ApCoCoA-1:BBSGen.Wmat

BBSGen.Wmat

This function computes the Weight Matrix with respect to the arrow grading.

Syntax

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

Description

Let c_ij be an indeterminate from the Ring K[c_ij]. Let OO be an order ideal and BO be its border. Let Mu:=Len(OO) and Nu:=Len(BO). Let m be an integer that is equal to Mu*Nu. The ring K[c_ij] is Z^m-graded if we define deg_{W}(c_ij)=log(b_j)-log(t_i)=(u_1,...,u_m)=u\in Z^m, where W is the grading matrix.

We shall name this grading the arrow grading. The Function WMat(OO,BO,N) computes this grading matrix.

• @param The order ideal OO, the border BO and the number of Indeterminates of the Polynomial Ring.

• @return Weight Matrix.

Example

Use R::=QQ[x[1..2]];
OO:=$apcocoa/borderbasis.Box([1,1]); 
BO:=$apcocoa/borderbasis.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]
])