Polynomial and matrix computations (vol. 1): fundamental algorithms
Polynomial and matrix computations (vol. 1): fundamental algorithms
Modern computer algebra
The complexity of resolvent resolved
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Deformation techniques for efficient polynomial equation solving
Journal of Complexity
A Gröbner free alternative for polynomial system solving
Journal of Complexity
A probabilistic algorithm to test local algebraic observability in polynomial time
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
When Polynomial Equation Systems Can Be "Solved" Fast?
AAECC-11 Proceedings of the 11th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Complexity of quantifier elimination in the theory of ordinary differential equations
EUROCAL '87 Proceedings of the European Conference on Computer Algebra
Fast computation of discrete invariants associated to a differential rational mapping
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Notes on triangular sets and triangulation-decomposition algorithms II: differential systems
SNSC'01 Proceedings of the 2nd international conference on Symbolic and numerical scientific computation
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We prove upper bounds on the order and degree of the polynomials involved in a resolvent representation of the prime differential ideal associated with a polynomial differential system for a particular class of ordinary first order algebraic-differential equations arising in control theory. We also exhibit a probabilistic algorithm which computes this resolvent representation within time polynomial in the natural syntactic parameters and the degree of a certain algebraic variety related to the input system. In addition, we give a probabilistic polynomial-time algorithm for the computation of the differential Hilbert function of the ideal.