Polynomial and matrix computations (vol. 1): fundamental algorithms
Polynomial and matrix computations (vol. 1): fundamental algorithms
A computational method for diophantine approximation
Algorithms in algebraic geometry and applications
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
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)
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.