Computational Algebraic Geometry

Inhaltsverzeichnis

• Computation of Real Radicals of Polynomial Ideals.
• Semialgebraic geometry of polynomial control problems.
• The Resultant via a Koszul Complex.
• Gröbner Bases and Standard Monomial Theory.
• A Continuous and rational solution to Hubert’s 17th problem and several cases of the Positivstellensatz.
• The analytic spread of the ideal of a monomial curve in projective 3-space.
• Computational Complexity of Sparse Real Algebraic Function Interpolation.
• Shade, Shadow and Shape.
• Arrangements of singularities and proper partitions of Dynkin diagrams.
• Versal deformations of powers of volume forms.
• Computing subfields: Reverse of the primitive element problem.
• Applications of Eisenbud-Levine’s theorem to real algebraic geometry.
• Applications of Algebraic Geometry to Computer Vision.
• Disproving Hibi’s Conjecture with CoCoA or Projective Curves with bad Hilbert Functions.
• Counting real zeros in the multivariate case.
• Finding the number of distinct real roots of sparse polynomials of the form p(x, xn).
• Locally effective objects and algebraic topology.
• Decision of Algebra Isomorphisms using Gröbner Bases.
• Complexity of Bezout’s Theorem II: Volumes and Probabilities.
• A Parametrized Nullstellensatz.
• An Elimination Method Based on Seidenberg’s Theory and Its Applications.