38 citations · 281 across the 52 of their papers we have counts for
6 papers · 1 filter
Minimal Involutive Bases
Vladimir P. Gerdt, Yuri A. Blinkov
In this paper we present an algorithm for construction of minimal involutive polynomial bases which are Groebner bases of the special form. The most general involutive algorithms a…
Construction of Involutive Monomial Sets for Different Involutive Divisions
Vladimir P. Gerdt, Vladimir V. Kornyak, Matthias Berth +1
We consider computational and implementation issues for the completion of monomial sets to involution using different involutive divisions. Every of these divisions produces its ow…
Involutive Bases of Polynomial Ideals
Vladimir P. Gerdt, Yuri A. Blinkov
In this paper we consider an algorithmic technique more general than that proposed by Zharkov and Blinkov for the involutive analysis of polynomial ideals. It is based on a new con…
Involutive Division Technique: Some Generalizations and Optimizations
Vladimir P. Gerdt
In this paper, in addition to the earlier introduced involutive divisions, we consider a new class of divisions induced by admissible monomial orderings. We prove that these divisi…
Completion of Linear Differential Systems to Involution
Vladimir P. Gerdt
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…
Constrained Hamiltonian Systems and Groebner Bases
Vladimir P. Gerdt, Soso A. Gogilidze
In this paper we consider finite-dimensional constrained Hamiltonian systems of polynomial type. In order to compute the complete set of constraints and separate them into the firs…