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: | |
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| Format: | eBook |
| Language: | English |
| Published: |
Cambridge :
Cambridge University Press,
2016.
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| Series: | Encyclopedia of mathematics and its applications ;
158. |
| Subjects: | |
| Online Access: | CONNECT CONNECT |
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| 100 | 1 | |a Mora, Teo, |e author. | |
| 245 | 1 | 0 | |a Solving polynomial equation systems. |n Volume IV, |p Buchberger theory and beyond / |c Teo Mora. |
| 246 | 3 | 0 | |a Buchberger theory and beyond |
| 264 | 1 | |a Cambridge : |b Cambridge University Press, |c 2016. | |
| 264 | 4 | |c ©2016 | |
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| 490 | 1 | |a Encyclopedia of mathematics and its applications ; |v 158 | |
| 520 | |a 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. | ||
| 504 | |a Includes bibliographical references (pages 803-812) and index. | ||
| 505 | 0 | |a Zacharias -- Bergman -- Ufnarovski -- Weispfenning -- Spear 2 -- Weispfenning II -- Sweedler -- Hironaka -- Hironaka II -- Janet -- Macaulay V -- Gerdt and Faugere. | |
| 588 | 0 | |a Print version record. | |
| 590 | 0 | |a EBSCO eBook Academic Comprehensive Collection North America | |
| 650 | 0 | |a Commutative rings. | |
| 650 | 0 | |a Commutative algebra. | |
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| 830 | 0 | |a Encyclopedia of mathematics and its applications ; |v 158. | |
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