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 | + | 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> | ||
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 -------------------------------
