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Generalities

To ensure exact results ALG48 only works with integer and rational numbers and produces a ``Bad Argument Type'' error if it finds a fractional number in the input. If the expressions you have contain fractional numbers, you must convert them first into rational numbers by using the command ->Q or ->Qp of the HP48, or by using the program QPI © by Mika Heiskanen. An advantage of QPI is that it will also convert real arrays into symbolic matrices and complex numbers in (a,b) form into the a+bi form, appropriate for ALG48.

The commands in ALG48 can be divided into eight groups, according to the kind of operations they perform:

  1. Simplification commands: RSIM FCTR ASIM RORD RAT->
    They are used to simplify symbolic expressions or all the elements of a symbolic matrix or vector.
  2. Basic operations commands: AADD ASUB ANEG AMUL ADIV AINV APOW
    They are used to do basic calculation (+ - +/- * / 1/x ^ ) on several kind of objects:
  3. Gröbner bases commands: GBASIS GSIMP GSOLVE
    They are used to solve systems of nonlinear polynomial equations.
  4. Symbolic matrix commands: MDET MLU MTRN MIDN
    Perform specific operations on symbolic matrices.
  5. Calculus commands: PF RINT
    Perform partial fraction expansion and integration on symbolic rational functions.
  6. Algebraic commands: GCD LCM
    Perform specific operations on polynomials or unlimited precision integers.
  7. Modular arithmetic: MOD+ MOD- MOD* MOD/ MODPOW MODINV
    Perform modular arithmetic operations on unlimited precision integers.
  8. Prime number operations: PRIM? PRIM+ PRIM-
    Perform operations related to prime numbers on unlimited precision integers.

We describe below how to use these groups of commands to manipulate different kinds of objects. The Command Reference in appendix gives a brief definition and the stack diagram of each command.


Claude-Nicolas Fiechter (fiechter@cs.pitt.edu), 12 May 1998