Category:ApCoCoA-1:Package bbsmingensys

From ApCoCoAWiki

Let Tau be the set of defining equations of a border basis scheme. The package bbsmingensys contains programs, which focus on this generating set.

Let O be an order ideal and let Len(O)=Mu. Let BO be its border and Len(BO)=Nu.(see the functions BB. Border and BB.Box in the package borderbasis) Let k,l in {1,...,N} and k is not equal to l. We denote a polynomial entry of a commutator operation


in the position (p,q) by tau_pq^kl where p,q in {1,...,Mu}. These entries generate the vanishing ideal of the border basis scheme.We denote the set of such polynomials by Tau, thus we have

    I(B_O)= < Tau >.

Further we will represent every element from Tau ( tau_pq^kl_{1<= p,q<= Mu,1<=k<l<=N} ) as an indeterminate t[k,l,p,q]. Therefore, we construct the ring


with respect to the order ideal and its border defined on R=K[x_1,..,x_N]. Throughout this package, defining this ring exactly as given in the examples is crucial.

NOTE: This package is designed for experimenting for some specific shape of order ideals and rings. Functions <commandref>BBSGen.TraceSyzFull</commandref>, <commandref>BBSGen.JacobiFull</commandref>, <commandref>BBSGen.LinIndep</commandref> and <commandref>BBSGen.BBFinder</commandref> may not give results due to the growth of indeterminates in XX or due to the growth of polynomials during matrix multiplications.

The global alias for this package is BBSGen.


  • M.Huibregtse, Some Syzygies of the Generators of the Ideal of a Border Basis Scheme,??? (2009),
  • M.Kreuzer and L.Robbiano, Deformations of Border Basis, Coll Math. 59 (2008),275-297.