Solving polynomial equation systems.: Volume IV, Buchberger 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...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge :
Cambridge University Press,
2016.
|
| Series: | Encyclopedia of mathematics and its applications ;
158. |
| Subjects: | |
| Online Access: | DE-862 DE-863 |
| 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. |
| Physical Description: | 1 online resource (xi, 820 pages) |
| Bibliography: | Includes bibliographical references (pages 803-812) and index. |
| ISBN: | 9781316271902 1316271900 9781316384985 1316384985 |
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| id | ZDB-4-EBA-ocn946609910 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-18T14:22:49Z |
| institution | BVB |
| isbn | 9781316271902 1316271900 9781316384985 1316384985 |
| language | English |
| oclc_num | 946609910 |
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| publisher | Cambridge University Press, |
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| series | Encyclopedia of mathematics and its applications ; |
| series2 | Encyclopedia of mathematics and its applications ; |
| spelling | Mora, Teo, author. http://id.loc.gov/authorities/names/n78023685 Solving polynomial equation systems. Volume IV, Buchberger theory and beyond / Teo Mora. Buchberger theory and beyond Cambridge : Cambridge University Press, 2016. ©2016 1 online resource (xi, 820 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of mathematics and its applications ; 158 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. Includes bibliographical references (pages 803-812) and index. Zacharias -- Bergman -- Ufnarovski -- Weispfenning -- Spear 2 -- Weispfenning II -- Sweedler -- Hironaka -- Hironaka II -- Janet -- Macaulay V -- Gerdt and Faugere. Print version record. Commutative rings. http://id.loc.gov/authorities/subjects/sh85029269 Commutative algebra. http://id.loc.gov/authorities/subjects/sh85029267 Anneaux commutatifs. Algèbre commutative. MATHEMATICS Algebra Intermediate. bisacsh Anillos conmutativos embne Álgebra conmutativa embne Commutative algebra fast Commutative rings fast Print version: Mora, Teo. Solving polynomial equation systems. Volume IV, Buchberger theory and beyond. Cambridge : Cambridge University Press, 2016 1107109639 (OCoLC)945641191 Encyclopedia of mathematics and its applications ; 158. http://id.loc.gov/authorities/names/n42010632 |
| spellingShingle | Mora, Teo Solving polynomial equation systems. Encyclopedia of mathematics and its applications ; Zacharias -- Bergman -- Ufnarovski -- Weispfenning -- Spear 2 -- Weispfenning II -- Sweedler -- Hironaka -- Hironaka II -- Janet -- Macaulay V -- Gerdt and Faugere. Commutative rings. http://id.loc.gov/authorities/subjects/sh85029269 Commutative algebra. http://id.loc.gov/authorities/subjects/sh85029267 Anneaux commutatifs. Algèbre commutative. MATHEMATICS Algebra Intermediate. bisacsh Anillos conmutativos embne Álgebra conmutativa embne Commutative algebra fast Commutative rings fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85029269 http://id.loc.gov/authorities/subjects/sh85029267 |
| title | Solving polynomial equation systems. |
| title_alt | Buchberger theory and beyond |
| title_auth | Solving polynomial equation systems. |
| title_exact_search | Solving polynomial equation systems. |
| title_full | Solving polynomial equation systems. Volume IV, Buchberger theory and beyond / Teo Mora. |
| title_fullStr | Solving polynomial equation systems. Volume IV, Buchberger theory and beyond / Teo Mora. |
| title_full_unstemmed | Solving polynomial equation systems. Volume IV, Buchberger theory and beyond / Teo Mora. |
| title_short | Solving polynomial equation systems. |
| title_sort | solving polynomial equation systems buchberger theory and beyond |
| topic | Commutative rings. http://id.loc.gov/authorities/subjects/sh85029269 Commutative algebra. http://id.loc.gov/authorities/subjects/sh85029267 Anneaux commutatifs. Algèbre commutative. MATHEMATICS Algebra Intermediate. bisacsh Anillos conmutativos embne Álgebra conmutativa embne Commutative algebra fast Commutative rings fast |
| topic_facet | Commutative rings. Commutative algebra. Anneaux commutatifs. Algèbre commutative. MATHEMATICS Algebra Intermediate. Anillos conmutativos Álgebra conmutativa Commutative algebra Commutative rings |
| work_keys_str_mv | AT morateo solvingpolynomialequationsystemsvolumeiv AT morateo buchbergertheoryandbeyond |