Computational Algebraic Geometry

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