ApCoCoA-1:BB.GenMultMat

This article is about a function from ApCoCoA-1.

BB.GenMultMat

Computes a generic multiplication matrix.

Syntax

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

Description

Computes the generic multiplication matrix for the I-th indeterminate with respect to 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 multiplication matrix will be computed.

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

• @return The generic multiplication matrix.

Example

Use QQ[x, y, z], DegRevLex;
BB.GenMultMat(1, [1, x, y, z]);

-------------------------------
Mat([
  [0, BBS :: c[1,6], BBS :: c[1,5], BBS :: c[1,3]],
  [1, BBS :: c[2,6], BBS :: c[2,5], BBS :: c[2,3]],
  [0, BBS :: c[3,6], BBS :: c[3,5], BBS :: c[3,3]],
  [0, BBS :: c[4,6], BBS :: c[4,5], BBS :: c[4,3]]
])
-------------------------------