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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 ¿[...]¿ implemented in Singular by the author, and serve as a User Manual for it.
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 ¿[...]¿ implemented in Singular by the author, and serve as a User Manual for it.
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 "[...]" library
Written by one of the leading experts in GC
| Erscheinungsjahr: | 2019 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Inhalt: |
xiv
276 S. 2 s/w Illustr. 51 farbige Illustr. 276 p. 53 illus. 51 illus. in color. |
| ISBN-13: | 9783030039035 |
| ISBN-10: | 303003903X |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-030-03903-5 |
| Einband: | Gebunden |
| Autor: | Montes, Antonio |
| Auflage: | 1st edition 2018 |
| Hersteller: |
Springer Nature Switzerland
Springer International Publishing |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 241 x 160 x 22 mm |
| Von/Mit: | Antonio Montes |
| Erscheinungsdatum: | 15.03.2019 |
| Gewicht: | 0,606 kg |
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 "[...]" library
Written by one of the leading experts in GC
| Erscheinungsjahr: | 2019 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Inhalt: |
xiv
276 S. 2 s/w Illustr. 51 farbige Illustr. 276 p. 53 illus. 51 illus. in color. |
| ISBN-13: | 9783030039035 |
| ISBN-10: | 303003903X |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-030-03903-5 |
| Einband: | Gebunden |
| Autor: | Montes, Antonio |
| Auflage: | 1st edition 2018 |
| Hersteller: |
Springer Nature Switzerland
Springer International Publishing |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 241 x 160 x 22 mm |
| Von/Mit: | Antonio Montes |
| Erscheinungsdatum: | 15.03.2019 |
| Gewicht: | 0,606 kg |
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