ApCoCoA-1:BBSGen.BBFinder

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]]]]

BB.Border

BB.Box

BBSGen.Wmat

BBSGen.BBTau