# 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) | + | We shall name this grading the arrow grading. The Function <ref>BBSGen.WMat</ref>(OO,BO,N) computes the grading matrix with respect to this grading. |

<itemize> | <itemize> |

## Revision as of 10:39, 19 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] ])