Solving polynomial equation systems, Volume 4, Buchberger's theory and beyond:
In this fourth and final volume the author extends Buchberger's Algorithm in three different directions. First, he extends the theory to group rings and other Ore-like extensions, and provides an operative scheme that allows one to set a Buchberger theory over any effective associative ring. Se...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2016
|
| Series: | Encyclopedia of mathematics and its applications
volume 158 |
| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| Summary: | In this fourth and final volume the author extends Buchberger's Algorithm in three different directions. First, he extends the theory to group rings and other Ore-like extensions, and provides an operative scheme that allows one to set a Buchberger theory over any effective associative ring. Second, he covers similar extensions as tools for discussing parametric polynomial systems, the notion of SAGBI-bases, Gröbner bases over invariant rings and Hironaka's theory. Finally, Mora shows how Hilbert's followers - notably Janet, Gunther and Macaulay - anticipated Buchberger's ideas and discusses the most promising recent alternatives by Gerdt (involutive bases) and Faugère (F4 and F5). This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Apr 2016) |
| Physical Description: | 1 online resource (xi, 820 pages) |
| ISBN: | 9781316271902 |
| DOI: | 10.1017/CBO9781316271902 |
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| contents | 1. Solving polynomial equation systems -- 2. Macaulay's Paradigm and Gröbner Technology -- 3. Algebraic Solving |
| ctrlnum | (ZDB-20-CBO)CR9781316271902 (OCoLC)967599621 (DE-599)BVBBV043940303 |
| dewey-full | 512.9/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/4 |
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| discipline | Mathematik |
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| id | DE-604.BV043940303 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:13Z |
| institution | BVB |
| isbn | 9781316271902 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029349273 |
| oclc_num | 967599621 |
| open_access_boolean | |
| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xi, 820 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Mora, Teo Verfasser aut Solving polynomial equation systems, Volume 4, Buchberger's theory and beyond Teo Mora Cambridge Cambridge University Press 2016 1 online resource (xi, 820 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 158 Title from publisher's bibliographic system (viewed on 05 Apr 2016) 1. Solving polynomial equation systems -- 2. Macaulay's Paradigm and Gröbner Technology -- 3. Algebraic Solving In this fourth and final volume the author extends Buchberger's Algorithm in three different directions. First, he extends the theory to group rings and other Ore-like extensions, and provides an operative scheme that allows one to set a Buchberger theory over any effective associative ring. Second, he covers similar extensions as tools for discussing parametric polynomial systems, the notion of SAGBI-bases, Gröbner bases over invariant rings and Hironaka's theory. Finally, Mora shows how Hilbert's followers - notably Janet, Gunther and Macaulay - anticipated Buchberger's ideas and discusses the most promising recent alternatives by Gerdt (involutive bases) and Faugère (F4 and F5). This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers Equations / Numerical solutions Polynomials Iterative methods (Mathematics) Erscheint auch als Druckausgabe 978-1-107-10963-6 https://doi.org/10.1017/CBO9781316271902 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Mora, Teo Solving polynomial equation systems, Volume 4, Buchberger's theory and beyond 1. Solving polynomial equation systems -- 2. Macaulay's Paradigm and Gröbner Technology -- 3. Algebraic Solving Equations / Numerical solutions Polynomials Iterative methods (Mathematics) |
| title | Solving polynomial equation systems, Volume 4, Buchberger's theory and beyond |
| title_auth | Solving polynomial equation systems, Volume 4, Buchberger's theory and beyond |
| title_exact_search | Solving polynomial equation systems, Volume 4, Buchberger's theory and beyond |
| title_full | Solving polynomial equation systems, Volume 4, Buchberger's theory and beyond Teo Mora |
| title_fullStr | Solving polynomial equation systems, Volume 4, Buchberger's theory and beyond Teo Mora |
| title_full_unstemmed | Solving polynomial equation systems, Volume 4, Buchberger's theory and beyond Teo Mora |
| title_short | Solving polynomial equation systems, Volume 4, Buchberger's theory and beyond |
| title_sort | solving polynomial equation systems volume 4 buchberger s theory and beyond |
| topic | Equations / Numerical solutions Polynomials Iterative methods (Mathematics) |
| topic_facet | Equations / Numerical solutions Polynomials Iterative methods (Mathematics) |
| url | https://doi.org/10.1017/CBO9781316271902 |
| work_keys_str_mv | AT morateo solvingpolynomialequationsystemsvolume4buchbergerstheoryandbeyond |