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Algorithms and Computation in Mathematics

The Gröbner Cover

Authors: Montes Lozano, Antonio

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  • 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
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eBook 83,29 €
price for Spain (gross)
  • ISBN 978-3-030-03904-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 103,99 €
price for Spain (gross)
  • ISBN 978-3-030-03903-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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.

Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook 83,29 €
price for Spain (gross)
  • ISBN 978-3-030-03904-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 103,99 €
price for Spain (gross)
  • ISBN 978-3-030-03903-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
The Gröbner Cover
Authors
Series Title
Algorithms and Computation in Mathematics
Series Volume
27
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-03904-2
DOI
10.1007/978-3-030-03904-2
Hardcover ISBN
978-3-030-03903-5
Series ISSN
1431-1550
Edition Number
1
Number of Pages
XIV, 276
Number of Illustrations
2 b/w illustrations, 51 illustrations in colour
Topics