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Efficient Computation of Algebraic Local Cohomology Classes and Change of Ordering for Zero-Dimensional Standard Bases

Nabeshima, Katsusuke ; Tajima, Shinichi Vorozhtsov, Evgenii V ; Seiler, Werner M ; Gerdt, Vladimir P ; Koepf, Wolfram ; Seiler, Werner M. ; Koepf, Wolfram ; Gerdt, Vladimir P. ; Vorozhtsov, Evgenii V.

Computer Algebra in Scientific Computing, 2015, Vol.9301, p.334-348 [Peer Reviewed Journal]

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Title:
Efficient Computation of Algebraic Local Cohomology Classes and Change of Ordering for Zero-Dimensional Standard Bases
Author: Nabeshima, Katsusuke ; Tajima, Shinichi
Vorozhtsov, Evgenii V ; Seiler, Werner M ; Gerdt, Vladimir P ; Koepf, Wolfram ; Seiler, Werner M. ; Koepf, Wolfram ; Gerdt, Vladimir P. ; Vorozhtsov, Evgenii V.
Subjects: algebraic local cohomology ; Algorithms & data structures ; Discrete mathematics ; Maths for computer scientists ; singularities ; standard bases
Is Part Of: Computer Algebra in Scientific Computing, 2015, Vol.9301, p.334-348
Description: A new effective algorithm for computing a set of algebraic local cohomology classes is presented. The key ingredient of the proposed algorithm is to utilize a standard basis. As the application, an algorithm is given for the conversion of a standard basis of a zero-dimensional ideal with respect to any given local ordering into a standard basis with respect to any other local ordering, in the formal power series ring. The new algorithm always outputs a reduced standard basis.
Related Titles: Lecture Notes in Computer Science
Publisher: Switzerland: Springer International Publishing AG
Language: English

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