Matrices [HB 62]

New Features:

• The algorithm to compute determinants of matrices over $\mbox{\bf Z}$ or $\mbox{\bf Q}$ has been greatly improved by first using the sparse Smith-algorithm techniques, and then using the modular algorithm of Abbott, Bronstein and Mulders.
• A new algorithm of Allan Steel for computing minimal and characteristic polynomials of matrices over $\mbox{\bf Z}$ or $\mbox{\bf Q}$ has been implemented. This is based on the p-adic nullspace algorithm and so is very much faster than the previous algorithm.
• New function MinimalAndCharacteristicPolynomials to compute the minimal and characteristic polynomials simultaneously (faster over some rings than calling the separate functions), and new functions FactoredMinimalAndCharacteristicPolynomials, FactoredMinimalPolynomial, and FactoredCharacteristicPolynomial which are faster over some rings than calling Factorization on the minimal or characteristic polynomials.
• New function AntisymmetricMatrix to create an antisymmetric matrix.