TY  - GEN
AU  - Mora, Teo 
TI  - Solving Polynomial Equation Systems III: algebraic solving, Vol. 157
SN  - 9780521811552
U1  - 512.94 
PY  - 2015///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Mathematics
KW  - Equations
KW  - Intermediate
KW  - Algebra
KW  - Numerical Solutions
KW  - Polynomials
N1  - Includes bibliographical references and index
N2  - This third volume of four finishes the program begun in Volume 1 by describing all the most important techniques, mainly based on Gröbner 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 Bézout 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
ER  -