# ApCoCoA-1:LinBox.CharPoly

From ApCoCoAWiki

## 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 -------------------------------