Name: The Gröbner Cover (Algorithms and Computation in Mathematics) (en Inglés)
Price: 532322.00 COP
Availability: InStock
Author: Antonio Montes
ISBN: 9783030039035

portada The Gröbner Cover (Algorithms and Computation in Mathematics) (en Inglés)

Formato

Libro Físico

Editorial

Springer

Autor

Antonio Montes

Año

2019

Idioma

Inglés

N° páginas

276

Encuadernación

Tapa Dura

ISBN13

9783030039035

N° edición

Categorías

Ciencia y análisis de datos
Análisis y captura de datos

The Gröbner Cover (Algorithms and Computation in Mathematics) (en Inglés)

Antonio Montes (Autor) · Springer · Tapa Dura

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Reseña del libro "The Gröbner Cover (Algorithms and Computation in Mathematics) (en Inglés)"

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.