Difference between revisions of "ApCoCoA-1:BBSGen.BBFinder"
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(New page: <command> <title>BBSGen.BBFinder</title> <short_description>: Let Tau^kl_ij :=t[k,l,i,j] be the (i,j) ^th entry of matrix the operation [A_k,A_l]. This function finds the polynomial ...) |
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<see>BBSGen.Wmat</see> | <see>BBSGen.Wmat</see> | ||
<see>BBSGen.BBTau</see> | <see>BBSGen.BBTau</see> | ||
| − | + | <see>BBSGen.NonTriv</see> | |
| + | <see>BBSGen.Poldeg</see> | ||
<key>Wmat</key> | <key>Wmat</key> | ||
<key>BBSGen.Wmat</key> | <key>BBSGen.Wmat</key> | ||
Revision as of 20:49, 31 May 2012
BBSGen.BBFinder
- Let Tau^kl_ij :=t[k,l,i,j] be the (i,j) ^th entry of matrix the operation [A_k,A_l]. This function finds the polynomial and its degree which corresponds to the elements given in the list.
Syntax
BBFinder(LF,OO,N,Poly); BBFinder(LF:LIST,OO:LIST,BO:LIST,N:INTEGER,W:MATRIX):LIST
Description
@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]]]]
