Difference between revisions of "ApCoCoA-1:LinBox.CharPoly"

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   <see>Introduction to CoCoAServer</see>
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   <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see>
   <see>LinAlg.CharPoly</see>
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   <see>ApCoCoA-1:LinAlg.CharPoly|LinAlg.CharPoly</see>
   <see>CharPoly</see>
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   <key>characteristic polynomial</key>
 
   <key>characteristic polynomial</key>
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Latest revision as of 10:11, 7 October 2020

This article is about a function from ApCoCoA-1.

LinBox.CharPoly

Computes the characteristic polynomial of a matrix.

Syntax

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

Example

Use R ::= ZZ[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
-------------------------------

Introduction to CoCoAServer

LinAlg.CharPoly

CharPoly