ApCoCoA-1:LinAlg.CharPoly

This article is about a function from ApCoCoA-1.

LinAlg.CharPoly

Computes the characteristic polynomial of a matrix.

Syntax

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

Description

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.

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

• @param M A matrix with arbitrary entries over the current ring, but 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 ::= ZZ/(19)[x];
LinAlg.CharPoly(BringIn(Mat([[1,2,3],[4,5,6],[7,8,9]])), x);

-------------------------------
x^3 + 4x^2 + x
-------------------------------

Example

Use R ::= ZZ[x];
LinAlg.CharPoly(Mat([[1,2,3],[4,5,6],[7,8,9]]), x);

-------------------------------
x^3 - 15x^2 - 18x
-------------------------------

Introduction to CoCoAServer

LinBox.CharPoly

CharPoly