Journal of Symbolic Computation
On the combinatorial and algebraic complexity of quantifier elimination
Journal of the ACM (JACM)
A computational method for diophantine approximation
Algorithms in algebraic geometry and applications
The space complexity of elimination theory: upper bounds
FoCM '97 Selected papers of a conference on Foundations of computational mathematics
Solving some overdetermined polynomial systems
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Journal of the ACM (JACM)
Bounds on numers of vectors of multiplicities for polynomials which are easy to compute
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Some Effectivity Problems in Polynomial Ideal Theory
EUROSAM '84 Proceedings of the International Symposium on Symbolic and Algebraic Computation
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Numerical algebraic geometry and symbolic computation
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Sum of roots with positive real parts
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
On using bi-equational constraints in CAD construction
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
An open problem on metric invariants of tetrahedra
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
A theoretical basis for the reduction of polynomials to canonical forms
ACM SIGSAM Bulletin
Solving parametric polynomial systems
Journal of Symbolic Computation
Solving parametric polynomial systems
Journal of Symbolic Computation
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Dynamic balancing of planar mechanisms using toric geometry
Journal of Symbolic Computation
Solution of algebraic riccati equations using the sum of roots
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
A package for solving parametric polynomial systems
ACM Communications in Computer Algebra
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Consider a parametric system of n polynomial equations and r polynomial inequations in n unknowns and s parameters, with rational coefficients. A recurrent problem is to determine some open set in the parameter space where the considered parametric system admits a constant number of real solutions. Following the works of Lazard and Rouillier, this can be done by the computation of a discriminant variety. Let d bound the degree of the input's polynomials, and σ bound the bit-size of their coefficients. Based on some usual assumptions for the applications we prove that the degree of the computed minimal discriminant variety is bounded by D := (n+r)d(n+1). Moreover we provide in this case a deterministic method which computes the minimal discriminant variety in σO(1)DO(n+s) bit-operations on a deterministic Turing machine.