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

From ApCoCoAWiki
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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 LinBox functions.
+
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>

Revision as of 13:29, 7 July 2009

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

CharPoly