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Gröbner bases

✍ Scribed by Arnab Chakraborty

Publisher
Indian Academy of Sciences
Year
2000
Tongue
English
Weight
920 KB
Volume
5
Category
Article
ISSN
0971-8044

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Multiplicative Bases, Gröbner Bases, and
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✍ 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

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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

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✍ 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

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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

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In this paper we contribute with one main result to the interesting problem initiated by Hong (1998, J. Symb. Comput. 25, 643-663) on the behaviour of Gröbner bases under composition of polynomials. Polynomial composition is the operation of replacing the variables of a polynomial with other polynom