There are numerous algorithms that calculate the roots of single-variable nonlinear functions. The most popular of such algorithms is Newton's method. The slowest and simplest root seeking algorithm is the Bisection method. This method has the user select an interval that contains the sought root. The method iteratively shrinks the root-bracketing interval to zoom in on the sought root.
Calculates a bolt pattern given X (center, X coordinate), Y (center, Y coordinate), N (number of bolts), and D (diameter of the circle). No angle of rotation is assumed.
An initial version of a library of complex functions, including the argument of a complex number given in Cartesian form (x,y) and conversion from polar to Cartesian form.
Performs operations with Gaussian reduction (elimination), extending the tools that the Prime has already (LU, pivot, ref, RREF, etc.). Contains the following tools: Pivots (an algorithm to calculate pivots that does a "partial pivoting", returning a matrix with pivots in diagonal and upper matrix), LU_ext (an extension of the lu() command, to treat also a non square matrix and echelon forms), LDLt (performs a transposition of a symmetric and square matrix into lower, diagonal and upper), LDU (a factorization of lower, diagonal, and upper for a square matrix), echelon (returns both ref(m) and RREF(m), echelon forms), and permMatrix (given a list {} or a matrix [] with the number of rows to permute, it gives the matrix of permutation).
Horizontal curve calculator where you enter the curve data you have and let it calculate the rest. If one of your inputs is degree curve it will prompt for chord or arc definition. After it calculates the curve data you press OK or "Enter" to bring up the next screen with the areas.
Lambda Calculus expression evaluator based on the Spreadsheet app. Use the spreadsheet as a dictionary of lambda expressions, each named with an ID. Perform evaluations by specifying 2 or 3 IDs to be applied to each other. This version uses De Brujin indices instead of normal notation. The next version will use De Brujin indices behind-the-scenes. Various expressions are included. Church Numerals are recognized automatically. This version is also limited to performing applications with 2 or 3 terms; a future version will support free-form entry of terms (using ID, not lambda expressions) for evaluation.
Two little CAS programs to calculate line integral (vector functions) and curvilinear integral (scalar function). These programs work with 2 or 3 components (parametric expression: [r(t), r(t), r(t)] or [r(t), r(t)]).
Also known as a pseudoinverse, calculates the Moore-Penrose inverse of a matrix, denoted by A^+ (capital A with a supersubscript of a plus sign), is an inverse of matrix. Different from the "true" matrix inverse, the Moore-Penrose inverse allows for non-square matrices. Primarily, the Moore-Penrose inverses are calculated is assist in solving linear least-square equations.
Two versions of a program to calculate multinomial coefficients. The program accepts an integer for "n" (total of k) and a list with brackets {} for the list of the k (like {1,4,4,2}) and gives an integer that represents permutations in a multi set.
PDQ finds best rational approximations, with infinite precision. This means it finds the two smallest integers whose ratio is equal to some target real number plus or minus some desired tolerance. In other words, it finds the simplest fraction in any given interval. Unlike other methods, it always finds the unique best answer, and uses the infinite precision of CAS long integers.
A set of three tools for dealing with primitive roots. One returns the smallest primitive root, one returns a list of all primitive roots, and one returns the next primitive root that is larger than the given value.
Two functions for solving differential equations using the Runge Kutta 4th Order, one that takes all five arguments as parameters and the other that uses an input box.
Helps you to find the distance, the slope and the equation between two points, the perpendicular distance between a point and a straight line, Collinearity of three points: (the middle-point & the End-Point coordinates), the equation of a straight line that goes through a point with a slope, transforms linear equations back and forth between standard and slope-intercept forms, generates the coordinate representation of a straight line, determines whether two straight lines are parallel or perpendicular, finds the (x) & (y) intercepts of a straight line, finds the intersection point of 2 straight lines, transform a none standard from equation into a standardized form of it.
Creates a list with station and elevation information in L0. If a value between the VPC and VPT is entered in "Special Station", it returns data for that station only, if left at 0 the entire curve will be returned at the interval specified.