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

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{{Version|1}}
 
<command>
 
<command>
<title>Det</title>
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  <title>LinBox.Det</title>
<short_description>the determinant of a matrix</short_description>
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  <short_description>Computes the determinant of a matrix.</short_description>
 +
 
 
<syntax>
 
<syntax>
LinBox.Det(M:MAT)
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LinBox.Det(M:MAT):RAT, INT or ZMOD
 
 
the resulting type depends on the entries of the matrix.
 
 
</syntax>
 
</syntax>
<description>
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  <description>
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.
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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.
 
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<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 <tt>RAT</tt>, <tt>INT</tt> or <tt>ZMOD</tt>. The resulting type depends on the types of the entries of the matrix.
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<itemize>
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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>
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  <item>@return The determinant of <tt>A</tt>.</item>
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</itemize>
 
<example>
 
<example>
Use R ::= Q[x];
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Use R ::= QQ[x];
 
LinBox.Det(Mat([[1,2],[0,5]]));
 
LinBox.Det(Mat([[1,2],[0,5]]));
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
Line 17: Line 22:
 
5
 
5
 
-------------------------------
 
-------------------------------
 
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</example>
Use Z[x];
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<example>
 +
Use ZZ[x];
 
LinBox.Det(Mat([[1,2],[1,4]]));
 
LinBox.Det(Mat([[1,2],[1,4]]));
 
-- WARNING: Coeffs are not in a field
 
-- WARNING: Coeffs are not in a field
Line 31: Line 37:
 
-------------------------------
 
-------------------------------
 
</example>
 
</example>
</description>
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  </description>
<see>Det</see>
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<types>
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  <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see>
  <type>cocoaserver</type>
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  <see>ApCoCoA-1:LinAlg.Det|LinAlg.Det</see>
</types>
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  <see>ApCoCoA-1:Det|Det</see>
<key>det</key>
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  <types>
<key>determinant</key>
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    <type>matrix</type>
<key>kaspar</key>
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    <type>apcocoaserver</type>
<wiki-category>Package_LinBox</wiki-category>
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  </types>
 +
  <key>Det</key>
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  <key>LinBox.Det</key>
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  <key>linbox.Det</key>
 +
  <key>determinant</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.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

LinAlg.Det

Det