Next: Implementation notes.
Up: Introduction.
Previous: Introduction.
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.