Algorithms in local algebra
TL;DR: This work uses the generalization of Mora's tangent cone algorithm to arbitrary term orders to give a detailed description of the necessary modifications and restrictions for term orders of mixed type.
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About: This article is published in Journal of Symbolic Computation. The article was published on 01 Jun 1995. and is currently open access. The article focuses on the topics: Polynomial ring & Ideal (ring theory).
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Citations
•Book
A Singular Introduction to Commutative Algebra
Gert-Martin Greuel,Gerhard Pfister +1 more
- 12 Aug 2008
TL;DR: A singular introduction to commutative algebra as mentioned in this paper is one of the most widely used works in algebraic geometry, with a broad coverage of theoretical topics in the portions of the algebra closest to algebraic geometrical geometry.
955
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Solving Polynomial Equation Systems I
Teo Mora
- 01 Jan 2003
TL;DR: Mora as mentioned in this paper extended Buchberger's algorithm to group rings and other Ore-like extensions, and provided an operative scheme that allows one to set a Buchberger theory over any effective associative ring.
111
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Cited References
Johannes Grabmeier,Erich Kaltofen,Volker Weispfenning +2 more
- 01 Jan 2003
TL;DR: Transliteration of Russian names has essentially followed the system adopted by the Library of Congress, but with no distinction between e and e or between Η and fi, and with yu used for κ> and ya for H .
66
•Posted Content
Computer Algebra and Algebraic Geometry - Achievements and Perspectives
TL;DR: The aims of this paper are to show, by means of examples, the usefulness of computer algebra to mathematical research and the fruitful interaction between algebraic geometry and computer algebra and, more generally, between mathematics and computer science.
16
•Posted Content
A Combinatorial Approach to Involution and delta-Regularity I: Involutive Bases in Polynomial Algebras of Solvable Type
TL;DR: In this paper, the parts concerning involutive bases over rings have been significantly changed and some proofs have been improved, in particular the part concerning the involutive base over rings over rings.
12
References
Gröbner bases and primary decomposition of polynomial ideals
TL;DR: This work presents an algorithm to compute the primary decomposition of any ideal in a polynomialring over a factorially closed algorithmic principal ideal domain R and shows how the reduction process can be applied to computing radicals and testing ideals for primality.
513
Gröbner-Bases, Gaussian elimination and resolution of systems of algebraic equations
Daniel Lazard
- 28 Mar 1983
TL;DR: In this article, the authors give upper and lower bounds for the degrees of the elements of a Gr6bner base, which are based on projective algebraic geometry and the choice of the ordering appears to be critical.
496
The Gröbner fan of an ideal
Teo Mora,Lorenzo Robbiano +1 more
TL;DR: To every ideal I in the polynomial ring A:=k[X"1,..., X"n] new invariants are attached, such as the Grobner Fan F(I), theGrobner region G(I) and the set ATO(I).
253
On the theory of graded structures
TL;DR: A new structural algebraic framework is given for the concept and the construction of the so-called generalised standard bases, which should help to shape and direct future research in the algorithmic aspects of commutative algebra.
147