|
| Author(s) |
Eissette, F. (ed.) Galligo, A. (ed.) |
|---|---|
| Title | Computational Algebraic Geometry |
| Publisher | Birkhäuser |
| Year of publication | 1992 |
| Reviewed by | Bazil Pârv |
This volume, the 1O9th of the series "Progress in Mathematics", edited by Birkhäuser, gathers together 21 papers on new theoretical and practical aspects of algebraic geometry, presented at MEGA-92 conference (Effective Methods in Algebraic Geometry, Nice, France, April 21-25, 1992). The first MEGA conference was held in Livorno, Italy, on April 17-21, 1990; the 94th issue of the -above mentioned series contains papers presented there.
The main two topics on which the papers are oriented can be: effective methods and complexity issues in commutative algebra, projective geometry, real geometry, algebraic number theory; algebro-geometric methods in algebraic computing and applications. The above mentioned papers are the following:
E. Becker and R. Neuhaus: Computation of real radicals of polynomial ideals
M. Briskin and Y. Yomdin: Semialgebraic geometry of polynomial control problems
M. Chardin: The resultant via a Koszul complex
A.M. Cohen and R.H. Cushman: Gröbner bases and standard monomial theory
C.N. Delzell, L. Gonzalez-Vega, and H. Lombardi: A continuous and rational solution to Hilbert's 17th problem and several cases of the Positivstellensatz
P. Gimenez, M. Morales, and A. Simis: The analytic spread of the ideal of a monomial curve in projective 3-space
D. Grigoriev, M. Karpinski, and M.F. Singer: Computational complexity of sparse real algebraic function interpolation
J.-P. Henry and M. Merle: Shade, shadow and shape
P. Jaworski: Arrangements of singularities and proper partitions of Dynkin diagrams
V.P. Kostov and S.K. Lando: Versal deformations of powers of volume forms
D. Lazard and A. Valibouze: Computing subfields: Reverse of the primitive element problem
A. Lecki and Z. Szafraniec: Applications of Eisenbud-Levine's theorem to real algebraic geometry
S.J. Maybank: Applications of algebraic geometry to computer vision
G. Niesi and L. Robbiano: Disproving Hibi's conjecture with CoCoA or projective curves with bad Hilbert functions
P. Pedersen, M.-F. Roy, and A. Szpirglas: Counting real zeros in the multivariate case
D. Richardson: Finding the number of distinct real roots of sparse polynomials of the form p(x,x^n)
J. Rubio and F. Sergeraet: Locally effective objects and algebraic topology
K. Shirayanagi: Decision of algebra isomorphisms using Gröbner bases
M. Shub and S. Smale: Complexity of Bezout's theorem II: volumes and probabilities
F. Smietanski: A parametrized Nullstellensatz
D. Wang: An ellimination method based on Seidenberg's theory and its applications
The book is typeset; even if it contains several contributions from different authors, the manner in which the text is ranged is unitary and makes the papers pleasant to read.
The volume, whose price/consistency ratio is high enough, is available, in my opinion, only for professional mathematicians and graduate students working in this field.