𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A Gröbner Approach to Involutive Bases

✍ Scribed by Joachim Apel

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
574 KB
Volume
19
Category
Article
ISSN
0747-7171

No coin nor oath required. For personal study only.

✦ Synopsis

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 involutive bases of Pommaret type. In fact, they turn out to be generalized left Gröbner bases of ideals in the commutative polynomial ring with respect to a non-commutative grading. The introduced theory will allow not only the verification of the results of Zharkov and Blinkov but it will also provide some new facts.

📜 SIMILAR VOLUMES

Multiplicative Bases, Gröbner Bases, and
Multiplicative Bases, Gröbner Bases, and Right Gröbner Bases
✍ Edward L. Green 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 314 KB

In this paper, we study conditions on algebras with multiplicative bases so that there is a Gröbner basis theory. We introduce right Gröbner bases for a class of modules. We give an elimination theory and intersection theory for right submodules of projective modules in path algebras. Solutions to h

Regular Gröbner Bases
Regular Gröbner Bases
✍ Jonas MÅnsson; Patrik Nordbeck 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 366 KB

In this paper we introduce the concept of bi-automaton algebras, generalizing the automaton algebras previously defined by Ufnarovski. A bi-automaton algebra is a quotient of the free algebra, defined by a binomial ideal admitting a Gröbner basis which can be encoded as a regular set; we call such a

Counting and Gröbner Bases
Counting and Gröbner Bases
✍ K. Kalorkoti 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 239 KB

We show how the complexity of counting relates to the well known phenomenon that computing Gröbner bases under a lexicographic order is generally harder than total degree orders. We give simple examples of polynomials for which it is very easy to compute their Gröbner basis using a total degree orde

Canonical comprehensive Gröbner bases
Canonical comprehensive Gröbner bases
✍ Volker Weispfenning 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 204 KB

Comprehensive Gröbner bases for parametric polynomial ideals were introduced, constructed, and studied by the author in 1992. Since then the construction has been implemented in the computer algebra systems ALDES/SAC-2, MAS, REDUCE and MAPLE. A comprehensive Gröbner basis is a finite subset G of a p