | → |
BUFLEN, CLOSEIO, SBRK, SRECV, XMIT
Command
Store Command: Stores an object into a specified variable or object. Storing a graphics object into PICT makes it the current graphics object. To create a backup object, store the obj into the desired backup location (identified as :nport:namebackup). STO will not overwrite an existing backup object. To store backup objects and library objects, specify a port number (0 through 3). After storing a library object in a port, it must then be attached to its directory before it can be used. The easiest way to do this is to execute a warm start (by pressing $& C). This also causes the calculator to perform a system halt, which clears the stack, the LAST stack, and all local variables. STO can also replace a single element of an array or list stored in a variable. Specify the variable in level 1 as name(index), which is a user function with index as the argument. The index can be n or n,m, where n specifies the row position in a vector or list, and n,m specifies the row-and-column position in a matrix.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| obj | `name` | → | |
| grob | PICT | → | |
| obj | :nport :namebackup | → | |
| obj | `name(index)` | → | |
| backup | nport | → | |
| library | nport | → | |
| library | :nport :nlibrary | → | |
| Example 1: `A+B+C+D` `SUMAD` STO stores the expression A+B+C+D in the variable SUMAD. | |||
| Example 2: 5 `A(3)` STO stores the integer 5 in the third element in a list or vector A. | |||
| Example 3: 2 `A(3,5)` STO stores the integer 2 in the element in the third row and fifth column of | |||
| matrix A. | |||
DEFINE, RCL, →,
Command
Store Alarm Command: Stores an alarm in the system alarm list and returns its alarm index number. If the argument is a real number xtime, the alarm date will be the current system date by default. If objaction is a string, the alarm is an appointment alarm, and the string is the alarm message. If objaction is any other object type, the alarm is a control alarm, and the object is executed when the alarm comes due. xrepeat is the repeat interval for the alarm in clock ticks, where 8192 ticks equals 1 second.
nindex is a real integer identifying the alarm based on its chronological position in the system alarm list.
Date Format (–42), Repeat Alarms Not Rescheduled (–43), Acknowledged Alarms Saved (–44)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| xtime | → | nindex |
| { date time } | → | nindex |
| { date time objaction } | → | nindex |
| { date time objaction xrepeat } | → | nindex |
With flag –42 clear, this command: { 11.06 15.2530 RUN 491520 } STOALARM sets a repeating alarm for November 6 of the currently specified year, at 3:25:30 pm. The alarm action is to execute variable RUN. The repeat interval is 491520 clock ticks (1 minute).
DELALARM, FINDALARM, RCLALARM
Command
Store Flags Command: Sets the states of the system flags or the system and user flags. With argument #nsystem, STOF sets the states of the system flags (–1 through –128) only. With argument { #nsystem, #nuser, #nsystem2 #nuser2 }, STOF sets the states of both the system and user flags. A bit with value 1 sets the corresponding flag; a bit with value 0 clears the corresponding flag. The rightmost (least significant) bit of #nsystem and #nuser correspond to the states of system flag –1 and user flag +1, respectively. STOF can preserve the states of flags before a program executes and changes the states. RCLF can then recall the flag’s states after the program is executed.
Binary Integer Wordsize (–5 through –10)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| #nsystem | → | |
| { #nsystem #nuser #nsystem2 #nuser2 } | → |
RCLF, PUSH, POP, STWS, RCWS
Command
Store Key Assignments Command: Defines multiple keys on the user keyboard by assigning objects to specified keys. xkey is a real number of the form rc.p specifying the key by its row number r, its column number c, and its plane (shift) p. (For a definition of plane, see the entry for ASN). The optional initial list parameter or argument S restores all keys without user assignments to their standard key assignments on the user keyboard. This is meaningful only when all standard key assignments had been suppressed (for the user keyboard) by the command S DELKEYS. If the argument obj is the name SKEY, the specified key is restored to its standard key assignment.
User-Mode Lock (–61) and User Mode (–62) affect the status of the user keyboard
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| { obj1, xkey 1, ... objn, xkey n } | → | |
| { S, obj1, xkey 1, ... objn, xkey n } | → | |
| `S` | → |
ASN, DELKEYS, RCLKEYS
Function
Stores a number in a global variable. Given an expression as input, STORE evaluates the expression and stores the numerical value, unlike DEF which stores the expression.
Level 2/Argument 1: A number or an expression that evaluates to a numeric value. Level 1/Argument 2: The name of the variable in which the number is to be stored. If this variable does not already exist in the current directory path then it is created.
Level 1/Item 1: The number to which the first argument is evaluated, and which is stored in the variable.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Store in variable Z the result of calculating 17*Y. Assume that Y contains the integer number 2.
| Command | STORE(17*Y, Z) |
|---|---|
| Result | 34 |
DEF, DEFINE, UNASSIGN
Command
Stores a name or list of names in the current CAS variable. This is the same as storing into the VX variable in the CASDIR directory. By default, the CAS variable is called X; this command allows a program to change that name.
Level 1/Argument 1: A name or list of names.
None in RPN mode, NOVAL in Algebraic mode.
RCLVX
Command
Store Plus Command: Adds a number or other object to the contents of a specified variable. The object on the stack and the object in the variable must be suitable for addition to each other. STO+ can add any combination of objects suitable for addition. Using STO+ to add two arrays (where obj is an array and name is the global name of an array) requires less memory than using the stack to add them.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| obj | `name` | → | |
| `name` | obj | → |
STO–, STO*, STO/, +
Command
Store Minus Command: Calculates the difference between a number (or other object) and the contents of a specified variable, and stores the new value in the specified variable. The object on the stack and the object in the variable must be suitable for subtraction with each other. STO– can subtract any combination of objects suitable for stack subtraction. Using STO– to subtract two arrays (where obj is an array and name is the global name of an array) requires less memory than using the stack to subtract them.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| obj | `name` | → | |
| `name` | obj | → |
STO+, STO*, STO/, –
Command
Store Times Command: Multiplies the contents of a specified variable by a number or other object. The object on the stack and the object in the variable must be suitable for multiplication with each other. When multiplying two arrays, the result depends on the order of the arguments. The new object of the named variable is the level 2 array times the level 1 array. The arrays must be conformable for multiplication. Using STO* to multiply two arrays or to multiply a number and an array (where obj is an array or a number and name is the global name of an array) requires less memory than using the stack to multiply them.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| obj | `name` | → | |
| `name` | obj | → |
STO+, STO–, STO/, *
Command
Store Divide Command: Calculates the quotient of a number (or other object) and the contents of a specified variable, and stores the new value in the specified variable. The new object of the specified variable is the level 2 object divided by the level 1 object. The object on the stack and the object in the variable must be suitable for division with each other. If both objects are arrays, the divisor (level 1) must be a square matrix, and the dividend (level 2) must have the same number of columns as the divisor.
Using STO/ to divide one array by another array or to divide an array by a number (where obj is an array or a number and name is the global name of an array) requires less memory than using the stack to divide them.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| obj | `name` | → | |
| `name` | obj | → |
STO+, STO–, STO*, /
Command
Store Sigma Command: Stores obj in the reserved variable ΣDAT. STOΣ accepts any object and stores it in ΣDAT. However, if the object is not a matrix or the name of a variable containing a matrix, an Invalid ΣDATA error occurs upon subsequent execution of a statistics command.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| obj | → |
CLΣ, RCLΣ, Σ+, Σ–
Command
Evaluate String Command: Evaluates the text of a string as if the text were entered from the command line. OBJ→ also includes this function. STR→ is included for compatibility with the HP 28S.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| “obj” | → | evaluated-object |
ARRY→, DTAG, EQ→, LIST→, OBJ→, →STR
Command
Object to String Command: Converts any object to string form. The full-precision internal form of a number is not necessarily represented in the result string. To ensure that →STR preserves the full precision of a number, select Standard number display format or a wordsize of 64 bits (or both) before executing →STR. The result string includes the entire object, even if the displayed form of the object is too large to fit in the display. If the argument object is normally displayed in two or more lines, the result string will contain newline characters (character 10) at the end of each line. The newlines are displayed as the character ␍. If the argument object is already a string, →STR returns the string.
Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12), Number Display Format (–49, –50)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| obj | → | “obj” |
→STR can create special displays to label program output or provide prompts for input. The sequence "Result = " SWAP →STR + 1 DISP 1 FREEZE displays Result = object in line 1 of the display, where object is a string form of an object taken from level 1.
→ARRY, →LIST, STR→, →TAG, →UNIT
Command
Stream Execution Command: Moves the first two elements from the list onto the stack, and executes obj. Then moves the next element (if any) onto the stack, and executes obj again using the previous result and the new element. Repeats this until the list is exhausted, and returns the final result. STREAM is nominally designed for obj to be a program or command that requires two arguments and returns one result.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| { list } | obj | → | result |
| Example 1: { 1 2 3 4 5 } « * » STREAM returns 120. | |||
| Example 2: « + » STREAM is equivalent to ΣLIST. | |||
DOSUBS
Command
Starts the StreamSmart application.
None
Command
For a polynomial P, STURM returns a list containing Sturm’s sequences of P and their multiplicities
A polynomial P
A list containing the Sturm’s sequences for P, and the multiplicity for each (as a real number).
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Find the Sturm sequences and their multiplicities for the polynomial: 3 x +1
| Command | STURM(X^3+1) |
|---|---|
| Result | {[1],-1.,[1],1.,[X^3+1,-(3*X^2),-1],1.} |
STURMAB
Command
For a polynomial P and a closed interval [a, b], STURMAB determines the number of zeroes P has in [a, b]
A polynomial P
A list containing a number that is the same sign as P(a) and the number of zeroes P has in [a, b].
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
For the polynomial: 3 x +2 in the interval [-2,0] find the sign at the lower bound, and the number of zeroes
| Command | STURMAB(X^3+2, -2, 0) |
|---|---|
| Result | {-6,1} |
STURM, ZEROS
Command
Set Wordsize Command: Sets the current binary integer wordsize to n bits, where n is a value from 1 through 64 (the default is 64). Values of n less than 1 or greater than 64 are interpreted as 1 or 64, respectively. If the wordsize is smaller than an integer entered on the command line, then the most significant bits are not displayed upon entry. The truncated bits are still present internally (unless they exceed 64), but they are not used for calculations and they are lost when a command uses this binary integer as an argument. Results that exceed the given wordsize are also truncated to the wordsize.
Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| n | → | |
| #n | → |
BIN, DEC, HEX, OCT, RCWS
Command Operation
Subset Command: Returns the portion of a string or list defined by specified positions, or returns the rectangular portion of a graphics object or PICT defined by two corner pixel coordinates. If nend position is less than nstart position, SUB returns an empty string or list. Values of n less than 1 are treated as 1; values of n exceeding the length of the string or list are treated as that length. For graphics objects, a user-unit coordinate less than the minimum user-unit coordinate of the graphics object is treated as that minimum. A pixel or user-unit coordinate greater than the maximum pixel or user-unit coordinate of the graphics object is treated as that maximum.
| Level 3/Argument 1 | Level 2/Argument 2 | Level 1/Argument 3 | Level 1/Item 1 | |
|---|---|---|---|---|
| [[ matrix ]]1 | nstartposition | nendposition | → | [[ matrix ]]2 |
| [[ matrix ]]1 | {nrow, ncolumn } | nendposition | → | [[ matrix ]]2 |
| [[ matrix ]]1 | nstartposition | {nrow,, ncolumn } | → | [[ matrix ]]2 |
| [[ matrix ]]1 | {nrow, ncolumn } | {nrow,, ncolumn } | → | [[ matrix ]]2 |
| “stringtarget” | nstartposition | nendposition | → | “stringresult” |
| { listtarget } | nstartposition | nendposition | → | { listresult } |
| grobtarget | { #n1, #m1 } | { #n2 #m2 } | → | grobresult |
| grobtarget | ( x 1 , y1 ) | ( x 2 , y2 ) | → | grobresult |
| PICT | { #n1, #m1 } | { #n2 #m2 } | → | grobresult |
| PICT | ( x 1 , y1 ) | ( x 2 , y2 ) | → | grobresult |
| Example 1: { A B C D E } 2 4 SUB returns { B C D }. | ||||
| Example 2: "ABCDE" 0 10 SUB returns "ABCDE". | ||||
| Example 3: PICT { # 10d #20d } { # 20d # 40d } SUB returns | ||||
| Graphic 11 x 21. | ||||
CHR, GOR, GXOR, NUM, POS, REPL, SIZE
Function
Substitutes a value for a variable in an expression. The value can be numeric or an expression. This is similar to the Where function, denoted by the symbol |, but SUBST substitutes without evaluating the resulting expression.
Level 2/Argument 1: An expression. Level 1/Argument 2: The value or expression to be substituted.
The expression with the substitution made.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Substitute x = z+1 for x in the following expression, and apply the EXPAND command to simplify the result: 2 x + 3x + 7
Command: SUBST(X^2+3*X+7,X=Z+1)
EXPAND(ANS(1))
Result: Z^2+5*Z+11
| (where command)
Function
Performs a subtraction, modulo the current modulus.
Level 2/Argument 1: The object or number to be subtracted from. Level 1/Argument 2: The object or number to subtract.
The result of the subtraction, modulo the current modulus.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Command
Singular Value Decomposition Command: Returns the singular value decomposition of an m × n matrix. SVD decomposes A into 2 matrices and a vector. U is an m × m orthogonal matrix, V is an n × n orthogonal matrix, and S is a real vector, such that A = U × diag(S) × V . S has length MIN(m,n) and contains the singular values of A in nonincreasing order. The matrix diag(S) is an m×n diagonal matrix containing the singular values S. The computed results should minimize (within computational precision): A – U ⋅ diag ( S ) ⋅ V -------------------------------------------------- min ( m, n ) ⋅ A where diag(S) denotes the m × n diagonal matrix containing the singular values S.
| Level 1/Argument 1 | Level 3/Item 1 | Level 2/Item 2 | Level 1/Item 3 | |
|---|---|---|---|---|
| [[ matrix ]]A | → | [[ matrix ]]U | [[ matrix ]]V | [ vector ]S |
DIAG→, MIN, SVL
Command
Singular Values Command: Returns the singular values of an m × n matrix. SLV returns a real vector that contains the singular values of an m × n matrix in non-increasing order. The vector has length MIN(m,n).
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| [[ matrix ]] | → | [ vector ] |
MIN, SVD
RPL Command
Swap Objects Command: Swaps the position of the two inputs.
| Level 2 | Level 1 | Level 2 | Level 1 | |
|---|---|---|---|---|
| obj1 | obj2 | → | obj2 | obj1 |
DUP, DUPN, DUP2, OVER, PICK, ROLL, ROLLD, ROT
Command
Evaluate System Object Command: Evaluates unnamed operating system objects specified by their memory addresses. WARNING: Use extreme care when executing this function. Using SYSEVAL with random addresses will almost always cause a memory loss. Do not use this function unless you know what you are doing.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| #naddress | → |
Display the version string of a calculator by executing #2F389h SYSEVAL. This should display "HPHP49-C".
