Bounds for Substituting Algebraic Functions into D-finite Functions

Manuel Kauers; Gleb Pogudin

doi:10.48550/arXiv.1701.07802

Bounds for Substituting Algebraic Functions into D-finite Functions

Manuel Kauers, Gleb Pogudin

Institute for Algebra

Research output: Working paper and reports › Preprint

Abstract

It is well-known that the composition of a D-finite function with an algebraic function is again D-finite. We give the first estimates for the orders and the degrees of annihilating operators for the compositions. We find that the analysis of removable singularities leads to an order-degree curve which is much more accurate than the order-degree curve obtained from the usual linear algebra reasoning.

Original language	English
Number of pages	14
DOIs	https://doi.org/10.48550/arXiv.1701.07802
Publication status	Published - Jan 2017

Publication series

Name	arXiv.org
ISSN (Print)	2331-8422

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101013 Mathematical logic
102031 Theoretical computer science

JKU Focus areas

Computation in Informatics and Mathematics
Engineering and Natural Sciences (in general)

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10.48550/arXiv.1701.07802

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AU - Pogudin, Gleb

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AB - It is well-known that the composition of a D-finite function with an algebraic function is again D-finite. We give the first estimates for the orders and the degrees of annihilating operators for the compositions. We find that the analysis of removable singularities leads to an order-degree curve which is much more accurate than the order-degree curve obtained from the usual linear algebra reasoning.

UR - https://arxiv.org/abs/1701.07802

U2 - 10.48550/arXiv.1701.07802

DO - 10.48550/arXiv.1701.07802

M3 - Preprint

T3 - arXiv.org

BT - Bounds for Substituting Algebraic Functions into D-finite Functions

ER -

Bounds for Substituting Algebraic Functions into D-finite Functions

Abstract

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