Overview.

 

ALGB is made of:

• a library (24.5K for the G/GX version or 27K for the SX version):
  • integer, complex, quadratic irrational, polynomial and fraction arithmetic (operations, integration, derivation, simplifications, GCD algorithm, factorization over or ,...)
  • polynomial symbolic/numeric rootfinder (symbolic roots of a numerical polynomial, roots of some symbolic polynomials)
  • symbolic/numeric matrices utilities (operations, trace, transpose, inverse, characteristic polynomial, determinant, row reduction to echelon form with the possibility to follow the reduction step by step).
  • conversions (symbolic fractions to lists, symbolic to numeric matrices, symbolic to numeric polynomials, ...)
• modules (0 to 20K): other functions. They are independant, you can install 0, 1, 2, ... or all modules.
  • TSIMP program for simplification of transcendental functions
  • risch program for symbolic integration
  • MATR directory for symbolic or numeric matrices:
    • DIAG: eigenvalues and eigenvectors (including Jordan cycles of characteristic vectors),
    • RED: rank of a matrix, formal inverse and determinant by row reduction, solution of linear systems (including underdetermined systems).
  • FUNC directory with the enhanced TAYLR to get Taylor expansion,
  • INTG directory, the complement of risch:
    • INT: symbolic integration of rational fraction of x or of or of and of , partial fraction decomposition over or , inverse Laplace transform of rational fractions,
    • LDEC: solutions of systems of first order linear differential equations with constant coefficient.
    • LIN: linearization of trigonometric polynomials
  • QUADR directory with the GAUSS program to get Gauss orthogonalization of quadratic forms
  • ARIT has some arithmetic utilities.