EVAL, LIBEVAL, FLASHEVAL
Command
For a symmetric matrix A, returns D and P where D is a diagonal matrix and A = PTDP
A symmetric matrix.
Level 2/Item 1: the diagonal matrix, D. Level 1/Item 2: The matrix P.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Rewrite in PTDP form the matrix: 12 24
| Command | SYLVESTER([1, 2][2, 4]) |
|---|---|
| Result | {[1, 0], [[1, 2][0, 1]]} |
Command
Converts a system of linear equations in algebraic form to matrix form.
Level 2/Argument 1: A vector containing a system of linear equations. An expression with no equal sign is treated as an equation setting the expression equal to zero. Level 1/Argument 2: A vector whose elements are the system’s variables. The variables must not exist in the current path.
A matrix that represents the system of linear equations.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Convert this system to a matrix: X–Y=0 2X + Y = 5
Command: SYST2MAT([X-Y, 2*X+Y=5],[X, Y])
1 –1 0
Result: 2 1 –5
Function
Percent of Total Function: Returns the percent of the first argument that is represented by the second argument. If both arguments are unit objects, the units must be consistent with each other. The dimensions of a unit object are dropped from the result, but units are part of the calculation. For more information on using temperature units with arithmetic functions, refer to the entry for +.
Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| x | y | → | 100y/x |
| x | `symb` | → | `%T(x,symb)` |
| `symb` | x | → | `%T(symb,x)` |
| `symb1` | `symb2` | → | `%T(symb1, symb2)` |
| x_unit1 | y_unit2 | → | 100y_unit2/x_unit1 |
| x_unit | `symb` | → | `%T(x_unit,symb)` |
| `symb` | x_unit | → | `%T(symb,x_unit)` |
| Example 1: 1_m 500_cm %T returns 500, because 500 cm represents 500% of 1 m. | |||
| Example 2: 100_K 50_K %T returns 50. | |||
+, %, %CH
Command
For an expression and a list of values, stores the expression in EQ, and returns the results of substituting the values for the current variable in the expression.
Level 2/Argument 1: An algebraic expression in terms of the current variable. Level 1/Argument 2: A list of values for which the expression is to be evaluated.
Level 2/Item 1: The algebraic expression. Level 1/Item 2: A list containing two lists: a list of the values and a list of the corresponding results.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). 2
Substitute 1, 2, and 3 into x + 1 .
| Command | TABVAL(X^2+1,{1, 2, 3}) |
|---|---|
| Result | { X^2+1,{{1, 2, 3},{2, 5, 10}}} |
Command
For a function of the current variable, with a rational derivative, computes the variation table, that is the turning points of the function and where the function is increasing or decreasing.
An expression in terms of the current variable, which has a rational derivative.
Level 3/Item 1: The original rational function. Level 2/Item 2: A list of two lists. The first list indicates the variation of the function (where it is increasing or decreasing) in terms of the independent variable. The second list indicates the variation in terms of the dependent variable, the function value. Level 1/Item 3: A graphic object that shows how the variation table was computed.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Tabulate the variation of the function: 2 x –1
Command: TABVAR(X^2-1)
Result: {`X^2-1` {{ `-∞` – 0 + `∞` }{ `+∞` ↓ `-1` ↑ `+∞` }} Graphic 96 × 55 }
Viewing the graphic, one sees the original function F and its derivative, as functions of X, and the variation table for X and F, shown as a matrix
SIGNTAB
Command
Stack to Tag Command: Combines objects in levels 1 and 2 to create tagged (labeled) object. The “tag” argument is a string of fewer than 256 characters.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| obj | “tag” | → | :tag:obj |
| obj | `name` | → | :name:obj |
| obj | x | → | :x:obj |
→ARRY, DTAG, →LIST, OBJ→, →STR, →UNIT
Command
Last Listed Elements Command: Returns all but the first element of a list or string.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| { obj1 ... objn } | → | { obj2 ... objn } |
| “string1” | → | “string2” |
"tall" TAIL returns "all".
HEAD
Analytic function
Tangent Analytic Function: Returns the tangent of the argument. For real arguments, the current angle mode determines the number’s interpretation as an angle, unless the angular units are specified. For a real argument that is an odd-integer multiple of 90 in Degrees mode, an Infinite Result exception occurs. If flag –22 is set (no error), the sign of the result (MAXR) matches that of the argument. For complex arguments: ( sin x) ( cos x ) + i ( sinh y ) ( cosh y ) tan ( x + iy ) = ------------------------------------------------------------------------------
2 2
sin h y + cos x If the argument for TAN is a unit object, then the specified angular unit overrides the angle mode to determine the result. Integration and differentiation, on the other hand, always observe the angle mode. Therefore, to correctly integrate or differentiate expressions containing TAN with a unit object, the angle mode must be set to Radians (since this is a “neutral” mode).
Numerical Results (–3), Angle Mode (–17, –18), Infinite Result Exception (–22)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| z | → | tan z |
| `symb` | → | `TAN(symb)` |
| x_unitangular | → | tan (x_unitangular) |
ATAN, COS, SIN
Command
Replaces tan(x) terms in an expression with (1-cos(2x))/sin(2x) terms.
An expression
The transformed expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Replace tan(x) terms in the function: ( tan ( x ) ) 2
| Command | TAN2CS2(TAN(X)^2) |
|---|---|
| Result | ((1-COS(2*X))/SIN(2*X))^2 |
TAN2SC, TAN2SC2
Command
Replaces tan(x) sub-expressions with sin(x)/cos(x).
An expression
The transformed expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Replace tan(x) terms in the function: ( tan ( x ) ) 2
| Command | TAN2SC(TAN(X)^2) |
|---|---|
| Result | (SIN(X)/COS(X))^2 |
HALFTAN, TAN2CS2, TAN2SC2
Command
Replaces tan(x) terms in an expression with sin(2x)/1+cos(2x) terms.
An expression
The transformed expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). In previous versions of the CAS, if flag –116 was set (Prefer sin()), then TAN2SC2 replaced tan(x) terms with: 1 – cos(2x)/sin(2x). This action is now performed by the TAN2CS2 command.
Replace tan(x) terms in the function: ( tan ( x ) ) 2
| Command | TAN2SC2(TAN(X)^2) |
|---|---|
| Result | (SIN(2*X)/(1+COS(2*X)))^2 |
HALFTAN, TAN2CS2, TAN2SC
Analytic function
Hyperbolic Tangent Analytic Function: Returns the hyperbolic tangent of the argument. For complex arguments, sinh 2x + i sin 2y tanh ( x + iy ) = -------------------------------------- cosh 2x + cos 2y
Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| z | → | tanh z |
| `symb` | → | `TANH(symb)` |
ATANH, COSH, SINH
Function
Performs a fourth-order Taylor expansion of an expression at x = 0.
An expression
The Taylor expansion of the expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Obtain the fourth-order Taylor series expansion of cos(x) at x=0.
| Command | TAYLOR0(COS(X)) |
|---|---|
| Result | 1/24*X^4+-1/2*X^2+1 |
DIVPC, lim, TAYLR, SERIES
Command
Taylor Polynomial Command: Calculates the nth order Taylor polynomial of symb in the variable global. The polynomial is calculated at the point global = 0. The expression symb may have a removable singularity at 0. The order, n, is the relative order of the Taylor polynomial — the difference in order between the largest and smallest power of global in the polynomial. TAYLR always returns a symbolic result, regardless of the state of the Numeric Results flag (–3).
| Level 3/Argument 1 | Level 2/Argument 2 | Level 1/Argument 3 | Level 1/Item 1 | |
|---|---|---|---|---|
| `symb` | `global` | norder | → | `symbTaylor` |
The command sequence `1+SIN(X)^2` `X` 5 TAYLR returns `1+X^2-8/4!*X^4`.
∂, ∫, Σ
Function
Returns the nth Tchebycheff polynomial.
A non-negative integer, n.
The nth Tchebycheff polynomial.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Obtain the fourth Tchebycheff polynomial.
| Command | TCHEBYCHEFF(4) |
|---|---|
| Result | 8*X^4-8*X^2+1 |
HERMITE, LEGENDRE
Command
Linearizes products in a trigonometric expression by collecting sine and cosine terms, and by combining sine and cosine terms of the same argument.
An expression with trigonometric terms.
The simplified expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Collect terms in the expression: sin 2x + cos 2x
| Command | TCOLLECT(SIN(2*X)+COS(2*X)) |
|---|---|
| Result | √2*COS(2*X-π/4) |
TEXPAND, TLIN
Function
Temperature Delta Function: Calculates a temperature change. TDELTA subtracts two points on a temperature scale, yielding a temperature increment (not an actual temperature). x or x_unit1 is the final temperature, and y or y_unit2 is the initial temperature. If unit objects are given, the increment is returned as a unit object with the same units as x_unit1. If real numbers are given, the increment is returned as a real number.
Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| x | y | → | xdelta |
| x_unit1 | x_unit2 | → | x_unit1delta |
| x_unit | `symb` | → | `TDELTA(x_unit, symb)` |
| `symb` | y_unit | → | `TDELTA(symb, y_unit)` |
| `symb1` | `symb2` | → | `TDELTA(symb1, symb2)` |
TINC
Command
Displays a menu or list containing the ASSUME and UNASSUME commands, and tests that can be included in algebraic expressions.
If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered list. If the flag is set, displays the operations as a menu of function keys.
ALGB, ARIT, CONSTANTS, DIFF, EXP&LN, INTEGER, MAIN, MATHS, MATR, MODULAR, POLYNOMIAL, REWRITE, TRIGO
Function
For the specified operation, performs the same function as EVAL, and returns the time taken to perform the evaluation as well as the result.
| Level 1/Argument 1 | Level 2/Item 2 | Level 1/Item 1 | |
|---|---|---|---|
| Object | → | result | time taken |
EVAL
Command
Expands transcendental functions.
An expression.
The transformation of the expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Expand the following expression: ln(sin(x+y))
| Command | TEXPAND(LN(SIN(X+Y))) |
|---|---|
| Result | LN(COS(Y)*SIN(X)+SIN(Y)* COS(X)) |
TCOLLECT, TLIN
Command
Show Stack Display Command: Displays the stack display. TEXT switches from the graphics display to the stack display. TEXT does not update the stack display.
None
The command sequence DRAW 5 WAIT TEXT selects the graphics display and plots the contents of the reserved variable EQ (or reserved variable ΣDAT). It subsequently waits for 5 seconds, and then switches back from the graphics display to the stack display.
PICTURE, PVIEW
Command
THEN Command: Starts the true-clause in conditional or error-trapping structure. See the IF and IFFER entries for more information.
None
CASE, ELSE, END, IF IFERR
Command
Ticks Command: Returns the system time as a binary integer, in units of 1/8192 second.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | #ntime |
If the result from a previous invocation from TICKS is on level 1 of the stack, then the command sequence TICKS SWAP - B->R 8192 / returns a real number whose value is the elapsed time in seconds between the two invocations.
TIME
Command
Time Command: Returns the system time in the form HH.MMSSs. time has the form HH.MMSSs, where HH is hours, MM is minutes, SS is seconds, and s is zero or more digits (as many as allowed by the current display mode) representing fractional seconds. time is always returned in 24-hour format, regardless of the state of the Clock Format flag (–41).
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | time |
DATE, TICKS, TSTR
Command
Set System Time Command: Sets the system time. time must have the form HH.MMSSs, where HH is hours, MM is minutes, SS is seconds, and s is zero or more digits (as many as allowed by the current display mode) representing fractional seconds. time must use 24-hour format.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| time | → |
CLKADJ, →DATE
Function
Temperature Increment Command: Calculates a temperature increment. TINC adds a temperature increment (not an actual temperature) to a point on a temperature scale. Use a negative increment to subtract the increment from the temperature. xinitial or x_unit1 is the initial temperature, and ydelta or y_unit2delta is the temperature increment. The returned temperature is the resulting final temperature. If unit objects are given, the final temperature is returned as a unit object with the same units as x_unit1. If real numbers are given, the final temperature is returned as a real number.
Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| xinitial | ydelta | → | xfinal |
| x_unit1 | y_unit2delta | → | x_unit1final |
| x_unit | `symb` | → | `TINC(x_unit, symb)` |
| `symb` | y_unitdelta | → | `TINC(symb, y_unitdelta)` |
| `symb1` | `symb2` | → | `TINC(symb1, symb2)` |
TDELTA
Command
Linearizes and simplifies trigonometric expressions. Note that this function does not collect sin and cos terms of the same angle.
An expression.
The transformation of the expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Linearize and simplify the following: 4 ( cos ( x ) )
| Command | TLIN(COS(X)^4) |
|---|---|
| Result | (1/8)*COS(4X)+(1/2)*COS(2X)+(3/8) |
SIMPLIFY, TCOLLECT, TEXPAND
Command
Toggle Line Command: For each pixel along the line in PICT defined by the specified coordinates, TLINE turns off every pixel that is on, and turns on every pixel that is off.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| (x1,y1) | (x2,y2) | → | |
| { #n1 #m1 } | { #n2 #m2 } | → |
The following program toggles on and off 10 times the pixels on the line defined by user-unit coordinates (1,1) and (9,9). Each state is maintained for .25 seconds. « ERASE 0 10 XRNG 0 10 YRNG { # 0d # 0d } PVIEW « 1 10 START (1,1) (9,9) TLINE .25 WAIT NEXT » »
ARC, BOX, LINE
Command
Temporary Menu Command: Displays a built-in menu, library menu, or user-defined menu. TMENU works just like MENU, except for user-defined menus (specified by a list or by the name of a variable that contains a list). Such menus are displayed like a custom menu and work like a custom menu, but are not stored in reserved variable CST. Thus, a menu defined and displayed by TMENU cannot be redisplayed by evaluating CST. See Appendix H for a list of the calculator’s built-in menus and the corresponding menu numbers (xmenu).
