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

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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>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>

Revision as of 15:12, 12 May 2010

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