SharedMeatAxe 1.0
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zcp Options [-Gfm] Matrix
This program reads in a square matrix and calculates its characteristic or minimal polynomial. With no options, the characteristic polynomial is computed in a partially factored form (see below). With "-m" the polynomial is split into irreducible factors. Without "-G", the output is in text format. Each line contains one factor of the characteristic or minimal polynomial. The "-G" option may be used to generate output which is readable by the GAP computer program. The output, then, is a sequence of sequences of finite field elements, representing the coefficients of the factors in ascending order.
The characteristic polynomial of a matrix A is computed by constructing a sequence
of A-invariant subspaces, where
The algorithm for the minimal polynomial uses the same technique of constructing a sequence