Computing with D-algebraic power series

DOI10.1007/s00200-018-0358-yzbMath1462.68243OpenAlexW2799934948MaRDI QIDQ669617

Joris van der Hoeven

Publication date: 15 March 2019

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

Full work available at URL: https://doi.org/10.1007/s00200-018-0358-y

zbMATH Keywords

algorithmimplicit functionD-algebraic power serieszero test

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Implicit ordinary differential equations, differential-algebraic equations (34A09) Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Differential algebra (12H05)

Related Items (3)

Effective power series computations ⋮ On the exponential generating function of labelled trees ⋮ On existence and uniqueness of formal power series solutions of algebraic ordinary differential equations

Cites Work

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• Newton's method and FFT trading
• Power series solutions of algebraic differential equations
• Fast on-line integer multiplication
• Relax, but don't be too lazy
• Effective power series computations
• Complexity bounds for zero-test algorithms
• Faster relaxed multiplication
• Algebraic Properties of the Elementary Functions of Analysis
• Zero-Equivalence in Function Fields Defined by Algebraic Differential Equations
• Fast Algorithms for Manipulating Formal Power Series
• Decision problems for differential equations

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