• Corpus ID: 10115415

Computation of Difference Gröbner Bases

@article{Gerdt2012ComputationOD,
  title={Computation of Difference Gr{\"o}bner Bases},
  author={Vladimir P. Gerdt and Daniel Robertz},
  journal={Comput. Sci. J. Moldova},
  year={2012},
  volume={20},
  pages={203-226}
}
  • V. GerdtD. Robertz
  • Published 15 June 2012
  • Mathematics, Computer Science
  • Comput. Sci. J. Moldova
This paper is an updated and extended version of our note [1] (cf. also [2]). To compute difference Gröbner bases of ideals generated by linear polynomials we adopt to difference polynomial rings the involutive algorithm based on Janet-like division. The algorithm has been implemented in Maple in the form of the package LDA (Linear Difference Algebra) and we describe the main features of the package. Its applications are illustrated by generation of finite difference approximations to linear… 

Tables from this paper

Criteria for Finite Difference Gröbner Bases of Normal Binomial Difference Ideals

In this paper, we give decision criteria for normal binomial difference polynomial ideals in the univariate difference polynomial ring F{y to have finite difference Gröbner bases and an algorithm to

A New Type of Difference Dimension Polynomials

  • A. Levin
  • Mathematics
    Mathematics in Computer Science
  • 2022
We introduce a new type of characteristic sets of difference polynomials using a generalization of the concept of effective order to the case of partial difference polynomials. Applying properties of

Strong Consistency and Thomas Decomposition of Finite Difference Approximations to Systems of Partial Differential Equations

An algorithmic approach that combines differential and difference algebra to analyze s(trong)-consistency of finite difference approximations of regular solution grids is suggested, which generalizes the definition given earlier for Cartesian grids.

Algebraic Construction of a Strongly Consistent, Permutationally Symmetric and Conservative Difference Scheme for 3D Steady Stokes Flow

By using symbolic algebraic computation, a strongly-consistent second-order finite difference scheme is constructed for steady three-dimensional Stokes flow and a Cartesian solution grid and it is shown that the scheme has the second order of accuracy and incorporates the pressure Poisson equation.

Algorithmic Approach to Strong Consistency Analysis of Finite Difference Approximations to PDE Systems

  • V. Gerdt
  • Computer Science, Mathematics
    MMCP
  • 2011
A difference analogue of the differential Thomas decomposition and an algorithm for verification of s-consistent difference approximations to the incompressible Navier-Stokes equations including the pressure Poisson equation are proposed.

Discretization of quasilinear evolution equations by computer algebra methods

An algorithmic approach to construction of finite difference schemes on regular grids developed by the first two authors is applied to quasilinear evolution equations in one spatial variable, which is strongly consistent and absolutely stable.

A Strongly Consistent Finite Difference Scheme for Steady Stokes Flow and its Modified Equations

A strongly consistent second-order finite difference scheme for the steady two-dimensional Stokes flow is constructed based on a combination of the finite volume method, difference elimination, and numerical integration and correlated with the differential ideal generated by the polynomials in the Stokes equations.

Binomial difference ideals

References

SHOWING 1-10 OF 29 REFERENCES

Involutive Algorithms for Computing Groebner Bases

An involutive algorithm for construct- ing Gröbner bases of polynomial ideals based on the concept of involutive monomial division which restricts the conventional division in a certain way is described.

On computation of Gröbner bases for linear difference systems

  • V. Gerdt
  • Mathematics, Computer Science
  • 2006

A Maple Package for Computing Groebner Bases for Linear Recurrence Relations

Detecting unnecessary reductions in an involutive basis computation

Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations

An algorithmic approach to the generation of fully con- servative difference schemes for linear partial differential equations based on enlargement of the equations in their integral conservation law form by extra integral relations between unknown functions and their derivatives.

Specialized computer algebra system GINV

Computer algebra system GINV (Gröbner INVolutive) is presented. It is designed for studying and solving systems of algebraic, differential, and difference equations of polynomial type by their

Gröbner bases - a computational approach to commutative algebra

This chapter discusses linear algebra in Residue Class Rings in Vector Spaces and Modules, and first applications of Gr bner Bases.

Gröbner Bases in Perturbative Calculations

Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)

Algebraic Geometry is the study of systems of polynomial equations in one or more variables, asking such questions as: Does the The denominator is taking on this, book interested. This book for

Experimental Analysis of Involutive Criteria

The experimental study shows that the role of criteria in the involutive approach is definitely weaker than that in Buchberger’s algorithm.