The Groebner Cover (Hardcover, 1st ed. 2018)

This book is divided into two parts, one theoretical and one focusing on applications, and offers a complete description of the Canonical Groebner Cover, the most accurate algebraic method for discussing parametric polynomial systems. It also includes applications to the Automatic Deduction of Geometric Theorems, Loci Computation and Envelopes. The theoretical part is a self-contained exposition on the theory of Parametric Groebner Systems and Bases. It begins with Weispfenning's introduction of Comprehensive Groebner Systems (CGS) in 1992, and provides a complete description of the Groebner Cover (GC), which includes a canonical discussion of a set of parametric polynomial equations developed by Michael Wibmer and the author. In turn, the application part selects three problems for which the Groebner Cover offers valuable new perspectives. The automatic deduction of geometric theorems (ADGT) becomes fully automatic and straightforward using GC, representing a major improvement on all previous methods. In terms of loci and envelope computation, GC makes it possible to introduce a taxonomy of the components and automatically compute it. The book also generalizes the definition of the envelope of a family of hypersurfaces, and provides algorithms for its computation, as well as for discussing how to determine the real envelope. All the algorithms described here have also been included in the software library "grobcov.lib" implemented in Singular by the author, and serve as a User Manual for it.

General

Imprint:	Springer Nature Switzerland AG
Country of origin:	Switzerland
Series:	Algorithms and Computation in Mathematics, 27
Release date:	March 2019
First published:	2018
Authors:	Antonio Montes
Dimensions:	235 x 155mm (L x W)
Format:	Hardcover
Pages:	276
Edition:	1st ed. 2018
ISBN-13:	978-3-03-003903-5
Categories:	Books > Computing & IT > General theory of computing > Mathematical theory of computation Books > Science & Mathematics > Mathematics > Algebra > General Books > Science & Mathematics > Mathematics > Applied mathematics > Mathematics for scientists & engineers Promotions
LSN:	3-03-003903-X
Barcode:	9783030039035

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