ApCoCoA-1:LinBox.CharPoly: Difference between revisions
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<command> | <command> | ||
<title>LinBox.CharPoly</title> | <title>LinBox.CharPoly</title> | ||
<short_description> | <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> | <description> | ||
< | <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/> | |||
This function returns the characteristic polynomial of <tt>M</tt> in the indeterminate <tt>X</tt> computed by the ApCoCoAServer using LinBox | 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> | <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> | <item>@return The characteristic polynomial of <tt>M</tt> in the indeterminate <tt>X</tt>.</item> | ||
</itemize> | </itemize> | ||
<example> | <example> | ||
Use R ::= | 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 | ||
| Line 21: | Line 23: | ||
x^3 + 4x^2 + x | x^3 + 4x^2 + x | ||
------------------------------- | ------------------------------- | ||
</example> | |||
Use R ::= | <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> | </description> | ||
<see>CharPoly</see> | |||
<types> | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> | ||
<see>ApCoCoA-1:LinAlg.CharPoly|LinAlg.CharPoly</see> | |||
</types> | <see>ApCoCoA-1:CharPoly|CharPoly</see> | ||
<key> | <types> | ||
<key> | <type>matrix</type> | ||
<key> | <type>apcocoaserver</type> | ||
<wiki-category>Package_linbox</wiki-category> | </types> | ||
<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 -------------------------------
