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Strategies for Computing Minimal Free Resolutions

✍ Scribed by R. La Scala; M. Stillman

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
503 KB
Volume
26
Category
Article
ISSN
0747-7171

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✦ Synopsis

In the present paper we study algorithms based on the theory of GrΓΆbner bases for computing free resolutions of modules over polynomial rings. We propose a technique which consists in the application of special selection strategies to the Schreyer algorithm. The resulting algorithm is efficient and, in the graded case, allows a straightforward minimalization algorithm. These techniques generalize to factor rings, skew commutative rings, and some non-commutative rings. Finally, the proposed approach is compared with other algorithms by means of an implementation developed in the new system Macaulay2.

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