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| xmenu | → | |
| { listdefinition } | → | |
| `namedefinition` | → | |
| Example 1: | 7 TMENU displays the first page of the MTH MATR menu. | |
| Example 2: | 48.02 TMENU displays the second page of the UNITS MASS menu. | |
| Example 3: | 256 TMENU displays the first page of commands in library 256. | |
| Example 4: | { A 123 "ABC" } TMENU displays the custom menu defined by the list argument. | |
| Example 5: | `MYMENU` TMENU displays the custom menu defined by the name argument. |
MENU, RCLMENU
Command
Total Command: Computes the sum of each of the m columns of coordinate values in the current statistics matrix (reserved variable ΣDAT). The sums are returned as a vector of m real numbers, or as a single real number if m = 1.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | xsum | |
| → | [ xsum 1, xsum 2, ... ,xsum m ] |
MAXΣ, MINΣ, MEAN, PSDEV, PVAR, SDEV, VAR
Command
Matrix Trace Command: Returns the trace of a square matrix. The trace of a square matrix is the sum of its diagonal elements.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| [[ matrix ]]n×n | → | xtrace |
CONJ, DET, IDN
Command
Transpose Matrix Command: Returns the transpose of a matrix. Same as TRN, but without conjugation of complex numbers.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| [[ matrix ]] | → | [[ matrix ]]transpose |
| `name` | → |
CONJ, TRN
Command
I/O Translation Command: Specifies the character translation option. These translations affect only ASCII Kermit transfers and files printed to the serial port. Legal values for n are as follows:
| n | Effect |
|---|---|
| 0 | No translation |
| 1 | Translate character 10 (line feed only) to /from characters 10 and 13 (line feed |
with carriage return, the Kermit protocol) (the default value)
| 2 | Translate characters 128 through 159 (80 through 9F hexadecimal) |
|---|---|
| 3 | Translate all characters (128 through 255) |
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| noption | → |
BAUD, CKSM, PARITY
Command
Converts complex logarithmic and exponential subexpressions into their equivalent trigonometric
2 2
expressions. It also simplifies trigonometric expressions by using: ( sin x ) + ( cos x ) = 1
A complex expression with logarithmic and/or exponential terms, or a trigonometric expression.
The transformed expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). Prefers cosine terms if “prefer cos” is selected (flag –116 clear), prefers sine terms if flag –116 is set. Must be in Complex mode (flag –103 set) if a complex expression is being simplified.
Express the following in trigonometric terms: ln ( x + i )
| Command: | TRIG(LN(X+i)) |
|---|---|
| 2 | 1 |
L N( X + 1 ) + 2 × i × A TA N- --- - x- ------------------------------------------------------------------------------ 2 Result:
TRIGCOS, TRIGSIN, TRIGTAN
Command
Simplifies a trigonometric expression by applying the identity:
2 2
( sin x ) + ( cos x ) = 1 Returns only cosine terms if possible.
An expression with trigonometric terms.
The transformed expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
TRIG, TRIGSIN, TRIGTAN
Command
Displays a menu or list containing the CAS commands for transforming trigonometric expressions.
If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered list. If the flag is set, displays the operations as a menu of function keys.
ALGB, ARIT, CONSTANTS, DIFF, EXP&LN, INTEGER, MAIN, MATHS, MATR, MODULAR, POLYNOMIAL, REWRITE, TESTS
Command
Simplifies a trigonometric expression by applying the identity:
2 2
( sin x ) + ( cos x ) = 1 Returns only sine terms if possible.
An expression with trigonometric terms.
The transformed expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
TRIG, TRIGCOS, TRIGTAN
Command
Replaces sine and cosine terms in a trigonometric expression with tangent terms.
An expression with trigonometric terms.
The transformed expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Express the following in tan terms: 2 ( sinx)
Command: TRIGTAN(SIN(X)^2)
TAN(X)^2/(TAN(X)^2+1)
TRIG, TRIGCOS, TRIGSIN
Command
Transpose Matrix Command: Returns the (conjugate) transpose of a matrix. TRN replaces an n × m matrix A with an m × n matrix AT, where: AijT = Aji for real matrices and AijT = CONJ(Aji) for complex matrices If the matrix is specified by name, AT replaces A in name.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| [[ matrix ]] | → | [[ matrix ]]transpose |
| `name` | → |
[[ 2 3 1 ][ 4 6 9]] TRN returns [[ 2 4 ][ 3 6 ][ 1 9 ]].
CONJ, TRAN
Function
Truncate Function: Truncates an object to a specified number of decimal places or significant digits, or to fit the current display format. ntruncate (or symbtruncate if flag –3 is set) controls how the level 2 argument is truncated, as follows:
| ntruncate | Effect on Level 2 Argument |
|---|---|
| 0 through 11 | truncated to n decimal places |
–1 through –11 truncated to n significant digits
12 truncated to the current display format
For complex numbers and arrays, each real number element is truncated. For unit objects, the number part of the object is truncated.
Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| z1 | ntruncate | → | z2 |
| z1 | `symbtruncate` | → | `TRNC(z1,symbtruncate)` |
| `symb1` | ntruncate | → | `TRNC(symb1,ntruncate)` |
| `symb1` | `symbtruncate` | → | `TRNC(symb1,symbtruncate)` |
| [ array ]1 | ntruncate | → | [ array ]2 |
| x_unit | ntruncate | → | y_unit |
| x_unit | `symbtruncate` → | `TRNC(x_unit,symbtruncate)` | |
| Example 1: (4.5792,8.1275) 2 TRNC returns (4.57,8.12). | |||
| Example 2: [ 2.34907 3.96351 2.73453 ] -2 TRNC returns [ 2.3 3.9 2.7 ]. | |||
RND
Function
Truncates a series expansion.
Level 2/Argument 1: The expression that you want to truncate. Level 1/Argument 2: The expression to truncate with respect to.
The expression from Level 2/Argument 1, with terms of order greater than or equal to the order of the expression in Level 1/Argument 2 removed.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Expand the expression (x+1)7, and remove all terms in x4 and higher powers of x
| Command | TRUNC((X+1)^7,X^4) |
|---|---|
| Result | 35*X^3+21*X^2+7*X+1 |
DIVPC, EXPAND, SERIES
Command
Truth Plot Type Command: Sets the plot type to TRUTH. When the plot type is TRUTH, the DRAW command plots the current equation as a truth-valued function of two real variables. The current equation is specified in the reserved variable EQ. The plotting parameters are specified in the reserved variable PPAR, which has this form: { (xmin, ymin) (xmax, ymax) indep res axes ptype depend } For plot type TRUTH, the elements of PPAR are used as follows:
None
BAR, CONIC, DIFFEQ, FUNCTION, GRIDMAP, HISTOGRAM, PARAMETRIC, PARSURFACE, PCONTOUR, POLAR, SCATTER, SLOPEFIELD, WIREFRAME, YSLICE
Command
Performs simplifications on expressions involving exponentials and logarithms. Converts base 10 logarithms to natural logarithms
An expression
The simplified expression.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Simplify log(x+x)
| Command | TSIMP(LOG(X+X)) |
|---|---|
| Result | (LN(2)+LN(X))/(LN(5)+LN(2)) |
TEXPAND, TLIN
Command
Date and Time String Command: Returns a string derived from the date and time. The string has the form "DOW DATE TIME", where DOW is a three-letter abbreviation of the day of the week corresponding to the argument date and time, DATE is the argument date in the current date format, and TIME is the argument time in the current time format.
Time Format (–41), Date Format (–42)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| date | time | → | “DOW DATE TIME“ |
With flags –42 and –41 clear, 2.061990 14.55 TSTR returns "TUE 02/06/90 02:55:00P".
DATE, TICKS, TIME
Command
Typed Variables Command: Lists all global variables in the current directory that contain objects of the specified types. If the current directory contains no variables of the specified types, TVARS returns an empty list. For a table of the object-type numbers, see the entry for TYPE.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| ntype | → | { global ... } |
| { ntype ...} | → | { global ... } |
PVARS, TYPE, VARS
Command
TVM Menu Command: Displays the TVM Solver menu.
None
AMORT, TVMBEG, TVMEND, TVMROOT
Command
Payment at Start of Period Command: Specifies that TVM calculations treat payments as being made at the beginning of the compounding periods.
None
AMORT, TVM, TVMEND, TVMROOT
Command
Payment at End of Period Command: Specifies that TVM calculations treat payments as being made at the end of the compounding periods.
None
AMORT, TVM, TVMBEG, TVMROOT
Command
TVM Root Command: Solves for the specified TVM variable using values from the remaining TVM variables.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `TVM variable` | → | xTVM variable |
AMORT, TVM, TVMBEG, TVMEND
Command
Type Command: Returns the type number of an object, as shown in the following table:
Object Type: Number: Object Type: Number:
User objects: User objects (continued):
Real number 0 Backup object 17
Complex number 1 Real integer 28
Character string 2 Symbolic vector/matrix 29
Real array 3 Built-in Commands:
Complex array 4 Built-in function 18
List 5 Built-in command 19
Global name 6 System Objects:
Local name 7 System binary 20
Program 8 Extended real 21
Algebraic object 9 Extended complex 22
Binary integer 10 Linked array 23
Graphics object 11 Character 24
Tagged object 12 Code object 25
Unit object 13 Library data 26
XLIB name 14 Mini font 27
Directory object 15 Font 30
Library 16 Extended object 31
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| obj | → | ntype |
SAME, TVARS, VTYPE, ==
Function
Convert to SI Base Units Function: Converts a unit object to SI base units.
Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x_unit | → | y_base-units |
| `symb` | → | `UBASE(symb)` |
30_knot UBASE returns 15.4333333333_m/s.
CONVERT, UFACT, →UNIT, UVAL
Command
Factor Unit Command: Factors the level 1 unit from the unit expression of the level 2 unit object.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| x1_unit1 | x2_unit2 | → | x3_unit2*unit3 |
1_W 1_N UFACT returns 1_N*m/s.
CONVERT, UBASE, →UNIT, UVAL
Command
Converts a UFL1 (universal font library) fontset to a minifont compatible with the calculator. You specify the fontset and give it an ID (0–255). The font must be a 6-by-4 font.
Level 2/Argument 1 Level 1/Argument 2 Level 1/Item 1
objfontset nID → The font converted to minifont.
→MINIFONT, MINIFONT→
Command
Removes global variables and returns their values. This is an algebraic version of the PURGE command.
Level 1/Item 1: The name of a global variable, or a list of global names, to be purged.
Level 1/Item 1: The value or list of values that were stored in the now purged variables. If a variable does not exist, or is not in the current directory path, it is not removed, and its name is returned.
The status of the purge confirm flag (flag –76) is ignored, variables are purged with no request for confirmation.
Try to remove the global variable U, which contains 17.5, and the global variable V, which is not on the current directory path.
| Command | UNASSIGN({U, V}) |
|---|---|
| Result | {17.5, V} |
ADDTOREAL, ASSUME, DEF, LOCAL, PURGE, STO, STORE, UNASSUME, UNBIND
Command
Removes all assumptions on specified global variables, whether created by default, by ADDTOREAL or by ASSUME. Does this by removing the variable names from the list REALASSUME. Returns the variable names. To remove assumptions on a variable but leave it in REALASSUME, use ADDTOREAL instead of UNASSUME.
Level 1/Item 1: The name of a global variable, or a list of global names, to be removed from the REALASSUME list.
Level 1/Item 1: The same name or list of names as was input, even if any of the named variables were not in REALASSUME.
Remove the variables S1 and S2 which are include in the REALASSUME list by default.
| Command | UNASSUME({S1, S2}) |
|---|---|
| Result | {S1, S2} |
ADDTOREAL, ASSUME, DEF, LOCAL, UNASSIGN, UNBIND
Command
Removes all local variables created by the LOCAL command, and returns their values. This is useful only if a program needs to remove local variables created earlier in the same program.
None
Level 1/Item 1: A list of the local variables that have been removed, with their values.
Remove the local variables ←A and ←B created by the example for LOCAL.
| Command | UNBIND |
|---|---|
| Result | {←B=2, ←A=0} |
DEF, LOCAL, STORE, UNASSIGN, UNASSUME
Command
Stack to Unit Object Command: Creates a unit object from a real number and the unit part of a unit object. →UNIT adds units to a real number, combining the number and the unit part of a unit object (the numerical part of the unit object is ignored). →UNIT is the reverse of OBJ→ applied to a unit object.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| x | y_unit | → | x_unit |
→ARRY, →LIST, →STR, →TAG
RPL Command
Replaces the object at level n+2 with the object at level 2 and deletes the objects at levels 1 and 2. Can be though of as a “stack poke”.
Ln+2 Ln+1 L3 L2 L1 Ln Ln–1 L1
objn objn-1 obj1 obj n → obj objn-1 obj1
Replace the fourth object with an "X": 55555 4444 333 22 1 "X" 4 UNPICK returns 55555 "X" 333 22 1.
OVER, PICK, ROLL, ROLLD, SWAP, ROT
RPL Command
Changes the order of the first three objects on the stack. The order of the change is the opposite to that of the ROT command.
| L3 | L2 | L1 | L3 | L2 | L1 | |
|---|---|---|---|---|---|---|
| obj3 | obj2 | obj1 | → | obj1 | obj3 | obj2 |
333 22 1 UNROT returns 1 333 22.
OVER, PICK, ROLL, ROLLD, SWAP, ROT
Command
UNTIL Command: Starts the test clause in a DO … UNTIL … END indefinite loop structure. See the DO entry for more information.
None
DO, END
Command
Up Directory Command: Makes the parent of the current directory the new current directory. UPDIR has no effect if the current directory is HOME.
None
CRDIR, HOME, PATH, PGDIR
Command
Upper Chi-Square Distribution Command: Returns the probability utpc(n, x) that a chi-square random variable is greater than x, where n is the number of degrees of freedom of the distribution. The defining equations are these:
1 ∞ n t
- t --2 – 1 ⋅ e– --2 dt utpc ( n, x ) = --------------- n
-- ∫
2 2 Γ ( n--2 ) x
Γ -- ---- = -- -- – 1-- !
| z | z |
|---|---|
| 2 | 2 |
| For any value z, | , where ! is the factorial command. |
The value n is rounded to the nearest integer and, when rounded, must be positive.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| n | x | → | utpc(n,x) |
UTPF, UTPN, UTPT
Command
Upper Snedecor’s F Distribution Command: Returns the probability utpf(n1, n2, x) that a Snedecor’s F random variable is greater than x, where n1 and n2 are the numerator and denominator degrees of freedom of the F distribution. The defining equations for utpf(n1, n2, x) are these:
n 1 + n 2- ( n1 + n2 )
----- Γ - ---------------- n1
∞ n1 – 2 – ----------------------
- n - -----1- 2
- 2 - -------------- n1 - 2
-
∫x t 2
- n - ------------------------------ 1 + ----- t dt
2 n n -n -
Γ -- ----1-- Γ -- ----2-- 2
2 2
Γ -- ---- = -- -- – 1-- !
| z | z |
|---|---|
| 2 | 2 |
| For any value z, | , where ! is the calculator’s factorial command. |
The values n1 and n2 are rounded to the nearest integers and, when rounded, must be positive.
| Level 3/Argument 1 | Level 2/Argument 2 | Level 1/Argument 3 | Level 1/Item 1 | |
|---|---|---|---|---|
| n1 | n2 | x | → | utpf(n1,n2,x) |
UTPC, UTPN, UTPT
Command
Upper Normal Distribution Command: Returns the probability utpn(m, v, x) that a normal random variable is greater than x, where m and v are the mean and variance, respectively, of the normal distribution. For all x and m, and for v > 0, the defining equation is this: 2 (t – m) ∞ – ------------------ 1 utpn ( m, v, x ) = ------------- 2v 2πv x
∫e dt
For v = 0, UTPN returns 0 for x ≥ m, and 1 for x < m.
| Level 3/Argument 1 | Level 2/Argument 2 | Level 1/Argument 3 | Level 1/Item 1 | |
|---|---|---|---|---|
| m | v | x | → | utpn(m,v,x) |
UTPC, UTPF, UTPT
Command
Upper Student’s t Distribution Command: Returns the probability utpt(n, x) that a Student’s t random variable is greater than x, where n is the number of degrees of freedom of the distribution. The following is the defining equation for all x: n+1 Γ -- ----------- -- ∞
| n+1 | – ----------- |
|---|---|
| 2 | 2 |
utpt ( n, x ) = ----------------------- ∫ -- 1 + --- --
2 t
dt n Γ -- ---- nπ
n x
2
Γ -- ---- = -- -- – 1-- !
| z | z |
|---|---|
| 2 | 2 |
| For any value z, | , where ! is the factorial command. |
The value n is rounded to the nearest integer and, when rounded, must be positive.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| n | x | → | utpt(n,x) |
UTPC, UTPF, UTPN
Function
Unit Value Function: Returns the numerical part of a unit object.
Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x_unit | → | x |
| `symb` | → | `UVAL(symb)` |
CONVERT, UBASE, UFACT, →UNIT
Command
Vector/Complex Number to Stack Command: Separates a vector or complex number into its component elements. For vectors with four or more elements, V→ executes independently of the coordinate system mode, and always returns the elements of the vector to the stack as they are stored internally (in rectangular form). Thus, V→ is equivalent to OBJ→ for vectors with four or more elements.
Coordinate System (–15 and –16)
| L1/A1 | Ln/I1 ... L3/In–2 | L2/In–1 | L1/In | |
|---|---|---|---|---|
| [xy] | → | x | y | |
| [ xr, ytheta ] | → | xr | ytheta | |
| [ x1 , x2 , x3 ] | → | x1 | x2 | x3 |
| [ x1, xtheta, xz ] | → | x1 | xtheta | xz |
| [ x1, xtheta, xphi ] | → | x1 | xtheta | xphi |
| [ x1, x2, ..., xn ] | → | x1 ... xn–2 | xn–1 | xn |
| (x, y) | → | x | y | |
| (xr, ytheta) | → | xr | ytheta | |
| L = Level; A = Argument; I = item | ||||
Example 1: With flag –16 clear (Rectangular mode), (2,3) V→ returns 2 to level 2 and 1 to level 1.
Example 2: With flag –15 clear and –16 set (Polar/Cylindrical mode), [ 2 7 4 ] V→ returns 2 to | ||||
| level 3, 7 to level 2, and 4 to level 1. | ||||
Example 3: [ 9 7 5 3 ] V→ returns 9 to level 4, 7 to level 3, 5 to level 2, and 3 to level 1, | ||||
| independent of the state of flags –15 and –16. | ||||
→V2, →V3
Command
Stack to Vector/Complex Number Command: Converts two specified numbers into a 2-element vector or a complex number. The result returned depends on the setting of flags –16 and –19, as shown in the following table:
Flag –19 clear Flag –19 set
Flag –16 clear (Rectangular mode) [xy] (x, y)
Flag –16 set (Polar mode) [xy] (x, y)
Coordinate System (–16), Complex Mode (–19)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| x | y | → | [xy] |
| x | y | → | [xy] |
| x | y | → | (x, y) |
| x | y | → | (x, y) |
| Example 1: With flags –19 and –16 clear, 2 3 →V2 returns [ 2 3 ]. | |||
| Example 2: With flags –19 and –16 set (Polar/Spherical mode), 2 3 →V2 returns (2,3). | |||
V→, →V3
Command
Stack to 3-Element Vector Command: Converts three numbers into a 3-element vector. The result returned depends on the coordinate mode used, as shown in the following table:
| Mode | Result |
|---|---|
| Rectangular (flag –16 clear) | [ x1 x2 x3 ] |
| Polar/Cylindrical (flag –15 clear and –16 set) | [ x1 xtheta xz ] |
| Polar/Spherical (flag –15 and –16 set) | [ x1 xtheta xphi ] |
Coordinate System (–15 and –16)
| Level 3/Argument 1 | Level 2/Argument 2 | Level 1/Argument 3 | Level 1/Item 1 | |
|---|---|---|---|---|
| x1 | x2 | x3 | → | [ x1 x2 x3 ] |
| x1 | xtheta | xz | → | [ x1 xtheta xz ] |
| x1 | xtheta | xphi | → | [ x1 xtheta xphi ] |
| Example 1: With flag –16 clear (Rectangular mode), 1 2 3 →V3 returns [ 1 2 3 ]. | ||||
| Example 2: With flag –15 clear and –16 set (Polar/Cylindrical mode), 1 2 3 →V3 returns | ||||
| [ 1 2 3 ]. | ||||
Example 3: With flags –15 and –16 set (Polar/Spherical mode), 1 2 3 →V3 returns [ 1 2 3 ]. | ||||
V→, →V2
Command
Builds the Vandermonde matrix (also called the alternant matrix) from a list of objects. That is, for a list of n objects, the command creates an n × n matrix. The ith column in the matrix consists of the list items raised to the power of (i–1). Sometimes the Vandermonde matrix is defined with the ith row containing the items raised to the power of (i–1); to obtain this, transpose the result with the command TRAN.
A list of objects. A vector is allowed too.
The corresponding Vandermonde matrix.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Build the row version of the Vandermonde matrix from the following list of objects: {x, y, z}
Command: TRAN(VANDERMONDE({x,y,z}))
1 1 1 x y z
2 2 2
x y z Result:
CON, HILBERT, IDN, RANM
Command
Variance Command: Calculates the sample variance of the coordinate values in each of the m columns in the current statistics matrix (ΣDAT).
The variance (equal to the square of the standard deviation) is returned as a vector of m real numbers, or as a single real number if m = 1. The variances are computed using this formula: n
1 2
----------- ⋅ ∑ ( x i – x ) n–1 i=1
where xi is the ith coordinate value in a column, x is the mean of the data in this column, and n is the number of data points.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | xvariance | |
| → | [ xvariance1, ..., xvariancem ] |
MAXΣ, MEAN, MINΣ, PSDEV, PVAR, SDEV, TOT
Command
Variables Command: Returns a list of the names of all variables in the VAR menu for the current directory.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | { global1 ... globaln } |
ORDER, PVARS, TVARS
Command
Returns the Computer Algebra System version number, and date of release.
No input required.
A real number giving the version and release date of the Computer Algebra System software.
The version and release date are given as a number of the form V.YYYYMMDD, so a display mode showing at least 8 digits after the fraction mark is needed to display the result in full.
Command
Software Version Command: Displays the software version and copyright message.
| Level 1/Argument 1 | Level 2/Item 1 | Level 1/Item 2 | |
|---|---|---|---|
| → | “version number” | “copyright message” |
Command
For a specified variable, opens the contents in the command-line editor.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| A variable name | → | The contents opened in the command line |
| editor. | ||
VISITB, EDIT, EDITB
Command
For a specified variable, opens the contents in the most suitable editor for the object type. For example, if the specified variable holds an equation, the equation is opened in Equation Writer.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| A variable name | → | The contents opened in the most suitable |
| editor. | ||
VISIT, EDIT, EDITB
Command
Find a vector potential function describing a field whose curl (or “rot”) is the input. This command is the opposite of CURL. Given a vector V it attempts to return a function U such that curl U is equal to V; ∇ × U = V . For this to be possible, DIV(V) must be zero, otherwise the command reports a “Bad Argument Value” error. Step-by-step mode is available with this command.
Level 2/Argument 1: A vector V of expressions. Level 1/Argument 2: A vector of the names of the variables.
Level 1/Item 1: A vector U of the variables that is the potential from which V is obtained. An arbitrary constant can be added, the command does not do this.
Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). Step-by-step mode can be set (flag –100 set).
To see if this command is the opposite of CURL, use the output of the example in CURL as input to VPOTENTIAL. Find a vector in the spatial variables x, y, and z whose curl is: (2yz)i + (0)j + (2xy – x2)k
Command: VPOTENTIAL([2*Y*Z, 0, 2*X*Y-X^2], [X,Y,Z])
EXPAND(ANS(1))
Result: [0, -((X^3-3*Y*X^2)/3), Z*Y^2]
This shows that the reversal is not unique – more than one vector can have the same curl.
However, obtaining the curl of the above result, and then applying VPOTENTIAL to it again will give the same result.
CURL, POTENTIAL
Command
Variable Type Command: Returns the type number of the object contained in the named variable. If the named variable does not exist, VTYPE returns –1. For a table of the objects’ type numbers, see the entry for TYPE.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `name` | → | ntype |
| :nport : namebackup | → | ntype |
| :nport : nlibrary | → | ntype |
TYPE
Command
Multiply Width Command: Multiplies the horizontal plot scale by xfactor. *W is provided for compatibility with the HP 48. *W is the same as SCALEW; see its listing for details.
Command
Wait Command: Suspends program execution for specified time, or until a key is pressed. The function of WAIT depends on the argument, as follows:
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | |
| 0 | → | xkey |
| –1 | → | xkey |
| Example 1: | This program: | |
| « "Press [1] to add Press any other key to subtract" 1 DISP 0 WAIT IF 92.1 SAME THEN + ELSE - END » displays a prompting message and halts program execution until a key is pressed. If the 1 key (location 92.1) is pressed, two numbers on the stack are added. If any other key is pressed, two numbers on the stack are subtracted. | ||
Example 2: This program: | ||
| « { ADD { } { } { } { } SUB } MENU "Press [ADD] to add Press [SUB] to subtract" 1 DISP -1 WAIT IF 11.1 SAME THEN + ELSE - END » builds a custom menu with labels ADD and SUB and a prompting message. Executing -1 WAIT displays the custom menu (note that it’s not active) and suspends execution for keyboard input. If the ADD menu key (location 11.1) is pressed, two numbers on the stack are added. If any other key is pressed, two numbers on the stack are subtracted. | ||
KEY
Command Operation
WHILE Indefinite Loop Structure Command: Starts the WHILE … REPEAT … END indefinite loop structure. WHILE … REPEAT … END repeatedly evaluates a test and executes a loop clause if the test is true. Since the test clause occurs before the loop-clause, the loop clause is never executed if the test is initially false. The syntax is this: WHILE test-clause REPEAT loop-clause END The test clause is executed and must return a test result to the stack. REPEAT takes the value from the stack. If the value is not zero, execution continues with the loop clause; otherwise, execution resumes following END.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| WHILE | → | |
| REPEAT | T/F | → |
| END | → |
DO, END, REPEAT
Command
WIREFRAME Plot Type Command: Sets the plot type to WIREFRAME. When the plot type is set to WIREFRAME, the DRAW command plots a perspective view of the graph of a scalar function of two variables. WIREFRAME requires values in the reserved variables EQ, VPAR, and PPAR.
VPAR has the following form: { xleft, xright, ynear, yfar, zlow, zhigh, xmin, xmax, ymin, ymax, xeye, yeye, zeye, xstep, ystep } For plot type WIREFRAME, the elements of VPAR are used as follows:
None
BAR, CONIC DIFFEQ, FUNCTION, GRIDMAP, HISTOGRAM, PARAMETRIC, PARSURFACE, PCONTOUR, POLAR, SCATTER, SLOPEFIELD, TRUTH, YSLICE
Command
Warmstart Log Command: Returns four strings recording the date, time, and cause of the four most recent warmstart events. Each string "logn" has the form "code–date time". The following table summarizes the legal values of code and their meanings.
| Code | Description |
|---|---|
| 0 | The warmstart log was cleared. |
| 1 | The interrupt system detected a very low battery condition at the battery contacts |
(not the same as a low system voltage), and put the calculator in “Deep Sleep mode” (with the system clock running). When $ is pressed after the battery voltage is restored, the system warmstarts and puts a 1 in the log.
| 2 | Hardware failed during transmission (timeout). |
|---|---|
| 3 | Run through address 0. |
| 4 | System time is corrupt |
| Code | Description |
| 5 | A Deep Sleep wakeup (for example, $, Alarm). |
| 6 | Not used |
| 7 | A 5-nibble word (CMOS test word) in RAM was corrupt. (This word is checked |
on every interrupt, but it is used only as an indicator of potentially corrupt RAM.)
| 8 | Not used |
|---|---|
| 9 | The alarm list is corrupt. |
| A | System RPL jump to #0. |
| B | The card module was removed (or card bounce). |
| C | Hardware reset occurred (for example, an electrostatic discharge or user reset) |
| D | An expected System (RPL) error handler was not found in runstream. |
The date and time stamp (date time) part of the log may be displayed as 00…0000 for one of three reasons:
Date Format (–42)
| Level 1/Argument 1 | Level 4/Item 1 ... Level 1/Item 4 | |
|---|---|---|
| → | “log4” ... “log1” |
Command
Sum of x-Values Command: Sums the values in the independent-variable column of the current statistical matrix (reserved variable ΣDAT). The independent-variable column is specified by XCOL and is stored as the first parameter in the reserved variable ΣPAR. The default independent-variable column number is 1.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | xsum |
NΣ, XCOL, ΣXY, ΣX2, ΣY, ΣY2
Command
Sum of Squares of x-Values Command: Sums the squares of the values in the independent- variable column of the current statistical matrix (reserved variable ΣDAT). The independent-variable column is specified by XCOL and is stored as the first parameter in the reserved variable ΣPAR. The default independent-variable column number is 1.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | Sum of X2 |
NΣ, ΣX, XCOL, ΣXY, ΣY, ΣY2
Command
Sum of Squares of x-Values Command: Sums the squares of the values in the independent- variable column of the current statistical matrix. ΣX^2 is provided for compatibility with the HP 28. ΣX^2 is the same as ΣX2; see its listing for details.
Command
Independent Column Command: Specifies the independent-variable column of the current statistics matrix (reserved variable ΣDAT). The independent-variable column number is stored as the first parameter in the reserved variable ΣPAR. The default independent-variable column number is 1. XCOL will accept a noninteger real number and store it in ΣPAR, but subsequent commands that utilize the XCOL specification in ΣPAR will cause an error.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| ncol | → |
BARPLOT, BESTFIT, COLΣ, CORR, COV, EXPFIT, HISTPLOT, LINFIT, LOGFIT, LR, PREDX, PREDY, PWRFIT, SCATRPLOT, YCOL
Command
XModem Get Command: Retrieves a specified filename via XMODEM from another calculator. The other calculator needs to be in server mode for the operation to work (G I/O FUNCTIONS START SERVER).
