Difference between revisions of "ApCoCoA-1:LinBox.Det"
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| + | {{Version|1}} | ||
<command> | <command> | ||
| − | <title>LinBox.Det</title> | + | <title>LinBox.Det</title> |
| − | <short_description>the determinant of a matrix</short_description> | + | <short_description>Computes the determinant of a matrix.</short_description> |
| + | |||
<syntax> | <syntax> | ||
| − | LinBox.Det(M:MAT) | + | LinBox.Det(M:MAT):RAT, INT or ZMOD |
| − | |||
| − | |||
</syntax> | </syntax> | ||
| − | <description> | + | <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. | + | <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 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> | ||
| + | <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 <tt>A</tt>.</item> | ||
| + | </itemize> | ||
<example> | <example> | ||
| − | Use R ::= | + | 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 | ||
------------------------------- | ------------------------------- | ||
| − | + | </example> | |
| − | Use | + | <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> | + | </description> |
| − | <see>Det</see> | + | |
| − | <types> | + | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> |
| − | + | <see>ApCoCoA-1:LinAlg.Det|LinAlg.Det</see> | |
| − | </types> | + | <see>ApCoCoA-1:Det|Det</see> |
| − | <key> | + | <types> |
| − | <key> | + | <type>matrix</type> |
| − | <key> | + | <type>apcocoaserver</type> |
| − | <wiki-category> | + | </types> |
| + | <key>Det</key> | ||
| + | <key>LinBox.Det</key> | ||
| + | <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 -------------------------------
