Probabilistic algorithms for computing resolvent representations of regular differential ideals

DOI10.1007/s00200-008-0079-8zbMath1192.12005OpenAlexW1998206344MaRDI QIDQ985372

Evelyne Hubert, Thomas Cluzeau

Publication date: 5 August 2010

Published in: Applicable Algebra in Engineering, Communication and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00200-008-0079-8

zbMATH Keywords

probabilistic algorithmsdifferential algebradifferential eliminationchange of rankingdifferential primitive elementresolvent representation

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Parallel algorithms in computer science (68W10) Differential algebra (12H05) Software, source code, etc. for problems pertaining to field theory (12-04)

Related Items (2)

A geometric index reduction method for implicit systems of differential algebraic equations ⋮ A primitive element theorem for fields with commuting derivations and automorphisms

Uses Software

• Kronecker
• ISOLATE
• DIFFALG

Cites Work

• Definability and fast quantifier elimination in algebraically closed fields
• A bound for the Rosenfeld-Gröbner algorithm
• Algebraic transformation of differential characteristic decompositions from one ranking to another
• Computing representations for radicals of finitely generated differential ideals
• Solving zero-dimensional systems through the rational univariate representation
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• Resolvent representation for regular differential ideals
• Factorization-free decomposition algorithms in differential algebra
• On the theories of triangular sets
• A bound for the order of characteristic set elements of an ordinary prime differential ideal and some applications
• Essential components of an algebraic differential equation
• On the complexity of the resolvent representation of some prime differential ideals
• Resolvent systems of difference polynomial ideals
• A Simple Algorithm for Cyclic Vectors
• Fast Probabilistic Algorithms for Verification of Polynomial Identities
• Improvements to a triangulation-decomposition algorithm for ordinary differential systems in higher degree cases
• Specializations in Differential Algebra
• Formal Solutions of Irregular Linear Differential Equations. Part II
• Some Basic Theorems in Differential Algebra (Characteristic p, Arbitrary)
• Unmixed-dimensional decomposition of a finitely generated perfect differential ideal
• A Gröbner free alternative for polynomial system solving
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