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

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{{Version|1}}
 
<command>
 
<command>
 
   <title>BB.MultMat</title>
 
   <title>BB.MultMat</title>
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</syntax>
 
</syntax>
 
   <description>
 
   <description>
Computes the <tt>I</tt>-th multiplication matrix associated to the given input <tt>OO</tt>-border basis <tt>BB</tt> where <tt>I</tt> is an index number in the range 1..<ref>NumIndets</ref>().
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Computes the <tt>I</tt>-th multiplication matrix associated to the given input <tt>OO</tt>-border basis <tt>BB</tt> of the ideal generated by the polynomials of <tt>BB</tt> where <tt>I</tt> is an index number in the range 1..<ref>ApCoCoA-1:NumIndets|NumIndets</ref>().
 
The output is a matrix.
 
The output is a matrix.
 
<itemize>
 
<itemize>
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   <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>@param <em>BB</em> A list of terms representing the <tt>OO</tt>-border basis of the ideal generated by the polynomials of <tt>BB</tt>.</item>
 
   <item>@param <em>BB</em> A list of terms representing the <tt>OO</tt>-border basis of the ideal generated by the polynomials of <tt>BB</tt>.</item>
   <item>@return A matrix.</item>
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   <item>@return The <tt>I</tt>-th multiplication matrix.</item>
 
</itemize>
 
</itemize>
 
<example>
 
<example>
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           [xy^2, x^3 + xy, y^4, xy^3, x^2y^2, x^3y]);
 
           [xy^2, x^3 + xy, y^4, xy^3, x^2y^2, x^3y]);
  
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-------------------------------
 
Mat([
 
Mat([
 
   [0, 0, 0, 0, 0, 0, 0, 0],
 
   [0, 0, 0, 0, 0, 0, 0, 0],
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   <types>
 
   <types>
 
     <type>borderbasis</type>
 
     <type>borderbasis</type>
    <type>multiplication</type>
 
 
     <type>matrix</type>
 
     <type>matrix</type>
 
   </types>
 
   </types>
   <see>BB.BBasis</see>
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   <see>ApCoCoA-1:BB.BBasis|BB.BBasis</see>
   <see>BB.BBasisForOI</see>
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   <see>ApCoCoA-1:BB.BBasisForOI|BB.BBasisForOI</see>
   <see>BB.GenMultMat</see>
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   <see>ApCoCoA-1:BB.GenMultMat|BB.GenMultMat</see>
 
   <key>MultMat</key>
 
   <key>MultMat</key>
 
   <key>BB.MultMat</key>
 
   <key>BB.MultMat</key>
 
   <key>borderbasis.MultMat</key>
 
   <key>borderbasis.MultMat</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 09:42, 7 October 2020

This article is about a function from ApCoCoA-1.

BB.MultMat

Computes the i-th multiplication matrix associated to a border basis.

Syntax

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

Description

Computes the I-th multiplication matrix associated to the given input OO-border basis BB of the ideal generated by the polynomials of BB where I is an index number in the range 1..NumIndets().

The output is a matrix.

  • @param I Index of indeterminate.

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

  • @param BB A list of terms representing the OO-border basis of the ideal generated by the polynomials of BB.

  • @return The I-th multiplication matrix.

Example

Use QQ[x,y];

BB.MultMat(1,
           [1, y, y^2, y^3, x, xy, x^2, x^2y],
           [xy^2, x^3 + xy, y^4, xy^3, x^2y^2, x^3y]);

-------------------------------
Mat([
  [0, 0, 0, 0, 0, 0, 0, 0],
  [0, 0, 0, 0, 0, 0, 0, 0],
  [0, 0, 0, 0, 0, 0, 0, 0],
  [0, 0, 0, 0, 0, 0, 0, 0],
  [1, 0, 0, 0, 0, 0, 0, 0],
  [0, 1, 0, 0, 0, 0, -1, 0],
  [0, 0, 0, 0, 1, 0, 0, 0],
  [0, 0, 0, 0, 0, 1, 0, 0]
])
-------------------------------

BB.BBasis

BB.BBasisForOI

BB.GenMultMat