ApCoCoA-1:BBSGen.Wmat

BBSGens.Wmat

This function computes the weight matrix with respect to the arrow grading.

Syntax

BBSGens.WMat(OO:LIST,BO:LIST,N:INTEGER):MATRIX

Description

This command computes the degree of the indeterminates from K[c_{ij}] with respect to the arrow grading. The coloumns of BBSGens.Wmat(OO,BO,N) give the degrees of {c_{11},..c_{1Nu},...,c_{MuNu}} with respect to the arrow grading, where Mu is the number of elements in OO and Nu is the number of elements from BO.

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

• @param BO A list of terms representing the border.

• @param N The number of elements of the Polynomila ring K[x_1,...x_n].

• @return Returns the weight matrix with respect to the arrow grading.

Example

Use R::=QQ[x[1..2]];
OO:=BB.Box([1,1]); 
BO:=BB.Border(OO);
N:=Len(Indets());
----------------------
W:=Wmat(OO,BO,N); 
W;
Mat([
  [0, 2, 1, 2, 0, 2, 1, 2, -1, 1, 0, 1, -1, 1, 0, 1],
  [2, 0, 2, 1, 1, -1, 1, 0, 2, 0, 2, 1, 1, -1, 1, 0]])

   <type>bbsmingensys</type>