ApCoCoA-1:BBSGen.BBFinder

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.

The functions BB.Border and BB.Box are from the package borderbasis.

• @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]]]]

BBSGen.Wmat

BBSGen.NonTriv

BBSGen.Poldeg