Solving Polynomial Equation Systems

This third volume of four finishes the program begun in Volume 1 by describing all the most important techniques mainly based on Grbner bases which allow one to manipulate the roots of the equation rather than just compute them. The book begins with the ''standard'' solutions (GianniKalkbrener Theorem Stetter Algorithm CardinalMourrain 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 Bzout 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.