Difference between revisions of "ApCoCoA-1:BBSGen.Wmat"
From ApCoCoAWiki
| Line 21: | Line 21: | ||
<example> | <example> | ||
Use R::=QQ[x[1..2]]; | Use R::=QQ[x[1..2]]; | ||
| − | OO:= | + | OO:=$apcocoa/borderbasis.Box([1,1]); |
| − | BO:= | + | BO:=$apcocoa/borderbasis.Border(OO); |
N:=Len(Indets()); | N:=Len(Indets()); | ||
---------------------- | ---------------------- | ||
| Line 42: | Line 42: | ||
<type>apcocoaserver</type> | <type>apcocoaserver</type> | ||
</types> | </types> | ||
| − | + | ||
| − | |||
<key>Wmat</key> | <key>Wmat</key> | ||
<key>BBSGen.Wmat</key> | <key>BBSGen.Wmat</key> | ||
Revision as of 23:31, 14 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 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] ])
