Difference between revisions of "ApCoCoA-1:LinAlg.EF"
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(New page: <command> <title>LinAlg.REF</title> <short_description>Computes a row echelon form of a matrix.</short_description> <syntax> LinAlg.REF(M:MAT, CompRREF:BOOL, BACKEND:STRING):MAT Lin...) |
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| − | <title>LinAlg. | + | <title>LinAlg.EF</title> |
| − | <short_description>Computes a row echelon form of a matrix.</short_description> | + | <short_description>Computes a row echelon form of a matrix with recond keeping.</short_description> |
<syntax> | <syntax> | ||
| − | LinAlg. | + | LinAlg.EF(M:MAT, L1:LIST, L2:LIST):MAT |
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</syntax> | </syntax> | ||
<description> | <description> | ||
<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. | ||
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| − | This function allows you to compute a | + | This function allows you to compute a row echelon form of a matrix <tt>M</tt> defined over the field <tt>F_2</tt>. |
<par/> | <par/> | ||
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The parameter <tt>CompRREF</tt> lets you specify if you want to compute a row echelon form or the reduced row echelon form of <tt>M</tt>. If <tt>CompRREF</tt> is set to <tt>TRUE</tt>, the reduced row echelon form will be computed, and if it is set to <tt>FALSE</tt>, a row echelon form where all pivot elements are equal to one will be computed. | The parameter <tt>CompRREF</tt> lets you specify if you want to compute a row echelon form or the reduced row echelon form of <tt>M</tt>. If <tt>CompRREF</tt> is set to <tt>TRUE</tt>, the reduced row echelon form will be computed, and if it is set to <tt>FALSE</tt>, a row echelon form where all pivot elements are equal to one will be computed. | ||
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<itemize> | <itemize> | ||
| − | <item>@param <em>M</em> A matrix whose | + | <item>@param <em>M:</em> A matrix whose row echelon form to compute.</item> |
| − | <item>@param <em> | + | <item>@param <em>L1:</em> List of integers.</item> |
| − | <item>@ | + | <item>@param <em>L2:</em> List of integers.</item> |
| − | + | <item>@return A row echelon form of <tt>M</tt> together with lists L1 and L2.</item> | |
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</itemize> | </itemize> | ||
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<example> | <example> | ||
| − | Use | + | Use ZZ/(2)[x,y]; |
M := Mat([[ 1/2, 1/3, 2], [200, 3000, 1], [2, 5, 17], [1, 1, 1]]); | M := Mat([[ 1/2, 1/3, 2], [200, 3000, 1], [2, 5, 17], [1, 1, 1]]); | ||
LinAlg.REF(M, FALSE); | LinAlg.REF(M, FALSE); | ||
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</example> | </example> | ||
<example> | <example> | ||
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LinAlg.REF(M, 17, TRUE); | LinAlg.REF(M, 17, TRUE); | ||
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</example> | </example> | ||
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</description> | </description> | ||
<see>Introduction to CoCoAServer</see> | <see>Introduction to CoCoAServer</see> | ||
Revision as of 11:53, 7 December 2010
LinAlg.EF
Computes a row echelon form of a matrix with recond keeping.
Syntax
LinAlg.EF(M:MAT, L1:LIST, L2:LIST):MAT
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 allows you to compute a row echelon form of a matrix M defined over the field F_2.
The parameter CompRREF lets you specify if you want to compute a row echelon form or the reduced row echelon form of M. If CompRREF is set to TRUE, the reduced row echelon form will be computed, and if it is set to FALSE, a row echelon form where all pivot elements are equal to one will be computed.
@param M: A matrix whose row echelon form to compute.
@param L1: List of integers.
@param L2: List of integers.
@return A row echelon form of M together with lists L1 and L2.
Example
Use ZZ/(2)[x,y]; M := Mat([[ 1/2, 1/3, 2], [200, 3000, 1], [2, 5, 17], [1, 1, 1]]); LinAlg.REF(M, FALSE);
Example
Use QQ[x,y]; M := Mat([[ 1, 1, 2], [200, 3000, 1], [2, 5, 17], [1, 1, 1]]); LinAlg.REF(M, 17, TRUE);
