Involutive bases of polynomial ideals

@article{Gerdt1998InvolutiveBO,
  title={Involutive bases of polynomial ideals},
  author={Vladimir P. Gerdt and Yuri A. Blinkov},
  journal={Mathematics and Computers in Simulation},
  year={1998},
  volume={45},
  pages={519-541}
}

Minimal involutive bases

TLDR
An algorithm for construction of minimal involutive polynomial bases which are Grobner bases of the special form is presented which provides correctness and termination of involutive algorithms for any finite set of input polynomials and any admissible monomial ordering.

The Theory of Involutive Divisions and an Application to Hilbert Function Computations

  • J. Apel
  • Mathematics
    J. Symb. Comput.
  • 1998
TLDR
This theory introduces the lattice of so-called involutive divisions and defines the admissibility of such an involutive division for a given set of terms and presents a new approach for building a general theory of involutive bases of polynomial ideals.

On Connection Between Constructive Involutive Divisions and Monomial Orderings

TLDR
It is proven that Janet division has the advantage in the minimal involutive basis size of the class of ≻ -divisions which possess many good properties of Janet division and can be considered as its analogs for orderings different from the lexicographic one.

Completion of Linear Differential Systems to Involution

. In this paper we generalize the involutive methods and algorithms devised for polynomial ideals to differential ones generated by a finite set of linear differential polynomials in the differential

Involutive Algorithms for Computing

TLDR
An efficient involutive algorithm based on the concept of involutive monomial division which restricts the conventional division in a certain way and which can be output without any extra computational costs is described.

Term-ordering free involutive bases

Involutive Algorithms for Computing Groebner Bases

TLDR
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.

Involutive Division Techniques: Some Generalizations and Optimizations

A new class of involutive divisions induced by certain orderings of monomials is considered. It is proved that these divisions are Noetherian and constructive. Therefore, each of them allows one to

Completion of Linear Differential Systems to Involution

TLDR
This paper considers posing of an initial value problem for a linear differential system providing uniqueness of its solution and Lie symmetry analysis of nonlinear differential equations to determine the structure of arbitrariness in general solution of linear systems and thereby to find the size of symmetry group.
...

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