Difference between revisions of "ApCoCoA-1:BBSGen.BBFinder"
From ApCoCoAWiki
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This function may not work properly for bigger order ideals and rings with more than three indeterminates, since the ring XX | This function may not work properly for bigger order ideals and rings with more than three indeterminates, since the ring XX | ||
also grows with respect to them. | also grows with respect to them. | ||
| + | |||
| + | We use the function <ref>BB.Border</ref> | ||
| + | <ref>BB.Box</ref> from the borderbasis package. | ||
<itemize> | <itemize> | ||
Revision as of 17:43, 7 June 2012
BBSGen.BBFinder
- Let t[k,l,i,j] represent the (i,j) ^th entry of matrix the operation [A_k,A_l] . Let LF be a list of such indeterminates from the ring XX. This function finds the polynomial \tau^kl_ij and its degree which corresponds to the elements given in the list LF.
Syntax
BBFinder(LF,OO,N,Poly); BBFinder(LF:LIST,OO:LIST,BO:LIST,N:INTEGER,W:MATRIX):LIST
Description
In order to use this function, one should define the ring XX as given in the example.
This function may not work properly for bigger order ideals and rings with more than three indeterminates, since the ring XX
also grows with respect to them.
We use the function BB.Border
BB.Box from the borderbasis package.
@param List of t[k,l,i,j] , order ideal OO, border BO, the number of Indeterminates of the Polynomial Ring and the Weight Matrix.
@return List of generators of the vanishing ideal of the border basis, their position in the matrix [A_k,A_l] and their degree wrt. arrow grading.
Example
Use R::=QQ[x[1..2]];
OO:=BB.Box([1,1]);
BO:=BB.Border(OO);
W:=BBSGen.Wmat(OO,BO,N);
Mu:=Len(OO);
Nu:=Len(BO);
N:=Len(Indets());
Use XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]];
BBSGen.BBFinder([t[1,2,3,4],t[1,2,2,4]],OO,BO,N,W);
[ [ [ R :: Vector(1, 2)],
[t[1,2,3,4]],
[ -c[2,4]c[3,1] + c[3,2]c[3,3] + c[3,4]c[4,3] - c[3,3]c[4,4] + c[1,3]]],
[[ R :: Vector(2, 1)],
[ t[1,2,2,4]],
[ -c[2,1]c[2,4] + c[2,2]c[3,3] + c[2,4]c[4,3] - c[2,3]c[4,4] - c[1,4]]]]
BB.Box
