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

From ApCoCoAWiki

(Added additional "see" entry and fixed typo.) |
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<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | <em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | ||

<par/> | <par/> | ||

− | This function returns the characteristic polynomial of <tt>M</tt> in the indeterminate <tt>X</tt> computed by the ApCoCoAServer using functions of the | + | This function returns the characteristic polynomial of <tt>M</tt> in the indeterminate <tt>X</tt> computed by the ApCoCoAServer using functions of the LinBox library. |

<itemize> | <itemize> | ||

<item>@param <em>M</em> A matrix with arbitrary entries over the current ring, but whose components do not contain the indeterminate <tt>X</tt>.</item> | <item>@param <em>M</em> A matrix with arbitrary entries over the current ring, but whose components do not contain the indeterminate <tt>X</tt>.</item> | ||

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<see>Introduction to CoCoAServer</see> | <see>Introduction to CoCoAServer</see> | ||

+ | <see>LinAlg.CharPoly</see> | ||

<see>CharPoly</see> | <see>CharPoly</see> | ||

<types> | <types> |

## Revision as of 18:11, 19 November 2010

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