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

From ApCoCoAWiki
(Key and see section update.)
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{{Version|1}}
 
<command>
 
<command>
<title>LinBox.CharPoly</title>
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  <title>LinBox.CharPoly</title>
<short_description>Compute the characteristic polynomial of a matrix.</short_description>
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  <short_description>Computes the characteristic polynomial of a matrix.</short_description>
 +
 
 
<syntax>
 
<syntax>
 
LinBox.CharPoly(M:MAT, X:POLY):LIST
 
LinBox.CharPoly(M:MAT, X:POLY):LIST
 
</syntax>
 
</syntax>
<description>
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  <description>
<tt>X</tt> is an indeterminate, and <tt>M</tt> is a square matrix whose entries do not involve <tt>X</tt>.
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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.
 
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<par/>
This function returns the characteristic polynomial of <tt>M</tt> in the indeterminate <tt>X</tt> computed by the ApCoCoAServer using LinBox functions.
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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 whose components do not contain the indeterminate X.</item>
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   <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>X</em> An indeterminate.</item>
 
   <item>@param <em>X</em> An indeterminate.</item>
   <item>@return The characteristic polynomial of M in the indeterminate X.</item>
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   <item>@return The characteristic polynomial of <tt>M</tt> in the indeterminate <tt>X</tt>.</item>
 
</itemize>
 
</itemize>
 
<example>
 
<example>
Use R ::= Z/(19)[x];
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Use R ::= ZZ/(19)[x];
 
LinBox.CharPoly(BringIn(Mat([[1,2,3],[4,5,6],[7,8,9]])), x);
 
LinBox.CharPoly(BringIn(Mat([[1,2,3],[4,5,6],[7,8,9]])), x);
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
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x^3 + 4x^2 + x
 
x^3 + 4x^2 + x
 
-------------------------------
 
-------------------------------
 
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</example>
Use R ::= Z[x];
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<example>
 +
Use R ::= ZZ[x];
 
LinBox.CharPoly(Mat([[1,2,3],[4,5,6],[7,8,9]]), x);
 
LinBox.CharPoly(Mat([[1,2,3],[4,5,6],[7,8,9]]), x);
 
-- WARNING: Coeffs are not in a field
 
-- WARNING: Coeffs are not in a field
Line 35: Line 38:
 
-------------------------------
 
-------------------------------
 
</example>
 
</example>
</description>
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  </description>
<see>CharPoly</see>
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<types>
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  <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see>
  <type>cocoaserver</type>
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  <see>ApCoCoA-1:LinAlg.CharPoly|LinAlg.CharPoly</see>
</types>
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  <see>ApCoCoA-1:CharPoly|CharPoly</see>
<key>CharPoly</key>
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  <types>
<key>BB.CharPoly</key>
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    <type>matrix</type>
<key>borderbasis.CharPoly</key>
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    <type>apcocoaserver</type>
<key>characteristic polynomial</key>
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  </types>
<wiki-category>Package_linbox</wiki-category>
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  <key>CharPoly</key>
 +
  <key>linbox.CharPoly</key>
 +
  <key>characteristic polynomial</key>
 +
  <wiki-category>ApCoCoA-1:Package_linbox</wiki-category>
 
</command>
 
</command>

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