On fast multiplication of polynomials over arbitrary algebras
Acta Informatica
An introduction to pseudo-linear algebra
Selected papers of the conference on Algorithmic complexity of algebraic and geometric models
Characterization of a linear differential system with a regular singularity
EUROCAL '83 Proceedings of the European Computer Algebra Conference on Computer Algebra
Factorization of differential systems in characteristic p
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
High-order lifting and integrality certification
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Multiplying matrices faster than coppersmith-winograd
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
A polynomial-time algorithm for the jacobson form of a matrix of ore polynomials
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
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Uncoupling algorithms transform a linear differential system of first order into one or several scalar differential equations. We examine two approaches to uncoupling: the cyclic-vector method (CVM) and the Danilevski-Barkatou-Zürcher algorithm (DBZ). We give tight size bounds on the scalar equations produced by CVM, and design a fast variant of CVM whose complexity is quasi-optimal with respect to the output size. We exhibit a strong structural link between CVM and DBZ enabling to show that, in the generic case, DBZ has polynomial complexity and that it produces a single equation, strongly related to the output of CVM. We prove that algorithm CVM is faster than DBZ by almost two orders of magnitude, and provide experimental results that validate the theoretical complexity analyses.