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 |
| 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. |
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| Physical Description: | 1 online resource (xi, 820 pages) |
| Bibliography: | Includes bibliographical references (pages 803-812) and index. |
| ISBN: | 9781316271902 1316271900 9781316384985 1316384985 |
