This third volume of four finishes the program begun in Volume 1 by describing all the most important techniques, mainly based on Groebner bases, which allow one to manipulate the roots of the equation rather than just compute them. The book begins with the 'standard' solutions Gianni-Kalkbrener Theorem, Stetter Algorithm, Cardinal-Mourrain result and then moves on to more innovative methods Lazard triangular sets, Rouillier's Rational Univariate Representation, the TERA Kronecker package. The author also looks at classical results, such as Macaulay's Matrix, and provides a historical survey of elimination, from Bezout to Cayley. This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers.
Number of Pages: 294 Format(s): Hardback - ISBN: 9780521811552 Publication Date:07/08/2015 Listed in:Algebra Publisher:CAMBRIDGE UNIVERSITY PRESS