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

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 determinant of the square matrix <tt>M</tt> computed by the ApCoCoAServer using LinBox functions. Please note that in contrary to the built in CoCoA <tt>Det</tt> function the entries of <tt>M</tt> are only allowed to be of type RAT, INT or ZMOD. The resulting type depends on the types of the entries of the matrix.
+
This function returns the determinant of the square matrix <tt>M</tt> computed by the ApCoCoAServer using LinBox functions. Please note that in contrary to the built in CoCoA <tt>Det</tt> function the entries of <tt>M</tt> are only allowed to be of type <tt>RAT</tt>, <tt>INT</tt> or <tt>ZMOD</tt>. The resulting type depends on the types of the entries of the matrix.
 
<itemize>
 
<itemize>
   <item>@param <em>M</em> A square matrix whose components are either of type INT, RAT or ZMOD.</item>
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   <item>@param <em>M</em> A square matrix whose components are either of type <tt>INT</tt>, <tt>RAT</tt> or <tt>ZMOD</tt>.</item>
   <item>@return The determinant of A.</item>
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   <item>@return The determinant of <tt>A</tt>.</item>
 
</itemize>
 
</itemize>
 
<example>
 
<example>

Revision as of 13:40, 7 July 2009

LinBox.Det

Computes the determinant of a matrix.

Syntax

LinBox.Det(M:MAT):RAT, INT or ZMOD

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 determinant of the square matrix M computed by the ApCoCoAServer using LinBox functions. Please note that in contrary to the built in CoCoA Det function the entries of M are only allowed to be of type RAT, INT or ZMOD. The resulting type depends on the types of the entries of the matrix.

  • @param M A square matrix whose components are either of type INT, RAT or ZMOD.

  • @return The determinant of A.

Example

Use R ::= QQ[x];
LinBox.Det(Mat([[1,2],[0,5]]));
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
5
-------------------------------

Example

Use ZZ[x];
LinBox.Det(Mat([[1,2],[1,4]]));
-- 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
-------------------------------
2
-------------------------------

Introduction to CoCoAServer

Det