On computing the determinant in small parallel time using a small number of processors
Information Processing Letters
Basic principles of mechanical theorem proving in elementary geometrics
Journal of Automated Reasoning
Some algebraic and geometric computations in PSPACE
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Gröbner bases and primary decomposition of polynomial ideals
Journal of Symbolic Computation
A new method for solving algebraic systems of positive dimension
Discrete Applied Mathematics - Special volume on applied algebra, algebraic algorithms, and error-correcting codes
Computation of Hilbert functions
Journal of Symbolic Computation
A generalized Euclidean algorithm for computing triangular representations of algebraic varieties
Journal of Symbolic Computation
Irreducible decomposition of algebraic varieties via characteristic sets and Gro¨bner bases
Computer Aided Geometric Design
Prime decompositions of radicals in polynomial rings
Journal of Symbolic Computation
Complexity of the Wu-Ritt decomposition
PASCO '97 Proceedings of the second international symposium on Parallel symbolic computation
Some complexity results for polynomial ideals
Journal of Complexity
Algorithmic properties of polynomial rings
Journal of Symbolic Computation
On the theories of triangular sets
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Parallel Arithmetic Computations: A Survey
Mathematical Foundations of Computer Science 1986
The computation of the Hilbert function
EUROCAL '83 Proceedings of the European Computer Algebra Conference on Computer Algebra
Randomized and deterministic algorithms for the dimension of algebraic varieties
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
The complexity of semilinear problems in succinct representation
Computational Complexity
Foundations of Computational Mathematics
Differential forms in computational algebraic geometry
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
On a generalization of Stickelberger's Theorem
Journal of Symbolic Computation
Effective de Rham cohomology: the hypersurface case
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Hi-index | 0.00 |
We give a uniform method for the two problems of counting the connected and irreducible components of complex algebraic varieties. Our algorithms are purely algebraic, i.e., they use only the field structure of C. They work in parallel polynomial time, i.e., they can be implemented by algebraic circuits of polynomial depth. The design of our algorithms relies on the concept of algebraic differential forms. A further important building block is an algorithm of Szanto computing a variant of characteristic sets. Furthermore, we use these methods to obtain a parallel polynomial time algorithm for computing the Hilbert polynomial of a projective variety which is arithmetically Cohen-Macaulay.