Gröbner bases, local cohomology and reduction number
نویسندگان
چکیده
منابع مشابه
Multiplicative Bases, Gröbner Bases, and Right Gröbner Bases
Before surveying the results of the paper, we introduce path algebras. Path algebras play a central role in the representation theory of finite-dimensional algebras (Gabriel, 1980; Auslander et al., 1995; Bardzell, 1997) and the theory of Gröbner bases (Bergman, 1978; Mora, 1986; Farkas et al., 1993) has been an important tool in some results (Feustel et al., 1993; Green and Huang, 1995; Bardze...
متن کاملCounting and Gröbner Bases
Gröbner bases were introduced by Buchberger (1965) and are now firmly established as a tool in Commutative Algebra and other areas. The reader is referred to Buchberger (1985), Cox, Little and O’Shea (1992) or Becker and Weispfenning (1993) for more information. Eisenbud (1995) places Gröbner bases within the context of more advanced Commutative Algebra. The ingredients for a Gröbner basis are ...
متن کاملGröbner Bases in Orders of Algebraic Number Fields
In the 1960s Bruno Buchberger presented his first critical-pair-completion algorithm, now called Buchberger’s algorithm. Since then Gröbner bases have become a powerful tool in computational algebra and algebraic geometry. What is not as well known is that Buchberger (1985, 1987) has also shown a way of computing Gröbner bases in the integers. This is not as trivial as it may seem. In the polyn...
متن کاملAutomating Elementary Number-Theoretic Proofs Using Gröbner Bases
We present a uniform algorithm for proving automatically a fairly wide class of elementary facts connected with integer divisibility. The assertions that can be handled are those with a limited quantifier structure involving addition, multiplication and certain number-theoretic predicates such as ‘divisible by’, ‘congruent’ and ‘coprime’; one notable example in this class is the Chinese Remaind...
متن کاملParallel Reduction of Matrices in Gröbner Bases Computations
Unfortunately the computation is time-and memory intensive. Mathematical knowledge is used to optimize the algorithms. Computer science provides another possibility to increase the computations: parallelization 2 / 24 Motivation Gröbner bases are used, to solve polynomial equation systems, move robotics, verify programs,. .. Unfortunately the computation is time-and memory intensive. Mathematic...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2000
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-00-05503-9