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. | ||
| + | We shall name this grading the arrow grading. The Function <ref>WMat(OO,BO,N)<\ref> computes this grading matrix. | ||
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Revision as of 21:37, 7 June 2012
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 <ref>WMat(OO,BO,N)<\ref> 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:=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] ])
