8 research outputs found
Matrix Formula of Differential Resultant for First Order Generic Ordinary Differential Polynomials
In this paper, a matrix representation for the differential resultant of two
generic ordinary differential polynomials and in the differential
indeterminate with order one and arbitrary degree is given. That is, a
non-singular matrix is constructed such that its determinant contains the
differential resultant as a factor. Furthermore, the algebraic sparse resultant
of treated as polynomials in is
shown to be a non-zero multiple of the differential resultant of .
Although very special, this seems to be the first matrix representation for a
class of nonlinear generic differential polynomials
Binomial Difference Ideal and Toric Difference Variety
In this paper, the concepts of binomial difference ideals and toric
difference varieties are defined and their properties are proved. Two canonical
representations for Laurent binomial difference ideals are given using the
reduced Groebner basis of Z[x]-lattices and regular and coherent difference
ascending chains, respectively. Criteria for a Laurent binomial difference
ideal to be reflexive, prime, well-mixed, perfect, and toric are given in terms
of their support lattices which are Z[x]-lattices. The reflexive, well-mixed,
and perfect closures of a Laurent binomial difference ideal are shown to be
binomial. Four equivalent definitions for toric difference varieties are
presented. Finally, algorithms are given to check whether a given Laurent
binomial difference ideal I is reflexive, prime, well-mixed, perfect, or toric,
and in the negative case, to compute the reflexive, well-mixed, and perfect
closures of I. An algorithm is given to decompose a finitely generated perfect
binomial difference ideal as the intersection of reflexive prime binomial
difference ideals.Comment: 72 page