Around the numeric-symbolic computation of differential Galois groups

DOI10.1016/j.jsc.2006.03.007zbMath1396.34054OpenAlexW2052179590MaRDI QIDQ2457420

Joris van der Hoeven

Publication date: 23 October 2007

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2006.03.007

zbMATH Keywords

algorithmalgebraic groupaccelero-summationStokes multipliersDifferential Galois group

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Differential algebra (12H05) Numerical methods for ordinary differential equations (65L99) Formal solutions and transform techniques for ordinary differential equations in the complex domain (34M25) Asymptotics and summation methods for ordinary differential equations in the complex domain (34M30) Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain (34M15) Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain (34M40)

Related Items (11)

A characterization of reduced forms of linear differential systems ⋮ Degree bound for toric envelope of a linear algebraic group ⋮ Reduced forms of linear differential systems and the intrinsic Galois-Lie algebra of Katz ⋮ Monads and distributive laws for Rota-Baxter and differential algebras ⋮ Liouville integrability: an effective Morales-Ramis-Simó theorem ⋮ Minimization of differential equations and algebraic values of 𝐸-functions ⋮ Efficient accelero-summation of holonomic functions ⋮ A new bound on Hrushovski’s algorithm for computing the Galois group of a linear differential equation ⋮ Confluence of meromorphic solutions of \(q\)-difference equations ⋮ Linear differential systems with small coefficients: various types of solvability and their verification ⋮ Computing the Lie algebra of the differential Galois group: the reducible case

Uses Software

• Mathemagix
• matrixss
• Mmxlib

Cites Work

• Multisummability and Stokes multipliers of linear meromorphic differential equations
• Computations with effective real numbers
• Factoring polynomials with rational coefficients
• Multisummability of formal power series solutions of nonlinear meromorphic differential equations
• Fast evaluation of holonomic functions
• Computation of invariants for reductive groups
• Galois groups of second and third order linear differential equations
• An algorithm for computing invariants of differential Galois groups
• Differential Galois groups of confluent generalized hypergeometric equations: An approach using Stokes multipliers
• Factorization of differential operators with rational functions coefficients
• Relax, but don't be too lazy
• Selecting base points for the Schreier-Sims algorithm for matrix groups
• Minimal heights and polarizations on group varieties
• Quantum automata and algebraic groups
• Effective analytic functions
• Efficient accelero-summation of holonomic functions
• Associative differential operations
• Fast computation of GCDs
• Acceleration of Euclidean algorithm and extensions
• Fast evaluation of holonomic functions near and in regular singularities
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