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

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{{Version|1}}
 
<command>
 
<command>
    <title>borderbasis.GenHomMultMat</title>
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  <title>BB.GenHomMultMat</title>
    <short_description>Compute generic hom. mult. matrix w.r.t. order ideal</short_description>
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  <short_description>Computes a generic homogeneous multiplication matrix.</short_description>
 +
 
 
<syntax>
 
<syntax>
$borderbasis.GenHomMultMat(I:INT,OO:LIST):MAT
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BB.GenHomMultMat(I:INT,OO:LIST):MAT
 
</syntax>
 
</syntax>
    <description>
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  <description>
Computes the generic homogeneous 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 homogeneous multiplication matrix for <tt>x[I]</tt> with respect to an order ideal. The inputs are an integer <tt>I</tt> and a list <tt>OO</tt> of terms that specify 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 homogeneous multiplication matrix will be computed.</item>
    <key>borderbasis.genhommultmat</key>
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  <item>@param <em>OO</em> A list of terms representing an order ideal.</item>
    <key>borderbasisgenhommultmat</key>
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  <item>@return The generic homogeneous multiplication matrix.</item>
    <wiki-category>Package_borderbasis</wiki-category>
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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.GenHomMultMat(1, [1, x, x^2, y, z]);
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 +
-------------------------------
 +
Mat([
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  [0, 0, 0, 0, 0],
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  [1, 0, 0, 0, 0],
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  [0, 1, 0, BBS :: c[3,5], BBS :: c[3,3]],
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  [0, 0, 0, 0, 0],
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  [0, 0, 0, 0, 0]
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])
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-------------------------------
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</example>
 +
  </description>
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  <types>
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     <type>borderbasis</type>
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     <type>matrix</type>
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  </types>
 +
  <key>GenHomMultMat</key>
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  <key>BB.GenHomMultMat</key>
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  <key>borderbasis.GenHomMultMat</key>
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  <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.GenHomMultMat

Computes a generic homogeneous multiplication matrix.

Syntax

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

Description

Computes the generic homogeneous multiplication matrix for x[I] with respect to an order ideal. The inputs are an integer I and a list OO of terms that specify 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 homogeneous multiplication matrix will be computed.

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

  • @return The generic homogeneous multiplication matrix.

Example

Use QQ[x, y, z], DegRevLex;
BB.GenHomMultMat(1, [1, x, x^2, y, z]);

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