ApCoCoA-1:LinBox.CharPoly

CharPoly

characteristic polynomial of a matrix

Syntax

LinBox.CharPoly(M:MAT, X:POLY):LIST

Description

X is an indeterminate, and M is a square matrix whose entries do not involve X.

This function returns the characteristic polynomial of M in the indeterminate X computed by the ApCoCoAServer using LinBox functions.

Example

Use R ::= Z/(19)[x];
LinBox.CharPoly(BringIn(Mat([[1,2,3],[4,5,6],[7,8,9]])), x);
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
x^3 + 4x^2 + x
-------------------------------

Use R ::= Z[x];
LinBox.CharPoly(Mat([[1,2,3],[4,5,6],[7,8,9]]), x);
-- WARNING: Coeffs are not in a field
-- GBasis-related computations could fail to terminate or be wrong

-------------------------------
-- WARNING: Coeffs are not in a field
-- GBasis-related computations could fail to terminate or be wrong
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
x^3 - 15x^2 - 18x
-------------------------------

CharPoly