# Category:ApCoCoA-1:Package bbsmingensys

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

[A_k,A_l]=A_k*A_l-A_l*A_k

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

XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]]

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**.

## References

- 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.

## Pages in category "ApCoCoA-1:Package bbsmingensys"

The following 15 pages are in this category, out of 15 total.

### B

- ApCoCoA-1:BBSGen.BBFinder
- ApCoCoA-1:BBSGen.JacobiFull
- ApCoCoA-1:BBSGen.JacobiLin
- ApCoCoA-1:BBSGen.JacobiStep
- ApCoCoA-1:BBSGen.LinIndepGen
- ApCoCoA-1:BBSGen.NonStand
- ApCoCoA-1:BBSGen.NonStandPoly
- ApCoCoA-1:BBSGen.NonTriv
- ApCoCoA-1:BBSGen.Poldeg
- ApCoCoA-1:BBSGen.PurPow
- ApCoCoA-1:BBSGen.TraceSyzFull
- ApCoCoA-1:BBSGen.TraceSyzLin
- ApCoCoA-1:BBSGen.TraceSyzLinStep
- ApCoCoA-1:BBSGen.TraceSyzStep
- ApCoCoA-1:BBSGen.Wmat