A polynomial-time algorithm to compute generalized Hermite normal forms of matrices over <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mo stretchy="false">[</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">]</mml:mo></mml:math>

Jing, Rui-Juan; Yuan, Chun-Ming; Gao, Xiao-Shan

doi:10.1016/j.tcs.2018.07.003

Cited by 2 publications

(6 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The following basic property for Gröbner basis is obviously true for Z[x]-lattices and a polynomial-time algorithm to compute Göbner bases for Z[x]-lattices is given in [15].…”

Section: For Brevitymentioning

confidence: 99%

Binomial difference ideals

Gao

Huang

Yuan

2017

Journal of Symbolic Computation

Self Cite

View full text Add to dashboard Cite

In this paper, binomial difference ideals are studied. Three canonical representations for Laurent binomial difference ideals are given in terms of the reduced Gröbner basis of Z[x]-lattices, regular and coherent difference ascending chains, and partial characters over Z[x]-lattices, respectively. Criteria for a Laurent binomial difference ideal to be reflexive, prime, well-mixed, and perfect are given in terms of their support lattices. The reflexive, well-mixed, and perfect closures of a Laurent binomial difference ideal are shown to be binomial. Most of the properties of Laurent binomial difference ideals are extended to the case of difference binomial ideals. Finally, algorithms are given to check whether a given Laurent binomial difference ideal I is reflexive, prime, well-mixed, or perfect, 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.

show abstract

“…The following basic property for Gröbner basis is obviously true for Z[x]-lattices and a polynomial-time algorithm to compute Göbner bases for Z[x]-lattices is given in [15].…”

Section: For Brevitymentioning

confidence: 99%

Binomial difference ideals

Gao

Huang

Yuan

2017

Journal of Symbolic Computation

Self Cite

View full text Add to dashboard Cite

show abstract

“…In Example 3.3, we need to use the difference characteristic set method to compute I U . Here, the only operation used to compute I U is Gröbner basis methods for Z[x]-lattices [17]. …”

Section: Toric σ-Idealmentioning

confidence: 99%

“…In [17], a polynomial-time algorithm to compute the Gröbner basis for Z[x]-lattices is given. Combining this with Schreyer's Theorem on page 224 of [3], we have an algorithm to compute a Gröbner basis for Syz(A) as a Z[x]-module.…”

Section: Toric σ-Idealmentioning

confidence: 99%

See 2 more Smart Citations

Toric difference variety

et al. 2017

Self Cite

View full text Add to dashboard Cite

In this paper, the concept of toric difference varieties is defined and four equivalent descriptions for toric difference varieties are presented in terms of difference rational parametrization, difference coordinate rings, toric difference ideals, and group actions by difference tori. Connections between toric difference varieties and affine N[x]-semimodules are established by proving the correspondence between the irreducible invariant difference subvarieties and the faces of the N[x]-submodules and the orbit-face correspondence. Finally, an algorithm is given to decide whether a binomial difference ideal represented by a Z[x]-lattice defines a toric difference variety.

show abstract

A polynomial-time algorithm to compute generalized Hermite normal forms of matrices over Z[x]

Cited by 2 publications

References 22 publications

Binomial difference ideals

Binomial difference ideals

Toric difference variety

Contact Info

Product

Resources

About