Computing difference-differential dimension polynomials by relative Gröbner bases in difference-differential modules

DOI10.1016/j.jsc.2008.02.001zbMath1149.13014OpenAlexW1987295165MaRDI QIDQ950422

Franz Winkler, Meng Zhou

Publication date: 22 October 2008

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2008.02.001

zbMATH Keywords

difference-differential dimension polynomialdifference-differential modulegeneralized term orderrelative Gröbner basis

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Derivations and commutative rings (13N15)

Related Items (10)

On computing uniform Gröbner bases for ideals generated by polynomials with parametric exponents ⋮ Characterization of relative Gröbner bases ⋮ Gröbner bases in difference-differential modules with coefficients in a commutative ring ⋮ Transforming linear functional systems into fully integrable systems ⋮ Relative reduction and Buchberger's algorithm in filtered free modules ⋮ Elimination of unknowns for systems of algebraic differential-difference equations ⋮ Noetherian quotients of the algebra of partial difference polynomials and Gröbner bases of symmetric ideals ⋮ Multivariate difference-differential dimension polynomials ⋮ Hilbert-Type Dimension Polynomials of Intermediate Difference-Differential Field Extensions ⋮ Termination of algorithm for computing relative Gröbner bases and difference differential dimension polynomials

Cites Work

• Gröbner bases for ideals in Laurent polynomial rings and their application to systems of difference equations
• A Gröbner basis method for modules over rings of differential operators
• Differential Gröbner bases in one variable and in the partial case
• Reduced Gröbner bases, free difference-differential modules and difference-differential dimension polynomials
• Gröbner bases with respect to several orderings and multivariable dimension polynomials
• Gröbner bases in difference-differential modules
• Gröbner basis and the problem of contiguous relations
• CHARACTERISTIC POLYNOMIALS OF FILTERED DIFFERENCE MODULES AND OF EXTENSIONS OF DIFFERENCE FIELDS
• Kahler Differentials and Differential Algebra in Arbitrary Characteristic
• The notion of dimension in the theory of algebraic differential equations
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