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

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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>Len</ref>(OO) x <ref>Len</ref>(OO) over the ring <tt>BBS=K[c_{ij}]</tt>.
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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>.
 
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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>I</em> An integer which specifies the indeterminate for which the generic homogeneous multiplication matrix will be computed.</item>
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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]
])
-------------------------------