Some algebraic and geometric computations in PSPACE
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
A subresultant theory for multivariate polynomials
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
On the Newton Polytope of the Resultant
Journal of Algebraic Combinatorics: An International Journal
Efficient incremental algorithms for the sparse resultant and the mixed volume
Journal of Symbolic Computation
Counting affine roots of polynomial systems via pointed Newton polytopes
Journal of Complexity
On the complexity of sparse elimination
Journal of Complexity
Mathematics of Computation
Complexity and real computation
Complexity and real computation
FoCM '97 Selected papers of a conference on Foundations of computational mathematics
Modern computer algebra
Solving degenerate sparse polynomial systems faster
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
A subdivision-based algorithm for the sparse resultant
Journal of the ACM (JACM)
A Gröbner free alternative for polynomial system solving
Journal of Complexity
Symbolic and numeric methods for exploiting structure in constructing resultant matrices
Journal of Symbolic Computation
Sparse resultant of composed polynomials I* mixed-unmixed case
Journal of Symbolic Computation
Sparse resultant of composed polynomials II unmixed--mixed case
Journal of Symbolic Computation
An Efficient Algorithm for the Sparse Mixed Resultant
AAECC-10 Proceedings of the 10th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Real solving for positive dimensional systems
Journal of Symbolic Computation
Multihomogeneous resultant formulae by means of complexes
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
The resultant of an unmixed bivariate system
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Computing the sign or the value of the determinant of an integer matrix, a complexity survey
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
The Computational Complexity of the Chow Form
Foundations of Computational Mathematics
Enumerating a subset of the integer points inside a Minkowski sum
Computational Geometry: Theory and Applications
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We describe algorithms for solving a given system of multivariate polynomial equations via the Rational Univariate Reduction (RUR). We compute the RUR from the toric resultant of the input system. Our algorithms derandomize several of the choices made in similar prior algorithms. We also propose a new derandomized algorithm for solving an overdetermined system. Finally, we analyze the computational complexity of the algorithm, and discuss its implementation and performance.