Computational Algebraic Geometry

E. Becker, R. Neuhaus (auth.), Frédéric Eyssette, André Galligo (eds.)9780817636784, 0817636781, 3764336781

Proceedings of a symposium held in Nice, France, in April 1992, on the themes of effective methods and complexity issues in commutative algebra, projective geometry, real geometry, algebraic number theory, and algebro-geometric methods in algebraic computing and applications. Papers discuss Koszul complex, Grobner bases and standard monomial theory, versal deformations of powers of volume forms, computer vision, counting real zeros in the multivariate case, locally effective objects and algebraic topology, and a parameterized nullstellensatz. No index. Annotation copyright Book News, Inc. Portland, Or.

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Table of contents :
Front Matter….Pages i-ix
Computation of Real Radicals of Polynomial Ideals….Pages 1-20
Semialgebraic geometry of polynomial control problems….Pages 21-28
The Resultant via a Koszul Complex….Pages 29-39
Gröbner Bases and Standard Monomial Theory….Pages 41-60
A continuous and rational solution to Hilbert’s 17 th problem and several cases of the Positivstellensatz….Pages 61-75
The analytic spread of the ideal of a monomial curve in projective 3-space….Pages 77-90
Computational Complexity of Sparse Real Algebraic Function Interpolation….Pages 91-104
Shade, Shadow and Shape….Pages 105-128
Arrangements of singularities and proper partitions of Dynkin diagrams….Pages 129-142
Versal deformations of powers of volume forms….Pages 143-162
Computing subfields: Reverse of the primitive element problem….Pages 163-176
Applications of the Eisenbud-Levine’s theorem to real algebraic geometry….Pages 177-184
Applications of Algebraic Geometry to Computer Vision….Pages 185-194
Disproving Hibi’s Conjecture with CoCoA or Projective Curves with bad Hilbert Functions….Pages 195-201
Counting real zeros in the multivariate case….Pages 203-224
Finding the number of distinct real roots of sparse polynomials of the form p(x,x n )….Pages 225-233
Locally effective objects and algebraic topology….Pages 235-251
Decision of Algebra Isomorphisms Using Gröbner Bases….Pages 253-265
Complexity of Bezout’s Theorem II Volumes and Probabilities….Pages 267-285
A Parametrized Nullstellensatz….Pages 287-300
An Elimination Method Based on Seidenberg’s Theory and Its Applications….Pages 301-328
Back Matter….Pages 329-332