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `name` | → |
BAUD, RECN, RECV, SEND, XRECV, XSERV, XPUT
Command
Serial Transmit Command: Sends a string serially without using Kermit protocol, and returns a single digit that indicates whether the transmission was successful. XMIT is useful for communicating with non-Kermit devices such as RS-232 printers. If the transmission is successful, XMIT returns a 1. If the transmission is not successful, XMIT returns the unsent portion of the string and a 0. Use ERRM to get the error message.
After receiving an XOFF command (with transmit pacing in the reserved variable IOPAR set), XMIT stops transmitting and waits for an XON command. XMIT resumes transmitting if an XON is received before the time-out set by STIME elapses; otherwise, XMIT terminates, returns a 0, and stores "Timeout" in ERRM.
I/O Device (–33), I/O Device for Wire (–78)
| Level 1/Argument 1 | Level 2/Item 1 | Level 1/Item 2 | |
|---|---|---|---|
| “string” | → | 1 | |
| “string” | → | “substringunsent” | 0 |
BUFLEN, SBRK, SRECV, STIME
Command
Converts an object or a list of objects to 12-digit decimal numeric format. Similar to →NUM except that →NUM does not work with lists, nor in programs in algebraic mode.
An object or list of objects.
The objects in numeric format.
Find the 12-digit numeric values of π/2, 3e, and 4cos(2).
| Command | XNUM({π/2,3*e,4*COS(2}) |
|---|---|
| Results | {1.5707963268 8.15484548538 -1.66458734619} |
I→R, →NUM
Function
Exclusive OR Function: Returns the logical exclusive OR of two arguments. When the arguments are binary integers or strings, XOR does a bit-by-bit (base 2) logical comparison:
| bit1 | bit2 | bit1 XOR bit2 |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| #n1 | #n2 | → | #n3 |
| “string1” | “string2” | → | “string3” |
| T/F1 | T/F2 | → | 0/1 |
| T/F | `symb` | → | `T/F XOR symb` |
| `symb` | T/F | → | `symb XOR T/F` |
| `symb1` | `symb2` | → | `symb1 XOR symb2` |
AND, NOT, OR
Function
Exponent Function: Returns the exponent of the argument.
Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | nexpon |
| `symb` | → | `XPON(symb)` |
| Example 1: | 1.2E34 XPON returns 34. | |
| Example 2: | 12.4E3 XPON returns 4. | |
| Example 3: | `A*1E34` XPON returns `XPON(A*1E34)`. |
MANT, SIGN
Command
XModem Send Command: Sends a specified filename via XMODEM to a calculator. The receiving calculator needs to be in Server mode (G I/O FUNCTIONS START SERVER).
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `name` | → |
BAUD, RECN, RECV, SEND XRECV, XSERV, XGET
Command
Converts a number, or a list of numbers in decimal format, to quotient (rational) format. Similar to the →Qπ command, but also clears numeric constants mode (flag –2) and sets exact mode (flag –105).
A number, or a list of numbers.
The number or list of numbers in rational format. This rational number converts to the input value to the accuracy of the current display setting.
| Example 1: Express .3658 in rational format, in Std mode: | |
|---|---|
| Command | XQ(.3658) |
| Results | 1829/5000 |
| Example 2: Express .3658 in rational format, in Fix 4 mode: | |
| Command | XQ(.3658) |
| Results | √(19/142) |
| Example 3: Express 1.04719755120 in rational format, in Eng 11 mode: | |
| Command | XQ(1.04719755120) |
| Results | 1/3*π |
→Q, →Qπ
Command
XModem Receive Command: Prepares the calculator to receive an object via XModem. The received object is stored in the given variable name. The transfer will start more quickly if you start the XModem sender before executing XRECV. Invalid object names cause an error. If flag –36 is clear, object names that are already in use also cause an error. If you are transferring data between two calculators, executing {AAA BBB CCC} XRECV receives AAA, BBB, and CCC. You also need to use a list on the sending end ({AAA BBB CCC} XSEND, for example).
I/O Device (–33), RECV Overwrite (–36), I/O Device for Wire (–78)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `name` | → |
BAUD, RECV, RECN, SEND, XSEND
Command
x-Axis Display Range Command: Specifies the x-axis display range. The x-axis display range is stored in the reserved variable PPAR as xmin and xmax in the complex numbers (xmin, ymin) and (xmax, ymax). These complex numbers are the first two elements of PPAR and specify the coordinates of the lower left and upper right corners of the display ranges. The default values of xmin and xmax are –6.5 and 6.5, respectively.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| xmin | xmax | → |
AUTO, PDIM, PMAX, PMIN, YRNG
Analytic function
xth Root of y Command: Computes the xth root of a real number. XROOT is equivalent to y1/x, but with greater accuracy. If y < 0, x must be an integer.
Numerical Results (–3)
Input/Output (RPN):
Level 2 Level 1 Level 1
y x → x y
`symb1` `symb2` → `XROOT(symb2,symb1)`
`symb` x → `XROOT(x,symb)`
y `symb` → `XROOT(symb,y)`
y_unit x → x y
_unit1/x
y_unit `symb` → `XROOT(symb,y_unit)`
Input/Output (ALG):
Argument 1 Argument 2 Level 1
y x
y x →
`symb1` `symb2` → `XROOT(symb1,symb2)`
`symb` x → `XROOT(symb,x)`
y `symb` → `XROOT(y,symb)`
x y_unit → x y
_unit1/x
`symb` y_unit → `XROOT(symb,y_unit)`
Command
XModem Send Command: Sends a copy of the named object via XModem. A receiving calculator must execute XRECV to receive an object via XModem. The transfer occurs more quickly if you start the receiving XModem after executing XSEND. Also, configuring the receiving modem not to do CRC checksums (if possible) will avoid a 30 to 60-second delay when starting the transfer. If you are transferring data between two calculators, executing {AAA BBB CCC} XSEND sends AAA, BBB, and CCC. You also need to use a list on the receiving end ({AAA BBB CCC} XRECV, for example).
I/O Device (–33), I/O Device for Wire (–78)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `name` | → |
BAUD, RECN, RECV, SEND XRECV
Command
XModem Server Command: Puts the calculator in XModem server mode. When in server mode, the following commands are available: P: Put a file in the calculator G: Get a file from the calculator E: Execute a command line
M Get the calculator memory L: List the files in the current directory
BAUD, RECN, RECV, SEND XRECV, XGET, XPUT
Command
X Volume Coordinates Command: Sets the width of the view volume in the reserved variable VPAR. xleft and xright set the x-coordinates for the view volume used in 3D plots. These values are stored in the reserved variable VPAR.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| xleft | xright | → |
EYEPT, XXRNG, YVOL, YYRNG, ZVOL
Command
X Range of an Input Plane (Domain) Command: Specifies the x range of an input plane (domain) for GRIDMAP and PARSURFACE plots. xmin and xmax are real numbers that set the x-coordinates for the input plane. These values are stored in the reserved variable VPAR.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| xmin | xmax | → |
EYEPT, NUMX, NUMY, XVOL, YVOL, YYRNG, ZVOL
Command
Sum of X times Y command: Sums the products of each of the corresponding values in the independent- and dependent-variable columns of the current statistical matrix (reserved variable ΣDAT). The independent column is the column designated as XCOL and the dependent column is the column designated as YCOL.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | Sum of X*Y |
NΣ, ΣX, XCOL, ΣXY, ΣX2, YCOL, ΣY2
Command
Sum of X times Y command: Sums the products of each of the corresponding values in the independent- and dependent-variable columns of the current statistical matrix. ΣX*Y is provided for compatibility with the HP 28. ΣX*Y is the same as ΣXY; see its listing for details.
Command
Sum of y-Values Command: Sums the values in the dependent variable column of the current statistical matrix (reserved variable ΣDAT). The dependent variable column is specified by YCOL, and is stored as the second parameter in the reserved variable ΣPAR. The default dependent variable column number is 2.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | Sum of Y |
NΣ, ΣX, XCOL, ΣXY, ΣX2, YCOL, ΣY2
Command
Sum of Squares of y-Values Command: Sums the squares of the values in the dependent-variable columns of the current statistical matrix (reserved variable ΣDAT). The dependent column is the column designated as YCOL
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | Sum of Y2 |
NΣ, ΣX, XCOL, ΣXY, ΣX2, YCOL
Command
Sum of Squares of y-Values Command: Sums the squares of the values in the dependent-variable columns of the current statistical matrix. ΣY^2 is provided for compatibility with the HP 28. ΣY^2 is the same as ΣY2; see its listing for details.
Command
Dependent Column Command: Specifies the dependent variable column of the current statistics matrix (reserved variable ΣDAT). The dependent variable column number is stored as the second parameter in the reserved variable ΣPAR. The default dependent variable column number is 2. YCOL will accept a noninteger real number and store it in ΣPAR, but subsequent commands that utilize the YCOL specification in ΣPAR will cause an error.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| ncol | → |
BARPLOT, BESTFIT, COLΣ, CORR, COV, EXPFIT, HISTPLOT, LINFIT, LOGFIT, LR, PREDX, PREDY, PWRFIT, SCATRPLOT, XCOL
Command
y-Axis Display Range Command: Specifies the y-axis display range. The y-axis display range is stored in the reserved variable PPAR as ymin and ymax in the complex numbers (xmin, ymin) and (xmax, ymax). These complex numbers are the first two elements of PPAR and specify the coordinates of the lower left and upper right corners of the display ranges. The default values of ymin and ymax are –3.1 and 3.2, respectively for the HP 48gII and -3.9 and 4.0, respectively for the HP 50g and 49g+.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| ymin | ymax | → |
AUTO, PDIM, PMAX, PMIN, XRNG
Command
Y-Slice Plot Command: Sets the plot type to YSLICE. When plot type is set YSLICE, the DRAW command plots a slicing view of a scalar function of two variables. YSLICE requires values in the reserved variables EQ, VPAR, and PPAR. VPAR has the following form: { xleft, xright, ynear, yfar, zlow, zhigh, xmin, xmax, ymin, ymax, xeye, yeye, zeye, xstep, ystep } For plot type YSLICE, the elements of VPAR are used as follows:
None
BAR, CONIC, DIFFEQ, FUNCTION, GRIDMAP, HISTOGRAM, PARAMETRIC, PARSURFACE, PCONTOUR, POLAR, SCATTER, SLOPEFIELD, TRUTH, WIREFRAME
Command
Y Volume Coordinates Command: Sets the depth of the view volume in the reserved variable VPAR. The variables ynear and yfar are real numbers that set the y-coordinates for the view volume used in 3D plots. ynear must be less than yfar. These values are stored in the reserved variable VPAR.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| ynear | yfar | → |
EYEPT, XVOL, XXRNG, YYRNG, ZVOL
Command
Y Range of an Input Plane (Domain) Command: Specifies the y range of an input plane (domain) for GRIDMAP and PARSURFACE plots. The variables yy near and yy far are real numbers that set the y-coordinates for the input plane. These values are stored in the reserved variable VPAR.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| ynear | yfar | → |
EYEPT, XVOL, XXRNG, YVOL, ZVOL
Command
Returns the zeros of a function of one variable, without multiplicity.
Level 2/Argument 1: An expression. Level 1/Argument 2: The variable to solve for.
The solution, or a list of solutions, for the expression equated to 0.
Radians mode must be set (flag –17 set). For a symbolic result, clear the CAS modes Numeric option (flag –3 clear). The following flag settings affect the result:
Find the roots of the following equation in x, without specifying that x=2 is a root twice. x3 – x2 – 8x + 12 = 0:
Command: ZEROS(X^3-X^2-8*X+12)
{-3, 2}
Function
Gas Compressibility Z Factor Function: Calculates the gas compressibility correction factor for non-ideal behavior of a hydrocarbon gas. xTr is the reduced temperature: the ratio of the actual temperature (T) to the pseudocritical temperature (Tc). (Calculate the ratio using absolute temperatures.) xTr must be between 1.05 and 3.0. yPr is the reduced pressure: the ratio of the actual pressure (P) to the pseudocritical pressure (Pc). yPr must be between 0 and 30. xTr and yPr must be real numbers or unit objects that reduce to dimensionless numbers.
Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| xTr | yPr | → | xZfactor |
| xTr | `symb` | → | `ZFACTOR(xTr,symb)` |
| `symb` | yPr | → | `ZFACTOR(symb,yPr)` |
| `symb1` | `symb2` | → | `ZFACTOR(symb1,symb2)` |
Command
Z Volume Coordinates Command: Sets the height of the view volume in the reserved variable VPAR. xlow and xhigh are real numbers that set the z-coordinates for the view volume used in 3D plots. These values are stored in the reserved variable VPAR.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| xlow | xhigh | → |
EYEPT, XVOL, XXRNG, YVOL, YYRNG
Function
Power Analytic Function: Returns the value of the level 2 object raised to the power of the level 1 object. This can also apply to a square matrix raised to a whole-number power. If either argument is complex, the result is complex. The branch cuts and inverse relations for wz are determined by this relationship: wz = exp(z(ln w))
Principal Solution (–1), Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| w | z | → | wz |
| z | `symb` | → | `z^(symb)` |
| `symb` | z | → | `(symb)^z` |
| `symb1` | `symb2` | → | `symb1^(`symb2)` |
| x_unit | y | → | xy_unity |
| x_unit | `symb` | → | `(x_unit)^(symb)` |
EXP, ISOL, LN, XROOT
Function
Where Function: Substitutes values for names in an expression. | is used primarily in algebraic objects, where its syntax is: `symbold | (name1 = symb1, name2 = symb2 …)` It enables algebraics to include variable-like substitution information about names. Symbolic functions that delay name evaluation (such as ∫ and ∂) can then extract substitution information from local variables and include that information in the expression, avoiding the problem that would occur if the local variables no longer existed when the local names were finally evaluated.
Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| `symbold` | { name1, `symb1`, name2, `symb2` … } | → | `symbnew` |
| x | { name1, `symb1`, name2, `symb2` … } | → | x |
| (x,y) | { name1, `symb1`, name2, `symb2` … } | → | (x,y) |
APPLY, QUOTE
Function
Integral Function: Integrates an integrand from lower limit to upper limit with respect to a specified variable of integration. The algebraic syntax for ∫ parallels its stack syntax: ∫ (lower limit, upper limit, integrand, name) where lower limit, upper limit, and integrand can be real or complex numbers, unit objects, names, or algebraic expressions. Evaluating ∫ in Symbolic Results mode (flag –3 clear) returns a symbolic result. Some functions that the calculator can integrate include the following:
Numerical Result (–3), Number Format (–45 to –50)
| L4/A1 | L3/A2 | L2/A3 | L1/A4 | L1/I1 | |
|---|---|---|---|---|---|
| lower limit | upper limit | integrand | `name` | → | `symbintegral` |
| L = Level; A = Argument; I = Item | |||||
In Symbolic Results mode (flag –3 clear) this command sequence: 1 2 `10*X` `X` „ returns 15. In Numeric Results mode (flag –3 set) the above command sequence returns the numeric approximation 15.. In addition, the variable IERR is created, and contains the error of integration .00000000015.
TAYLR, ∂, Σ
Function
The “undefined” symbol. Used to signify a numeric result that is not defined by the rules of arithmetic, such as the result of dividing zero by zero, or infinity by infinity. Mathematical operations on ? return ? as a result. Can be used in programs to check for an earlier undefined operation. This use of ? is unrelated to the use of ? as a spare unit in the units system. The unit ? can be used to create new units based on it, units that can not be expressed in terms of other base units. For
example you could define $=1_? Then other currencies could be defined as multiples or fractions of 1_? The calculator has symbols for Yen, Pounds and Euros; other currencies could be defined using their names. The unit conversion system would then check conversions between them for consistency because ? is recognized as a base unit.
Function
Infinity: used to signify a numeric result that is infinite by the rules of arithmetic, such as the result of dividing a non-zero number by zero. The calculator recognizes two kinds of infinity: signed and unsigned. Evaluating `1/0` gives an unsigned infinity `∞`. Selecting infinity from the keyboard, from the CHARS table, or from the catalog …µ returns `+∞` and the sign can be changed. Calculations with the unsigned infinity return unsigned infinity or ? as their result. Calculations with the signed infinity can return ordinary numeric results, as in the example. Positive infinity and unsigned infinity are equal if tested with ==, but are not identical if tested with SAME.
Exact mode must be set (flag –105 clear), and numeric mode must not be set (flag –3 clear) for mathematical operations to give ∞ as a result, and for executing ∞ from the keyboard or catalog to give +∞ and not an error.
Find the arc tangent of minus infinity. Assume that radians mode is set.
| Command | ATAN(-∞) |
|---|---|
| Results | -(π/2) Σ (Summation) |
Function
Summation Function: Calculates the value of a finite series. The summand argument smnd can be a real number, a complex number, a unit object, a local or global name, or an algebraic object. The algebraic syntax for Σ differs from the stack syntax. The algebraic syntax is: `Σ(index=initial,final,summand)`
Symbolic Constants (–2), Numerical Results (–3)
| L4/A1 | L3/A2 | L2/A3 | L1/A4 | L1/I1 | |
|---|---|---|---|---|---|
| `indx` | xinit | xfinal | smnd | → | xsum |
| `indx` | `init` | xfinal | smnd | → | `Σ(indx = init, xfinal, smnd)` |
| `indx` | xinit | `final` | smnd | → | `Σ(indx = xinit, final, smnd)` |
| `indx` | `init` | `final` | smnd | → | `Σ(indx = init, final, smnd)` |
| L = Level; A = Argument; I = Item | |||||
The command sequence `N` 1 5 `A^N` Σ returns `(EXP(6*LN(A))-A)/(A-1)`.
TAYLR, ∫, ∂
Command
Sigma Plus Command: Adds one or more data points to the current statistics matrix (reserved variable ΣDAT). For a statistics matrix with m columns, arguments for Σ+ can be entered several ways:
| Lm/A1 … L2/Am–1 | L1/Am | L1/I1 | |
|---|---|---|---|
| x | → | ||
| [ x1, x2, …, xm ] | → | ||
| [[ x1 1, …, x1 m ] [ xn 1, … ,xn m ]] | → | ||
| x1 … xm–1 | xm | → | |
| L = Level; A = Argument; I = Item | |||
The sequence CLΣ [ 2 3 4 ] Σ+ 3 1 7 Σ+ creates the matrix [[ 2 3 4 ][ 3 1 7 ]] in ΣDAT.
CLΣ, RCLΣ, STOΣ, Σ–
Command
Sigma Minus Command: Returns a vector of m real numbers (or one number x if m = 1) corresponding to the coordinate values of the last data point entered by Σ+ into the current statistics matrix (reserved variable ΣDAT). The last row of the statistics matrix is deleted. The vector returned by Σ– can be edited or replaced, then restored to the statistics matrix by Σ+.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | x | |
| → | [ x1 x2 … xm ] |
CLΣ, RCLΣ, STOΣ, Σ+
Function
π Function: Returns the symbolic constant ` π ` or its numerical representation, 3.14159265359. The number returned for π is the closest approximation of the constant π to 12-digit accuracy. In Radians mode with flag –2 and –3 clear (to return symbolic results), trigonometric functions of π and π/2 are automatically simplified. For example, evaluating `SIN(π)` returns zero. However, if
flag –2 or flag –3 is set (to return numerical results), then evaluating `SIN(π)` returns the numerical approximation –2.06761537357E–13.
Symbolic Constants (–2), Numerical Results (–3)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| → | `π` | |
| → | 3.14159265359… |
e, i, MAXR, MINR, →Qπ
Function
Derivative Function: Takes the derivative of an expression, number, or unit object with respect to a specified variable of differentiation. When executed in stack syntax, ∂ executes a complete differentiation: the expression `symb1` is evaluated repeatedly until it contains no derivatives. As part of this process, if the variable of differentiation name has a value, the final form of the expression substitutes that value substituted for all occurrences of the variable. The algebraic syntax for ∂ is `∂name(symb1`). When executed in algebraic syntax, ∂ executes a stepwise differentiation of symb1, invoking the chain rule of differentiation — the result of one evaluation of the expression is the derivative of the argument expression symb1, multiplied by a new subexpression representing the derivative of symb1’s argument. If ∂ is applied to a function for which the calculator does not provide a derivative, ∂ returns a new function whose name is der followed by the original function name.
Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| `symb1` | `name` | → | `symb2` |
| z | `name` | → | 0 |
| x_unit | `name` | → | 0 |
In Radians mode, the command sequence `ˆX(SIN(Y))` EVAL returns 0. When Y has the value `X^2`, the command sequence `SIN(Y)` `X` ˆ returns `COS(X^2)*(2*X)`. The differentiation has been executed in stack syntax, so that all of the steps of differentiation have been carried out in a single operation.
TAYLOR, ∫, Σ
Function
Factorial (Gamma) Function: Returns the factorial n! of a positive integer argument n, or the gamma function Γ(x+1) of a non-integer argument x. For x ≥ 253.1190554375 or n < 0, ! causes an overflow exception (if flag –21 is set, the exception is treated as an error). For non-integer x ≤ –254.1082426465, ! causes an underflow exception (if flag –20 is set, the exception is treated as an error). In algebraic syntax, ! follows its argument. Thus the algebraic syntax for the factorial of 7 is 7!. For non-integer arguments x, x! = Γ(x + 1), defined for x > –1 as:
∞ –t x Γ ( x + 1 ) = ∫ e t dt 0
and defined for other values of x by analytic continuation: Γ(x + 1) = n Γ(x)
Numerical Results (–3), Underflow Exception (–20), Overflow Exception (–21)
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| n | → | n! |
| x | → | Γ(x + 1) |
| `symb` | → | `(symb!)` |
COMB, PERM
Function
Percent Function: Returns x percent of y. Common usage is ambiguous about some units of temperature. When °C or °F represents a thermometer reading, then the temperature is a unit with an additive constant: 0 °C=273.15 K, and 0 °F=459.67 °R. But when °C or °F represents a difference in thermometer readings, then the temperature is a unit with no additive constant: 1 °C=1 K and 1 °F=1 °R. The arithmetic operators +, –, %, %CH, and %T treat temperatures as differences, without any additive constant. However, +, –, %CH, and %T require both arguments to be either absolute (K and °R), both °C, or both °F. No other combinations are allowed. For more information on using temperature units with arithmetic functions, see the entry for +.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| x | y | → | xy/100 |
| x | `symb` | → | `%(x,symb)` |
| `symb` | x | → | `%(symb,x)` |
| `symb1` | `symb2` | → | `%(symb1, symb2)` |
| x | y_unit | → | (xy/100)_unit |
| x_unit | y | → | (xy/100)_unit |
| `symb` | x_unit | → | `%(symb,x_unit)` |
| x_unit | `symb` | → | `%(x_unit,symb)` |
| Example 1: 23.7 995 % returns 235.815. | |||
| Example 2: 15 176_kg % returns 26.4_kg. | |||
| Example 3: 100_°C 50 % returns 50_°C. | |||
+, %CH, %T
Unit attachment
Unit attachment symbol: Attaches a unit type to a numeric value.
The calculator handles units by attaching the unit to a numeric value using the underscore symbol. For example, the value of 3 kilometers is shown as 3_km, and is created by entering 3 and then the underscore character, followed by attaching the kilometer unit.
Numeric value
Numeric value ready for a unit attachment
Object
Program delimiter object: Enters a pair of program delimiter objects. A program is a set of instructions enclosed by an open program object delimiter and a close program object delimiter. These can be nested to have a program procedure enclosed within an outer program object.
None
A pair of program delimiters
Function
Less Than Function: Tests whether one object is less than another object. The function < returns a true test result (1) if the first argument is less than the second argument, or a false test result (0) otherwise. If one object is a symbolic (an algebraic or a name), and the other is a number or symbolic or unit object, < returns a symbolic comparison expression that can be evaluated to return a test result. For real numbers and binary integers, “less than” means numerically smaller (1 is less than 2). For real numbers, “less than” also means more negative (–2 is less than –1). For strings, “less than” means alphabetically previous (“ABC” is less than “DEF”; “AAA” is less than “AAB”; “A” is less than “AA”). In general, characters are ordered according to their character codes. This means, for example, that “B” is less than “a”, since “B” is character code 66, and “a” is character code 97. For unit objects, the two objects must be dimensionally consistent, and are converted to common units for comparison. If you use simple temperature units, the calculator assumes the values represent temperatures and not differences in temperatures. For compound temperature units, the calculator assumes temperature units represent temperature differences. For more information on using temperature units with arithmetic functions, refer to the entry for +.
Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| x | y | → | 0/1 |
| #n1 | #n2 | → | 0/1 |
| “string1” | “string2” | → | 0/1 |
| x | `symb` | → | `x < symb` |
| `symb` | x | → | `symb < x` |
| `symb1` | `symb2` | → | `symb1 < symb2` |
| x_unit1 | y_unit2 | → | 0/1 |
| x_unit | `symb` | → | `x_unit < symb` |
| `symb` | x_unit | → | `symb < x_unit` |
≤, >, ≥, ==, ≠
Function
Less Than or Equal Function: Tests whether one object is less than or equal to another object. The function ≤ returns a true test result (1) if the first argument is less than or equal to the second argument, or a false test result (0) otherwise. If one object is a symbolic (an algebraic or a name), and the other is a number or symbolic or unit object, ≤ returns a symbolic comparison expression that can be evaluated to return a test result. For real numbers and binary integers, “less than or equal” means numerically equal or smaller (1 is less than 2). For real numbers, “less than or equal” also means equally or more negative (–2 is less than –1). For strings, “less than or equal” means alphabetically equal or previous (“ABC” is less than or equal to “DEF”; “AAA” is less than or equal to “AAB”; “A” is less than or equal to “AA”). In general, characters are ordered according to their character codes. This means, for example, that “B” is less than “a”, since “B” is character code 66, and “a” is character code 97. For unit objects, the two objects must be dimensionally consistent and are converted to common units for comparison. If you use simple temperature units, the calculator assumes the values represent temperature and not differences in temperatures. For compound temperature units, the calculator assumes temperature units represent temperature differences. For more information on using temperature units with arithmetic functions, refer to the entry for +.
Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| x | y | → | 0/1 |
| #n1 | #n2 | → | 0/1 |
| “string1” | “string2” | → | 0/1 |
| x | `symb` | → | `x ≤symb` |
| `symb` | x | → | `symb ≤x` |
| `symb1` | `symb2` | → | `symb1 ≤symb2` |
| x_unit1 | y_unit2 | → | 0/1 |
| x_unit | `symb` | → | `x_unit ≤symb` |
| `symb` | x_unit | → | `symb ≤x_unit` |
<, >, ≥, ==, ≠
Function
Greater Than Function: Tests whether one object is greater than another object. The function > returns a true test result (1) if the first argument is greater than the second argument, or a false test result (0) otherwise. If one object is a symbolic (an algebraic or a name), and the other is a number or symbolic or unit object, > returns a symbolic comparison expression that can be evaluated to return a test result. For real numbers and binary integers, “greater than” means numerically greater (2 is greater than 1). For real numbers, “greater than” also means less negative (–1 is greater than –2). For strings, “greater than” means alphabetically subsequent (“DEF” is greater than “ABC”; “AAB” is greater than “AAA”; “AA” is greater than “A”). In general, characters are ordered according to their character codes. This means, for example, that “a” is greater than “B”, since “B” is character code 66, and “a” is character code 97. For unit objects, the two objects must be dimensionally consistent and are converted to common units for comparison. If you use simple temperature units, the calculator assumes the values represent temperatures and not differences in temperatures. For compound temperature units, the calculator assumes temperature units represent temperature differences. For more information on using temperature units with arithmetic functions, refer to the entry for +.
Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| x | y | → | 0/1 |
| #n1 | #n2 | → | 0/1 |
| “string1” | “string2” | → | 0/1 |
| x | `symb` | → | `x > symb` |
| `symb` | x | → | `symb > x` |
| `symb1` | `symb2` | → | `symb1 > symb2` |
| x_unit1 | y_unit2 | → | 0/1 |
| x_unit | `symb` | → | `x_unit > symb` |
| `symb` | x_unit | → | `symb > x_unit` |
<, ≤, ≥, ==, ≠
Function
Greater Than or Equal Function: Tests whether one object is greater than or equal to another object. The function ≥ returns a true test result (1) if the first argument is greater than or equal to the second argument, or a false test result (0) otherwise. If one object is a symbolic (an algebraic or a name), and the other is a number or symbolic or unit object, ≥ returns a symbolic comparison expression that can be evaluated to return a test result. For real numbers and binary integers, “greater than or equal to” means numerically equal or greater (2 is greater than or equal to 1). For real numbers, “greater than or equal to” also means equally or less negative (–1 is greater than or equal to –2). For strings, “greater than or equal to” means alphabetically equal or subsequent (“DEF” is greater than or equal to “ABC”; “AAB” is greater than or equal to “AAA”; “AA” is greater than or equal to “A”). In general, characters are ordered according to their character codes. This means, for
example, that “a” is greater than or equal to “B”, since “B” is character code 66, and “a” is character code 97. For unit objects, the two objects must be dimensionally consistent and are converted to common units for comparison. If you use simple temperature units, the calculator assumes the values represent temperatures and not differences in temperatures. For compound temperature units, the calculator assumes temperature units represent temperature differences. For more information on using temperature units with arithmetic functions, refer to the entry for +.
Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| x | y | → | 0/1 |
| #n1 | #n2 | → | 0/1 |
| “string1” | “string2” | → | 0/1 |
| x | `symb` | → | `x ≥ symb` |
| `symb` | x | → | `symb ≥ x` |
| `symb1` | `symb2` | → | `symb1 ≥ symb2` |
| x_unit1 | y_unit2 | → | 0/1 |
| x_unit | `symb` | → | `x_unit ≥ symb` |
| `symb` | x_unit | → | `symb ≥ x_unit` |
<, ≤, >, ==, ≠
Function
Not Equal Function: Tests if two objects are not equal. The function ≠ returns a true result (1) if the two objects have different values, or a false result (0) otherwise. (Lists and programs are considered to have the same values if the objects they contain are identical.) If one object is algebraic or a name, and the other is a number, a name, or algebraic, ≠ returns a symbolic comparison expression that can be evaluated to return a test result. If the imaginary part of a complex number is 0, it is ignored when the complex number is compared to a real number, so, for example, 6 and (6,0) and considered to be equal. For unit objects, the two objects must be dimensionally consistent and are converted to common units for comparison. If you use simple temperature units, the calculator assumes the values represent temperatures and not differences in temperatures. For compound temperature units, the calculator assumes temperature units represent temperature differences. For more information on using temperature units with arithmetic functions, refer to the entry for +.
Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| obj1 | obj2 | → | 0/1 |
| (x,0) | x | → | 0/1 |
| x | (x,0) | → | 0/1 |
| z | `symb` | → | `z ≠ symb` |
| `symb` | z | → | `symb ≠ z` |
| `symb1` | `symb2` | → | `symb1 ≠symb2` |
SAME, TYPE, <, ≤, >,≥, ==, =
Function
Multiply Analytic Function: Returns the product of the arguments. The product of a real number a and a complex number (x, y) is the complex number (xa, ya). The product of two complex numbers (x1, y1) and (x2, y2) is the complex number (x1 x2 – y1 y2, x1 y2 + x2 y1). The product of a real array and a complex array or number is a complex array. Each element x of the real array is treated as a complex element (x, 0). Multiplying a matrix by an array returns a matrix product. The matrix must have the same number of columns as the array has rows (or elements, if it is a vector). Although a vector is entered and displayed as a row of numbers, the calculator treats a vector as an n × 1 matrix when multiplying matrices or computing matrix norms. Multiplying a binary integer by a real number returns a binary integer that is the product of the two arguments, truncated to the current wordsize. (The real number is converted to a binary integer before the multiplication.) The product of two binary integers is truncated to the current binary integer wordsize. When multiplying two unit objects, the scalar parts and the unit parts are multiplied separately.
Numerical Results (–3), Binary Integer Wordsize (–5 through –10)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| z1 | z2 | → | z1 z2 |
| [[ matrix ]] | [ array ] | → | [[ matrix × array ]] |
| z | [ array ] | → | [ z × array ] |
| [ array ] | z | → | [ array × z ] |
| z | `symb` | → | `z * symb` |
| `symb` | z | → | `symb * z` |
| `symb1` | `symb2` | → | `symb1 *symb2` |
| #n1 | n2 | → | #n3 |
| n1 | #n2 | → | #n3 |
| #n1 | #n2 | → | #n3 |
| x_unit | y_unit | → | xy_unitx × unity |
| x | y_unit | → | xy_unit |
| x_unit | y | → | xy_unit |
| `symb` | x_unit | → | `symb * x_unit` |
| x_unit | `symb` | → | `x_unit * symb` |
+, –, /, =
Function
Add Analytic Function: Returns the sum of the arguments. The sum of a real number a and a complex number (x, y) is the complex number (x+a, y). The sum of two complex numbers (x1, y1) and (x2, y2) is the complex number (x1+x2, y1+y2). The sum of a real array and a complex array is a complex array, where each element x of the real array is treated as a complex element (x, 0). The arrays must have the same dimensions. The sum of a binary integer and a real number is a binary integer that is the sum of the two arguments, truncated to the current wordsize. (The real number is converted to a binary integer before the addition.) The sum of two binary integers is truncated to the current binary integer wordsize. The sum of two unit objects is a unit object with the same dimensions as the second argument. The units of the two arguments must be consistent. The sum of two graphics objects is the same as the result of performing a logical OR, except that the two graphics objects must have the same dimensions. Common usage is ambiguous about some units of temperature. When °C or °F represents a thermometer reading, then the temperature is a unit with an additive constant: 0 °C = 273.15 K, and 0°F = 459.67°R. But when °C or °F represents a difference in thermometer readings, then the temperature is a unit with no additive constant: 1 °C=1 K and 1 °F =1 °R. The calculator assumes that the simple temperature units x_°C and x_°F represent thermometer temperatures when used as arguments to the functions <, >, ≤, ≥, ==, and ≠. This means that, in order to do the calculation, the calculator will first convert any Celsius temperature to Kelvin and any Fahrenheit temperature to Rankine. (For other functions or compound temperature units, such as x_°C/min, the calculator assumes temperature units represent temperature differences, so there is no additive constant involved, and hence no conversion.) The arithmetic operators +, –, %CH,
and %T treat temperatures as differences, without any additive constant, but require both arguments to be either absolute (K and °R), both °C, or both °F. No other combinations are allowed.
Numerical Results (–3), Binary Integer Wordsize (–5 through –10)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| z1 | z2 | → | z1 + z2 |
| [ array ]1 | [ array ]2 | → | [ array ]3 |
| z | `symb` | → | `z +symb` |
| `symb` | z | → | `symb +z` |
| `symb1` | `symb2` | → | `symb1 + symb2` |
| { list1 } | { list2 | → | { list1 list2 } |
| objA | { obj1 … objn } | → | { objA obj1 … objn } |
| { obj1 … objn } | objA | → | {obj1 … objn objA } |
| “string1” | “string2” | → | “string1 string2” |
| obj | “string” | → | “obj string” |
| “string” | obj | → | “string obj” |
| #n1 | n2 | → | #n3 |
| n1 | #n2 | → | #n3 |
| #n1 | #n2 | → | #n3 |
| x1_unit1 | y_unit2 | → | (x2 + y)_unit2 |
| `symb` | x_unit | → | `symb + x_unit` |
| x_unit | `symb` | → | `x_unit + symb` |
| grob1 | grob2 | → | grob3 |
| Example 1: { 1 2 3 } { A B C } + returns { 1 2 3 A B C }. | |||
| Example 2: 5_ft 9_in + returns 69_in. | |||
| Example 3: [[ 0 1 ][ 1 3 ]] [[ 2 1 ][ 0 1 ]] + returns | |||
| [[ 2 2 ][ 1 4 ]]. | |||
Example 4: `FIRST` `SECOND` + returns `FIRST+SECOND`. | |||
–, *, /, =, ADD
Function
Subtract Analytic Function: Returns the difference of the arguments. The difference of a real number a and a complex number (x, y) is (x–a, y) or (a–x, –y). The difference of two complex numbers (x1, y1) and (x2, y2) is (x1 – x2, y1 – y2). The difference of a real array and a complex array is a complex array, where each element x of the real array is treated as a complex element (x, 0). The two array arguments must have the same dimensions. The difference of a binary integer and a real number is a binary integer that is the sum of the first argument and the two’s complement of the second argument. (The real number is converted to a binary integer before the subtraction.)
The difference of two binary integers is a binary integer that is the sum of the first argument and the two’s complement of the second argument. The difference of two unit objects is a unit object with the same dimensions as the second argument. The units of the two arguments must be consistent. Common usage is ambiguous about some units of temperature. When °C or °F represents a thermometer reading, then the temperature is a unit with an additive constant: 0 °C = 273.15 K, and 0 °F = 459.67 °R. But when °C or °F represents a difference in thermometer readings, then the temperature is a unit with no additive constant: 1 °C = 1 K and 1 °F = 1 °R. The calculator assumes that the simple temperature units x_°C and x_°F represent thermometer temperatures when used as arguments to the functions <, >, ≤, ≥, ==, and ≠. This means that, in order to do the calculation, the calculator will first convert any Celsius temperature to Kelvin and any Fahrenheit temperature to Rankine. (For other functions or compound temperature units, such as x_°C/min, the calculator assumes temperature units represent temperature differences, so there is no additive constant involved, and hence no conversion.) The arithmetic operators +, –, %, %CH, and %T treat temperatures as differences, without any additive constant, but require both arguments to be either absolute (K and °R), both °C, or both °F. No other combinations are allowed.
Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| z1 | z2 | → | z1 – z2 |
| [ array ]1 | [ array ]2 | → | [ array ]1–2 |
| z | `symb` | → | `z – symb` |
| `symb` | z | → | `symb – z` |
| `symb1` | `symb2` | → | `symb1 – symb2` |
| #n1 | n2 | → | #n3 |
| n1 | #n2 | → | #n3 |
| #n1 | #n2 | → | #n3 |
| x1_unit1 | y_unit2 | → | (x2 – y)_unit2 |
| `symb` | x_unit | → | `symb – x_unit` |
| x_unit | `symb` | → | `x_unit – symb` |
| Example 1: 25_ft 8_in - returns 292_in. | |||
| Example 2: [[ 5 1 ][ 3 3 ]] [[ 2 1 ][ 0 1 ]] - returns | |||
| [[ 3 0 ][ 3 2 ]]. | |||
Example 3: `TOTAL` `PART` - returns `TOTAL-PART`. | |||
+, *, /, =
Function
Divide Analytic Function: Returns the quotient of the arguments: the first argument is divided by the second argument. A real number a divided by a complex number (x, y) returns:
- ---------------- ax , ------------------ ay
- 2 2 2 2
x +y x +y
A complex number (x, y) divided by a real number a returns the complex number (x/a, y/a). A complex number (x1, y1) divided by another complex number (x2, y2) returns this complex quotient: - x 1 x 2 + y 1 y 2 y 1 x 2 – x 1 y 2- - --------------------------- , ----------------------------
- x2 + y2 2
x +y - 2
2 2 2 2
An array B divided by a matrix A solves the system of equations AX=B for X; that is, X = A–1 B. This operation uses 15-digit internal precision, providing a more precise result than the calculation INV(A)*B. The matrix must be square, and must have the same number of columns as the array has rows (or elements, if the array is a vector). A binary integer divided by a real or binary number returns a binary integer that is the integral part of the quotient. (The real number is converted to a binary integer before the division.) A divisor of zero returns # 0. When dividing two unit objects, the scalar parts and the unit parts are divided separately.
Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| z1 | z2 | → | z1 / z2 |
| [ array ] | [[ matrix ]] | → | [[ matrix–1 ×array ]] |
| z | `symb` | → | `z /symb` |
| `symb` | z | → | `symb /z` |
| `symb1` | `symb2` | → | `symb1 / symb2` |
| #n1 | n2 | → | #n3 |
| n1 | #n2 | → | #n3 |
| #n1 | #n2 | → | #n3 |
| x_unit1 | y_unit2 | → | (x / y)_unit1/unit2 |
| x | y_unit | → | (x / y)_1/unit |
| x_unit | y | → | (x / y)_unit |
| `symb` | x_unit | → | `symb / x_unit` |
| x_unit | `symb` | → | `x_unit / symb` |
+, –, *, =
Function
Equals Analytic Function: Returns an equation formed from the two arguments. The equals sign equates two expressions such that the difference between them is zero. In Symbolic Results mode, the result is an algebraic equation. In Numerical Results mode, the result is the difference of the two arguments because = acts equivalent to –. This allows expressions and equations to be used interchangeably as arguments for symbolic and numerical rootfinders.
Common usage is ambiguous about some units of temperature. When °C or °F represents a thermometer reading, then the temperature is a unit with an additive constant: 0 °C = 273.15 K, and 0°F = 459.67°R. But when °C or °F represents a difference in thermometer readings, then the temperature is a unit with no additive constant: 1°C=1 K and 1°F = 1°R. The arithmetic operators +, –, %, %CH, and %T treat temperatures as differences, without any additive constant. However, +, –, %CH, and %T require both arguments to be either absolute (K and °R), both °C, or both °F. No other combinations are allowed.
Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| z1 | z2 | → | z1 = z2 |
| z | `symb` | → | `z = symb` |
| `symb` | z | → | `symb = z` |
| `symb1` | `symb2` | → | `symb1 = symb2` |
| y_unit | x | → | y_unit1 = x |
| y_unit | x_unit | → | y_unit1 = x_unit |
| `symb` | x_unit | → | `symb = x_unit` |
| x_unit | `symb` | → | `x_unit = symb` |
DEFINE, EVAL, –
Function
Logical Equality Function: Tests if two objects are equal. The function == returns a true result (1) if the two objects are the same type and have the same value, or a false result (0) otherwise. Lists and programs are considered to have the same values if the objects they contain are identical. If one object is algebraic (or a name), and the other is a number (real or complex) or an algebraic, == returns a symbolic comparison expression that can be evaluated to return a test result. Note that == is used for comparisons, while = separates two sides of an equation. If the imaginary part of a complex number is 0, it is ignored when the complex number is compared to a real number. For unit objects, the two objects must be dimensionally consistent and are converted to common units for comparison. If you use simple temperature units, the calculator assumes the values represent temperatures and not differences in temperatures. For compound temperature units, the calculator assumes temperature units represent temperature differences. For more information on using temperature units with arithmetic functions, refer to the entry for +.
Numerical Results (–3)
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| obj1 | obj2 | → | 0/1 |
| (x,0) | x | → | 0/1 |
| x | (x,0) | → | 0/1 |
| z | `symb` | → | `z == symb` |
| `symb` | z | → | `symb == z` |
| `symb1` | `symb2` | → | `symb1 == symb2` |
SAME, TYPE, <, ≤, >, ≥, ≠
Command
Store Command: Stores an object into a specified variable. To create a backup object, store the obj into the desired backup location (identified as :nport:namebackup). will not overwrite an existing backup object. To replace an element of an array or list, use STO. Also use STO to store a graphic object into PICT or a library or backup object into a port.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| obj | `name` | → | obj |
| obj | :nport :namebackup | → | obj |
DEFINE, RCL, →, STO
Command
Create Local Variables Command: Creates local variables. Local variable structures specify one or more local variables and a defining procedure.
