Authors:
- The book gives a complete description of the Canonical Gröbner Cover
- Detailed description of three selected problems for which GC gives a new perspective
- All the algorithms described have been included in the software “grobcov.lib” library
- Written by one of the leading experts in GC
Part of the book series: Algorithms and Computation in Mathematics (AACIM, volume 27)
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Table of contents (8 chapters)
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Front Matter
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Applications
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Front Matter
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Back Matter
About this book
This book is divided into two parts, one theoretical and one focusing on applications, and offers a complete description of the Canonical Gröbner 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 Gröbner Systems and Bases. It begins with Weispfenning’s introduction of Comprehensive Gröbner Systems (CGS) in 1992, and provides a complete description of the Gröbner 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 Gröbner 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.Reviews
Authors and Affiliations
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Universitat Politècnica de Catalunya, Barcelona, Spain
Antonio Montes
Bibliographic Information
Book Title: The Gröbner Cover
Authors: Antonio Montes
Series Title: Algorithms and Computation in Mathematics
DOI: https://doi.org/10.1007/978-3-030-03904-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Hardcover ISBN: 978-3-030-03903-5Published: 15 March 2019
eBook ISBN: 978-3-030-03904-2Published: 01 March 2019
Series ISSN: 1431-1550
Edition Number: 1
Number of Pages: XIV, 276
Number of Illustrations: 2 b/w illustrations, 51 illustrations in colour
Topics: Commutative Rings and Algebras, Field Theory and Polynomials, Symbolic and Algebraic Manipulation