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Given an ideal I in a polynomial ring K [ x 1 , … , x n ] over a field K, we present a complete algorithm to compute the binomial part of I, i.e., the subideal Bin ( I ) of I generated by all monomials and binomials in I. This is achieved step-by-...

The label code of a lattice plays a key role in the characterization of the lattice. Every lattice $\mathrm{\Lambda }$ can be described in terms of a label code L and an orthogonal sublattice ${\mathrm{\Lambda }}^{\prime }$ such that $\mathrm{\Lambda }/{\mathrm{\Lambda }}^{\prime }\cong L$. We identify the binomial ideal associated to an ...${}_{}$${}_{\mathrm{}}{}_{{\mathrm{}}^{}}{}_{}$${}_{\mathrm{}}{}_{{\mathrm{}}^{}}$${}_{}$$\mathrm{}{\mathrm{}}^{}$${}_{}$

Binomial ideals are special polynomial ideals with many algorithmically and theoretically nice properties. We discuss the problem of deciding if a given polynomial ideal is binomial. While the methods are general, our main motivation and source of ...

Each binary linear code can be associated to a binomial ideal which allows for a complete decoding. Two generalizations of the non-binary case given by the ordinary and generalized code ideals have been given which coincide in the binary case and are ...

A binomial ideal is an ideal of the polynomial ring which is generated by binomials. In a previous paper, we gave a correspondence between pure saturated binomial ideals of K[x"1,...,x"n] and submodules of Z^n and we showed that it is possible to ...

We study the problem of counting the total number of affine solutions of a system of n binomials in n variables over an algebraically closed field of characteristic zero. We show that we may decide in polynomial time if that number is finite. We give a ...