CMAT is a matrix calculator program. Calculations can be performed
on matrices with complex rational coefficients (cmatcr.exe), using exact
arithmetic routines (cmatr), as well as on matrices with elements mod p,
p prime (cmatm.exe). The program can handle integers of arbitrary size.
Some of the routines available: addition, complex-conjugate transpose, scalar
multiplication, multiplication, exponentiation, Kronecker product, evaluating
matrix polynomials at a square matrix, elementary row and column operations,
inverse, adjoint, determinant, characteristic polynomialand minimum
polynomial, P^(-1)AP, the Cholesky decomposition of a positive definite
matrix, dot product, length and using the Gram-Schmidt process to find an
orthogonal basis for the column-space of a matrix, the Smith canonical form
of a matrix B with polynomial entries, etc.
In addition, polynomial routines are available including: addition, subtraction,
multiplication, scalar-multiplication, exponentiation, derivative,
evaluation, quotient, remainder, greatest common divisor, expressing
the gcd as a linear combination of the polynomials involved, square-free
decomposition, the resultant of two polynomials, the discriminant
of a polynomial, the Berlekamp matrix of a squarefree polynomial
mod p, factorization of polynomials with rational, complex rational
or mod p coefficients into irreducibles, etc.
(modified from the documentation)