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Involutive Bases Under Composition

✍ Scribed by Zailiang Tang

Book ID
107347022
Publisher
Academy of Mathematics and Systems Science, Chinese Academy of Sciences
Year
2007
Tongue
English
Weight
171 KB
Volume
20
Category
Article
ISSN
1009-6124

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πŸ“œ SIMILAR VOLUMES

Involutive bases of polynomial ideals
Involutive bases of polynomial ideals
✍ Vladimir P. Gerdt; Yuri A. Blinkov πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 199 KB
SAGBI Bases Under Composition
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✍ Patrik Nordbeck πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 232 KB

Polynomial composition is the operation of replacing the variables in a polynomial with other polynomials. In this paper we give a sufficient and necessary condition on a set Θ of polynomials to assure that the set F β€’ Θ of composed polynomials is a SAGBI basis whenever F is.

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✍ V. P. Gerdt; M. V. Zinin; Yu. A. Blinkov πŸ“‚ Article πŸ“… 2010 πŸ› SP MAIK Nauka/Interperiodica 🌐 English βš– 291 KB
A GrΓΆbner Approach to Involutive Bases
A GrΓΆbner Approach to Involutive Bases
✍ Joachim Apel πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 574 KB

Recently, Zharkov and Blinkov introduced the notion of involutive bases of polynomial ideals. This involutive approach has its origin in the theory of partial differential equations and is a translation of results of Janet and Pommaret. In this paper we present a pure algebraic foundation of involut

Involutive Bases in the Weyl Algebra
Involutive Bases in the Weyl Algebra
✍ Marcus Hausdorf; Werner M. Seiler; Rainer Steinwandt πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 448 KB

We discuss the definition and the construction of involutive bases, a special kind of GrΓΆbner bases, for left ideals in the Weyl algebra. We consider not only term orders, for which the extension is straightforward, but also the more general case of multiplicative monomial orders.