TY - BOOK ID - 110789664 TI - Solving polynomial equation systems. PY - 2016 SN - 1316383180 1316359182 1316360385 1316359786 1316384985 1316271900 1316379582 PB - Cambridge : Cambridge University Press, DB - UniCat KW - Equations KW - Polynomials. KW - Iterative methods (Mathematics) KW - Numerical solutions. KW - Iteration (Mathematics) KW - Numerical analysis KW - Algebra KW - Graphic methods UR - https://www.unicat.be/uniCat?func=search&query=sysid:110789664 AB - 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. ER -