ApCoCoA-1:LinBox.CharPoly: Difference between revisions
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<command> | <command> | ||
<title>LinBox.CharPoly</title> | <title>LinBox.CharPoly</title> | ||
<short_description>Compute the characteristic polynomial of a matrix.</short_description> | <short_description>Compute the characteristic polynomial of a matrix.</short_description> | ||
<syntax> | <syntax>LinBox.CharPoly(M:MAT, X:POLY):LIST</syntax> | ||
LinBox.CharPoly(M:MAT, X:POLY):LIST | <description> | ||
</syntax> | <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. | ||
<description> | <par/> | ||
<tt>X</tt> is an indeterminate, and <tt>M</tt> is a square matrix whose entries do not involve <tt>X</tt>. | <tt>X</tt> is an indeterminate, and <tt>M</tt> is a square matrix whose entries do not involve <tt>X</tt>. 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 LinBox functions. | |||
<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 whose components do not contain the indeterminate X.</item> | ||
| Line 36: | Line 34: | ||
------------------------------- | ------------------------------- | ||
</example> | </example> | ||
</description> | </description> | ||
<see>CharPoly</see> | <see>CharPoly</see> | ||
<types> | <types> | ||
<type>matrix</type> | |||
<type>apcocoaserver</type> | |||
</types> | </types> | ||
<key>CharPoly</key> | <key>CharPoly</key> | ||
<key>BB.CharPoly</key> | <key>BB.CharPoly</key> | ||
<key>borderbasis.CharPoly</key> | <key>borderbasis.CharPoly</key> | ||
<key>characteristic polynomial</key> | <key>characteristic polynomial</key> | ||
<wiki-category>Package_linbox</wiki-category> | <wiki-category>Package_linbox</wiki-category> | ||
</command> | </command> | ||
Revision as of 11:48, 24 April 2009
LinBox.CharPoly
Compute 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.
X is an indeterminate, and M is a square matrix whose entries do not involve X. This function returns the characteristic polynomial of M in the indeterminate X computed by the ApCoCoAServer using LinBox functions.
@param M A matrix with 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 -------------------------------
