Difference between revisions of "ApCoCoA-1:BB.GenMultMat"

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m (insert version info)
 
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{{Version|1}}
 
<command>
 
<command>
    <title>borderbasis.GenMultMat</title>
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  <title>BB.GenMultMat</title>
    <short_description>generic multiplication matrix</short_description>
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  <short_description>Computes a generic multiplication matrix.</short_description>
 +
 
 
<syntax>
 
<syntax>
$borderbasis.GenMultMat(I:INT,OO:LIST):MAT
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BB.GenMultMat(I:INT,OO:LIST):MAT
 
</syntax>
 
</syntax>
    <description>
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  <description>
Computes the generic multiplication matrix for <formula>x[I]</formula> with respect to the order ideal OO. The input is a positive integer I and an order ideal OO (2nd element of type POLY). The output is a matrix of size <formula>Mu<times/>Mu</formula> over the ring <formula>BBS=K[c_{ij}]</formula>.
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Computes the generic multiplication matrix for the <tt>I</tt>-th indeterminate with respect to an order ideal. The second element of <tt>OO</tt> must be a non-constant polynomial. The output is a matrix of size <ref>CoCoA:Len|Len</ref>(OO) x <ref>CoCoA:Len|Len</ref>(OO) over the ring <tt>BBS=K[c_{ij}]</tt>.
     </description>
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<itemize>
     <key>kreuzer</key>
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  <item>@param <em>I</em> An integer which specifies the indeterminate for which the generic multiplication matrix will be computed.</item>
    <key>borderbasis.genmultmat</key>
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  <item>@param <em>OO</em> A list of terms representing an order ideal.</item>
    <wiki-category>Package_borderbasis</wiki-category>
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  <item>@return The generic multiplication matrix.</item>
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</itemize>
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<example>
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Use QQ[x, y, z], DegRevLex;
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BB.GenMultMat(1, [1, x, y, z]);
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 +
-------------------------------
 +
Mat([
 +
  [0, BBS :: c[1,6], BBS :: c[1,5], BBS :: c[1,3]],
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  [1, BBS :: c[2,6], BBS :: c[2,5], BBS :: c[2,3]],
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  [0, BBS :: c[3,6], BBS :: c[3,5], BBS :: c[3,3]],
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  [0, BBS :: c[4,6], BBS :: c[4,5], BBS :: c[4,3]]
 +
])
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-------------------------------
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</example>
 +
  </description>
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  <types>
 +
     <type>borderbasis</type>
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     <type>matrix</type>
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  </types>
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  <key>GenMultMat</key>
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  <key>BB.GenMultMat</key>
 +
  <key>borderbasis.GenMultMat</key>
 +
  <wiki-category>ApCoCoA-1:Package_borderbasis</wiki-category>
 
</command>
 
</command>

Latest revision as of 09:40, 7 October 2020

This article is about a function from ApCoCoA-1.

BB.GenMultMat

Computes a generic multiplication matrix.

Syntax

BB.GenMultMat(I:INT,OO:LIST):MAT

Description

Computes the generic multiplication matrix for the I-th indeterminate with respect to an order ideal. The second element of OO must be a non-constant polynomial. The output is a matrix of size Len(OO) x Len(OO) over the ring BBS=K[c_{ij}].

  • @param I An integer which specifies the indeterminate for which the generic multiplication matrix will be computed.

  • @param OO A list of terms representing an order ideal.

  • @return The generic multiplication matrix.

Example

Use QQ[x, y, z], DegRevLex;
BB.GenMultMat(1, [1, x, y, z]);

-------------------------------
Mat([
  [0, BBS :: c[1,6], BBS :: c[1,5], BBS :: c[1,3]],
  [1, BBS :: c[2,6], BBS :: c[2,5], BBS :: c[2,3]],
  [0, BBS :: c[3,6], BBS :: c[3,5], BBS :: c[3,3]],
  [0, BBS :: c[4,6], BBS :: c[4,5], BBS :: c[4,3]]
])
-------------------------------