A Computable Extension for Holonomic Functions: DD-Finite Functions

Antonio Jimenez Pastor; Veronika Pillwein

doi:10.1016/j.jsc.2018.07.002

A Computable Extension for Holonomic Functions: DD-Finite Functions

Antonio Jimenez Pastor, Veronika Pillwein

Research Institute for Symbolic Computation

Research output: Contribution to journal › Article › peer-review

Abstract

Differentiably finite (D-finite) formal power series form a large class of useful functions for which a variety of symbolic algorithms exists. Among these methods are several closure properties that can be carried out automatically. We introduce a natural extension of these functions to a larger class of computable objects for which we prove closure properties. These are again algorithmic. This extension can be iterated constructively preserving the closure properties.

Original language	English
Pages (from-to)	90-104
Number of pages	15
Journal	Journal of Symbolic Computation
Volume	94
DOIs	https://doi.org/10.1016/j.jsc.2018.07.002
Publication status	Published - Sept 2019

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101009 Geometry
101012 Combinatorics
101013 Mathematical logic
101020 Technical mathematics

JKU Focus areas

Digital Transformation

Access to Document

10.1016/j.jsc.2018.07.002

Cite this

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title = "A Computable Extension for Holonomic Functions: DD-Finite Functions",

abstract = "Differentiably finite (D-finite) formal power series form a large class of useful functions for which a variety of symbolic algorithms exists. Among these methods are several closure properties that can be carried out automatically. We introduce a natural extension of these functions to a larger class of computable objects for which we prove closure properties. These are again algorithmic. This extension can be iterated constructively preserving the closure properties.",

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AB - Differentiably finite (D-finite) formal power series form a large class of useful functions for which a variety of symbolic algorithms exists. Among these methods are several closure properties that can be carried out automatically. We introduce a natural extension of these functions to a larger class of computable objects for which we prove closure properties. These are again algorithmic. This extension can be iterated constructively preserving the closure properties.

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DO - 10.1016/j.jsc.2018.07.002

M3 - Article

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JO - Journal of Symbolic Computation

JF - Journal of Symbolic Computation

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