38 citations · 281 across the 52 of their papers we have counts for
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Involutive Bases Algorithm Incorporating F5 Criterion
Vladimir P. Gerdt, Amir Hashemi, Benyamin M. -Alizadeh
Faugere's F5 algorithm is the fastest known algorithm to compute Groebner bases. It has a signature-based and an incremental structure that allow to apply the F5 criterion for dele…
Noetherian quotients of the algebra of partial difference polynomials and Grobner bases of symmetric ideals
Vladimir P. Gerdt, Roberto La Scala
In this paper we develop a Grobner bases theory for ideals of partial difference polynomials with constant or non-constant coefficients. In particular, we introduce a criterion pro…
Algorithmic Thomas Decomposition of Algebraic and Differential Systems
Thomas Bächler, Vladimir Gerdt, Markus Lange-Hegermann +1
In this paper, we consider systems of algebraic and non-linear partial differential equations and inequations. We decompose these systems into so-called simple subsystems and there…
Thomas Decomposition of Algebraic and Differential Systems
Thomas Bächler, Vladimir Gerdt, Markus Lange-Hegermann +1
In this paper we consider disjoint decomposition of algebraic and non-linear partial differential systems of equations and inequations into so-called simple subsystems. We exploit…
On Computing Janet Bases for Degree Compatible Orderings
Vladimir P. Gerdt, Yuri A. Blinkov
We consider three modifications of our involutive algorithm for computing Janet bases. These modifications are related to degree compatible monomial orders and specify selection st…
Janet Bases of Toric Ideals
Vladimir P. Gerdt, Yuri A. Blinkov
In this paper we present a version of the general polynomial involutive algorithm for computing Janet bases specialized to toric ideals. The relevant data structures are Janet tree…
On the Relation Between Pommaret and Janet Bases
Vladimir P. Gerdt
In this paper the relation between Pommaret and Janet bases of polynomial ideals is studied. It is proved that if an ideal has a finite Pommaret basis then the latter is a minimal…
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…