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

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{{Version|1}}
 
<command>
 
<command>
 
   <title>BB.GenHomMultMat</title>
 
   <title>BB.GenHomMultMat</title>
   <short_description>Compute a generic homogeneous multiplication matrix.</short_description>
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   <short_description>Computes a generic homogeneous multiplication matrix.</short_description>
 
    
 
    
 
<syntax>
 
<syntax>
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</syntax>
 
</syntax>
 
   <description>
 
   <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 <ref>Len</ref>(OO) x <ref>Len</ref>(OO) over the ring BBS=K[c_{ij}].
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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>.
 
<itemize>
 
<itemize>
   <item>@param <em>I</em> The generic homogeneous multiplication matrix for the indeterminate x[I] will be computed.</item>
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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>
 
   <item>@param <em>OO</em> A list of terms representing an order ideal.</item>
 
   <item>@param <em>OO</em> A list of terms representing an order ideal.</item>
   <item>@return The generic homogeneous multiplication matrix for the indeterminate x[I] over the ring BBS=K[c_{ij}].</item>
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   <item>@return The generic homogeneous multiplication matrix.</item>
 
</itemize>
 
</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([
 +
  [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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</example>
 
   </description>
 
   </description>
 
   <types>
 
   <types>
 
     <type>borderbasis</type>
 
     <type>borderbasis</type>
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    <type>matrix</type>
 
   </types>
 
   </types>
 
   <key>GenHomMultMat</key>
 
   <key>GenHomMultMat</key>
 
   <key>BB.GenHomMultMat</key>
 
   <key>BB.GenHomMultMat</key>
 
   <key>borderbasis.GenHomMultMat</key>
 
   <key>borderbasis.GenHomMultMat</key>
   <wiki-category>Package_borderbasis</wiki-category>
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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]
])
-------------------------------