A local variable structure consists of the → command, followed by one or more names, followed
by a defining procedure — either a program or an algebraic. The → command stores objects into
local variables with the specified names. The resultant local variables exist only while the defining procedure is being executed. The syntax of a local variable structure is one of the following:
• → name1 name2 … namen « program »
• → name1 name2 … namen `algebraic expression`
| Leveln/Argument1 7 Level1/Argumentn | Level 1/Item 1 | |
|---|---|---|
| obj1 … objn | → | |
| Example 1: | This program: | |
| « → x y « x y * x y - + » » | ||
| takes an object from level 2 and stores it in local variable x, takes an object from level 1 and stores it in local variable y, and executes calculations with x and y in the defining procedure (in this case a program). When the defining procedure ends, local variables x and y disappear. | ||
Example 2: A user-defined function is a variable containing a program that consists solely of a local variable | ||
| structure. For example, the variable A, containing this program: | ||
« → x y z `x*y/2+z` » | ||
| is a user-defined function. Like a built-in function, a user-defined function can take its arguments in stack syntax or algebraic syntax, and can take symbolic arguments. In addition, a user-defined function is differentiable if its defining procedure is an algebraic expression that contains only differentiable functions. | ||
DEFINE, LOCAL, STO
Command
Drop Safe Command: Removes the level 1 object from the stack if there is one, otherwise does nothing.
| Level 1 | Level 1 | |
|---|---|---|
| obj | → | |
| → | ||
CLEAR, DROP, DROPN, DROP2
Command
Restores the calculator stack to the state immediately before the most recent operation. Repeated UNDOs walk back through the saved undo ring buffer. Stack-mutating ops (commits, pushes, pops, ops with side effects) are recorded; mode and entry-buffer changes are not.
None
REDO, LASTSTACK
Command
Replays the most recently undone stack state. After UNDO walks back N steps, REDO walks forward one step at a time so long as no new mutating op has been issued (any new push / pop / op clears the redo buffer).
None
UNDO, LASTSTACK
Command
Synonym for UNDO — restores the previous stack snapshot. Provided so HP50 programs that call LASTSTACK keep working unchanged.
None
UNDO, REDO
Command
Splits a tagged object into its underlying value and tag string. The value is left at level 2 with the tag string at level 1, allowing the tag to be inspected, edited, or reattached with →TAG.
| Level 1/Argument 1 | Level 2/Item 1 | Level 1/Item 2 | |
|---|---|---|---|
| "tag":obj | → | obj | "tag" |
→TAG, DTAG
Function
Decimal Hours to Hours-Minutes-Seconds: converts a real number representing hours (or any HMS-compatible value) into HH.MMSSss notation. The integer part is whole hours, the next two digits are minutes, and the remaining digits are decimal seconds.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | HH.MMSSss |
HMS→D, →HMS, HMS→
Function
Hours-Minutes-Seconds to Decimal Hours: converts an HMS-formatted real number HH.MMSSss to a plain decimal hours value. Inverse of D→HMS.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| HH.MMSSss | → | x |
D→HMS, →HMS, HMS→
Function
Complex to Real: splits a complex number into its real and imaginary parts as two separate real numbers, with the real part at level 2 and the imaginary part at level 1.
| Level 1/Argument 1 | Level 2/Item 1 | Level 1/Item 2 | |
|---|---|---|---|
| (x, y) | → | x | y |
R→C, RE, IM
Function
Cartesian to Polar: converts a complex number from rectangular form (x, y) into polar form (r, θ), where r = √(x² + y²) and θ is the argument. The angle uses the current angle mode (DEG / RAD / GRD).
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| (x, y) | → | (r, θ) |
P→C, R→C, ARG
Function
Polar to Cartesian: converts a complex number from polar form (r, θ) into rectangular form (x, y), where x = r cos θ and y = r sin θ. The angle is interpreted in the current angle mode.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| (r, θ) | → | (x, y) |
C→P, R→C, RECT, CYLIN
Function
Returns 1 if the calculator is currently in Complex mode, 0 otherwise. Use it inside programs that need to gate complex-aware logic.
| Level 1/Item 1 | ||
|---|---|---|
| → | 0/1 |
CMPLX
Function
Pushes the boolean literal 1 (true). Useful as an explicit return value for predicate programs.
| Level 1/Item 1 | ||
|---|---|---|
| → | 1 |
FALSE, AND, OR, NOT
Function
Pushes the boolean literal 0 (false).
| Level 1/Item 1 | ||
|---|---|---|
| → | 0 |
TRUE, AND, OR, NOT
Command
Sets the angle mode to gradians (400 grad = 360°). Subsequent trig calls (SIN, COS, TAN, …) interpret their argument in grads. Same effect as setting flag –17 / –18 to the GRD combination.
None
DEG, RAD, GRAD
Command
Selects textbook (pretty-printed) display of expressions on the stack — fractions stack vertically, exponents render as superscripts, etc. Toggle off with FLAT.
None
FLAT
Command
Selects flat (linear) display of expressions on the stack — everything renders on one line in monospaced ASCII. Inverse of TEXTBOOK.
None
TEXTBOOK
Command
Clears the display-base override applied by HEX / DEC / OCT / BIN. After CLB, each binary integer renders in its stored base and at minimum width (no STWS padding) — the HP50-default behavior before any base mode has been set.
None
HEX, DEC, OCT, BIN, STWS
Command
Sets numeric (approximate) evaluation mode: subsequent evaluations replace exact constants like π or fractions with their floating-point approximations and short-circuit symbolic results. Equivalent to setting flag –3.
None
EXACT, →NUM
Command
Sets exact (symbolic) evaluation mode: subsequent evaluations preserve constants like π and exact rationals instead of folding them to floats. Inverse of APPROX.
None
APPROX, →NUM
Function
Returns the HP50 numeric type code of the level-1 object. Same encoding as TYPE for the types this app supports — Real = 0, Complex = 1, String = 2, Vector/Matrix = 3, List = 5, Name = 6, Symbolic = 9, Tagged = 12, Directory = 15, etc. Use TYPE in new code; KIND is provided for HP50 compatibility.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| obj | → | n |
TYPE, VTYPE
Command
Composes a program object from objects on the stack. Argument 1 is a positive integer n; the next n stack levels become the program body in order (level n at the start, level 1 at the end). An n of 0 produces an empty program « ».
| Levels n+1…2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| objₙ … obj₁ | n | → | « objₙ … obj₁ » |
OBJ→, →LIST, →ARRY
Command
Unwinds the currently-executing program (and any nested IF / WHILE / CASE / etc. frames) and returns control to the user. ABORT is not catchable by IFERR; the stack is left as it was at the moment of ABORT.
None
HALT, KILL, IFERR, DOERR
Command
Resumes a halted program at full speed, suppressing any single-step / step-into mode that may be active. Equivalent to CONT after clearing debug flags.
None
CONT, HALT, DBUG, SST
Function
Extended Euclidean algorithm for two integers. Given a and b, returns three integers u, v, and d = gcd(a, b) such that a·u + b·v = d. Wraps Bézout’s identity for HP50-style integer arithmetic.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 3/Item 1 | Level 2/Item 2 | Level 1/Item 3 | |
|---|---|---|---|---|---|
| a | b | → | u | v | d |
GCD, IEGCD, IABCUV
Command
Decompiles a program object into its source-string form, the same text the editor would show. Intended as a programming aid for inspecting compiled programs at runtime.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| « prg » | → | "« prg »" |
→STR, OBJ→, STR→
Function
Splits a rational symbolic expression into its numerator and denominator. Works on Symbolic, Integer, or Real arguments — bare numerics return {x, 1}. Inverse companion to →Q.
| Level 1/Argument 1 | Level 2/Item 1 | Level 1/Item 2 | |
|---|---|---|---|
| `a/b` | → | `a` | `b` |
→Q, →QΠ
Function
Rewrites tan(x) in a symbolic expression as sin(x)/cos(x), expanding tangent factors into their sine-cosine equivalents. Inverse direction of TAN2SC.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `symb` | → | `COSSIN(symb)` |
TAN2SC, HALFTAN, SINCOS
Function
Heaviside unit step function H(x): returns 0 for x < 0 and 1 for x ≥ 0. Numerical arguments fold immediately; symbolic arguments produce `HEAVISIDE(expr)` for downstream LAPLACE / piecewise work.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | 0/1 |
| `symb` | → | `HEAVISIDE(symb)` |
DIRAC, LAPLACE, ILAP
Function
Dirac delta distribution δ(x): folds non-zero numerics to 0; an exact zero stays symbolic as `DIRAC(0)` since the spike at the origin is singular. Symbolic arguments wrap as `DIRAC(expr)` for further LAPLACE work.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x ≠ 0 | → | 0 |
| 0 | → | `DIRAC(0)` |
| `symb` | → | `DIRAC(symb)` |
HEAVISIDE, LAPLACE, ILAP
Function
Laplace transform of a symbolic expression with respect to the current CAS variable VX. Routes through the Giac engine; the input must be Symbolic. Use ILAP for the inverse transform.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| `f(x)` | → | `LAPLACE(f)(x)` |
ILAP, HEAVISIDE, DIRAC, VX, SVX
Function
Pushes the name of the current CAS independent variable (default `X`) onto the stack as a Name. Used as the implicit variable for ops like DERVX / INTVX / LAPLACE. Set with SVX.
| Level 1/Item 1 | ||
|---|---|---|
| → | `name` |
SVX, DERVX, INTVX, LAPLACE
Command
Stores a new CAS independent variable. Argument 1 is a Name or String; subsequent uses of VX, DERVX, INTVX, LAPLACE, etc. operate on this variable.
| Level 1/Argument 1 | ||
|---|---|---|
| `name` | → |
VX, DERVX, INTVX
Function
Natural logarithm of the gamma function: returns ln Γ(x). Faster and numerically safer than `GAMMA LN` for large x. Accepts Real, Integer, or Vector / Matrix; symbolic arguments wrap as `LNGAMMA(symb)`.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | ln Γ(x) |
GAMMA, PSI
Function
Beta function: B(a, b) = Γ(a)·Γ(b) / Γ(a + b). Takes two real arguments at levels 2 and 1; symbolic arguments wrap as `BETA(a, b)`.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| a | b | → | B(a, b) |
GAMMA, LNGAMMA
Function
Gauss error function: erf(x) = (2/√π) ∫₀ˣ e^(−t²) dt. Folds Real / Integer / Vector / Matrix inputs; symbolic arguments wrap as `ERF(symb)`.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | erf(x) |
ERFC, GAMMA
Function
Complementary error function: erfc(x) = 1 − erf(x). Numerically more accurate than `1 ERF -` for large x.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | erfc(x) |
ERF, GAMMA
Function
Exponential integral Ei(x) = −∫_{−x}^∞ (e^{−t}/t) dt for x > 0; the Cauchy principal value is taken at the singularity at t = 0. Real / Integer arguments fold numerically; symbolic arguments wrap as `Ei(symb)`.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | Ei(x) |
CI, SI, GAMMA
Function
Cosine integral Ci(x) = γ + ln x + ∫₀ˣ ((cos t − 1)/t) dt for x > 0. Folds Real / Integer; symbolic arguments wrap as `Ci(symb)`.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | Ci(x) |
SI, EI
Function
Sine integral Si(x) = ∫₀ˣ (sin t / t) dt. Folds Real / Integer; symbolic arguments wrap as `Si(symb)`.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | Si(x) |
CI, EI
Function
Riemann zeta function ζ(s) = Σ_{n=1}^∞ n^{−s}. Folds Real / Integer / Vector / Matrix; symbolic arguments wrap as `ZETA(symb)`.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| s | → | ζ(s) |
GAMMA
Function
Principal branch of the Lambert W function: returns the W₀(x) such that W·e^W = x for x ≥ −1/e. Folds Real / Integer / Vector / Matrix; symbolic arguments wrap as `LAMBERT(symb)`.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| x | → | W(x) |
EXP, LN
Function
Euclidean norm of a vector or matrix. For a vector, returns √(Σxᵢ²); for a matrix, the Frobenius norm √(Σ|aᵢⱼ|²). Equivalent to ABS for arrays.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| [ vector ] | → | |vector| |
| [[ matrix ]] | → | |matrix| |
ABS, CNRM, RNRM
Command
Decomposes a matrix into its columns. A matrix on level 1 is replaced by its column count `c` on level 1, with c column vectors below it (left-most column at the deepest level).
| Level 1/Argument 1 | Levels k+1…1/Items | |
|---|---|---|
| [[ matrix ]] | → | [col₁] … [colₖ] k |
→COL, ROW→, →ROW
Function
Appends an object to the end of a list. Level 2 must be a list; level 1 is the object to append (any type). Returns a new list with the original elements followed by the new one.
| Level 2/Argument 1 | Level 1/Argument 2 | Level 1/Item 1 | |
|---|---|---|---|
| { obj₁ … objₙ } | objₐ | → | { obj₁ … objₙ objₐ } |
+, HEAD, TAIL, →LIST
Function
First-difference list: returns a new list whose i-th element is xᵢ − xᵢ₋₁ for the input list { x₁ x₂ … xₙ }. The output is always one element shorter than the input. Useful for smoothing and discrete-difference programs.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| { x₁ … xₙ } | → | { x₂−x₁ … xₙ−xₙ₋₁ } |
ΣLIST, ΠLIST, DLIST
Function
Adds the elements of a list or vector. All elements must be numeric (Real, Integer, or Complex); empty arguments return Integer(0). Symbolic arguments wrap as `Σ(expr)` for downstream evaluation.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| { x₁ … xₙ } | → | Σxᵢ |
| [ x₁ … xₙ ] | → | Σxᵢ |
ΣLIST, MEAN, ΣX
Function
Median of a vector or per-column median of a matrix. Uses the standard "average of two middle values" rule for even-length samples.
| Level 1/Argument 1 | Level 1/Item 1 | |
|---|---|---|
| [ vector ] | → | med |
| [[ matrix ]] | → | [ med per column ] |
MEAN, VAR, SDEV
Command
Store Max Exponent: sets the magnitude of the real-number exponent range. The argument must be an integer in [10, 9 × 10¹⁵]; after STMXE, MAXR equals 9.99999999999 × 10ᵉ and MINR equals 1 × 10⁻ᵉ, and the Decimal arithmetic engine clamps overflow to ±MAXR using this exponent. This is an rpl5050 extension with no HP50 equivalent.
| Level 1/Argument 1 | ||
|---|---|---|
| n | → |
RCMXE, MAXR, MINR
Function
Recall Max Exponent: pushes the current real-number exponent magnitude (set by STMXE) onto the stack as an Integer. Default is 999. rpl5050 extension with no HP50 equivalent.
| Level 1/Item 1 | ||
|---|---|---|
| → | n |
STMXE, MAXR, MINR