Difference between revisions of "ApCoCoA-1:BBSGen.Wmat"

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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.
 
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 <ref>BBSGen.WMat(OO,BO,N)</ref> computes the grading matrix with respect to this grading matrix.
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We shall name this  grading the arrow grading. The Function <ref>BBSGen.WMat(OO,BO,N)</ref> computes the grading matrix with respect to this grading.
  
 
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Revision as of 15:10, 18 June 2012

BBSGen.Wmat

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

Syntax

BBSGen.WMat(OO,BO,N):
BBSGen.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 BBSGen.WMat(OO,BO,N) computes the grading matrix with respect to this grading.

  • @param The order ideal OO, the border BO and the number of indeterminates of the polynomial ring K[x_1,...,x_N].

  • @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:=BBSGen.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]
])