Difference between revisions of "ApCoCoA-1:BBSGen.Wmat"
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| − | <title>BBSGen. | + | <title>BBSGen.WMat</title> |
<short_description>This function computes the Weight Matrix with respect to the arrow grading. </short_description> | <short_description>This function computes the Weight Matrix with respect to the arrow grading. </short_description> | ||
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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 < | + | We shall name this grading the arrow grading. The Function <tt>BBSGen.Wmat(OO,BO,N)</tt> computes the grading matrix with respect to this grading. |
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<key>bbsmingensys.Wmat</key> | <key>bbsmingensys.Wmat</key> | ||
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Latest revision as of 09:52, 7 October 2020
| This article is about a function from ApCoCoA-1. |
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] ])
