ApCoCoA-1:LinBox.CharPoly

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LinBox.CharPoly

Compute the 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.

  • @param M A matrix with whose components do not contain the indeterminate X.

  • @param X An indeterminate.

  • @return The characteristic polynomial of M in the indeterminate X.

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