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Updated: April 9th, 2024 05:02

2024 journal article

Telescopers for differential forms with one parameter

*SELECTA MATHEMATICA-NEW SERIES*, *30*(3).

author keywords: Telescopers; Differential forms; D-finite elements; Parametrized Poincare's lemma

Source: Web Of Science

Added: April 8, 2024

2022 book

Integration in Finite Terms: Fundamental Sources

Ed(s): C. Raab^{*} & ^{ n}

Source: Crossref

Added: November 8, 2023

2021 journal article

On differentially algebraic generating series for walks in the quarter plane

*SELECTA MATHEMATICA-NEW SERIES*, *27*(5).

author keywords: Lattice walks; Mordell-Weil lattices; Kodaira-Neron model; Random walks; Generating functions; Difference Galois theory; Elliptic functions; Transcendence; Neron-Tate height

TL;DR:
Algorithms based on the theory of Mordell-Weil lattices, that, for each weighted model, yield polynomial conditions on the weights determining this property of the associated generating series, are given.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

4. Quality Education
(Web of Science)

Source: Web Of Science

Added: September 20, 2021

2021 article

On the Kernel Curves Associated with Walks in the Quarter Plane

*TRANSCENDENCE IN ALGEBRA, COMBINATORICS, GEOMETRY AND NUMBER THEORY, TRANS19*, Vol. 373, pp. 61–89.

author keywords: Random walks; Uniformization of algebraic curves

TL;DR:
The basic properties of the kernel curve (irreducibility, singularties, genus, parametrization, etc) are investigated.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

4. Quality Education
(Web of Science)

Source: Web Of Science

Added: May 31, 2022

2021 article

Sparse Interpolation in Terms of Multivariate Chebyshev Polynomials

Hubert, E., & Singer, M. F. (2021, September 9). *FOUNDATIONS OF COMPUTATIONAL MATHEMATICS*.

author keywords: Chebyshev polynomials; Hankel matrix; Root systems; Sparse interpolation; Weyl groups

TL;DR:
A deterministic algorithm is presented to recover a function that is the linear combination of at most r such polynomials from the knowledge of r and an explicitly bounded number of evaluations of this function.
(via Semantic Scholar)

Source: Web Of Science

Added: September 20, 2021

2020 journal article

Some structural results on D-n-finite functions

*ADVANCES IN APPLIED MATHEMATICS*, *117*.

author keywords: Holonomic functions; Closure properties; Differential Galois theory; Algorithms

TL;DR:
This paper investigates how D n -finite functions behave under composition and how they are related to algebraic and differentially algebraic functions.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

4. Quality Education
(Web of Science)

Source: Web Of Science

Added: April 27, 2020

2020 journal article

Walks in the quarter plane: Genus zero case

*JOURNAL OF COMBINATORIAL THEORY SERIES A*, *174*.

author keywords: Random walks; Difference Galois theory; q-Difference equations; Transcendence

TL;DR:
It is proved that the generating series of (weighted) walks in the quarter plane with genus zero kernel curve do not satisfy any nontrivial algebraic differential equation with rational coefficients.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

4. Quality Education
(Web of Science)

Source: Web Of Science

Added: May 18, 2020

2019 journal article

Consistent systems of linear differential and difference equations

*JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY*, *21*(9), 2751–2792.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

9. Industry, Innovation and Infrastructure
(Web of Science)

Source: Web Of Science

Added: August 5, 2019

2018 journal article

On the nature of the generating series of walks in the quarter plane

*INVENTIONES MATHEMATICAE*, *213*(1), 139–203.

UN Sustainable Development Goal Categories

4. Quality Education
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2017 journal article

Galois groups for integrable and projectively integrable linear difference equations

*JOURNAL OF ALGEBRA*, *480*, 423–449.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

9. Industry, Innovation and Infrastructure
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2016 journal article

Desingularization of Ore operators

*JOURNAL OF SYMBOLIC COMPUTATION*, *74*, 617–626.

author keywords: D-finite functions; Apparent singularities; Computer algebra; Ore operators

TL;DR:
It is shown that Ore operators can be desingularized by calculating a least common left multiple with a random operator of appropriate order, thereby turning a heuristic used for many years in several computer algebra systems into an algorithm.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

4. Quality Education
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2015 journal article

Reductive Linear Differential Algebraic Groups and the Galois Groups of Parameterized Linear Differential Equations

*INTERNATIONAL MATHEMATICS RESEARCH NOTICES*, *2015*(7), 1733–1793.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

9. Industry, Innovation and Infrastructure
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2014 journal article

On the summability of bivariate rational functions

*JOURNAL OF ALGEBRA*, *409*, 320–343.

author keywords: Gosper algorithm; Summability; Double zeta values

TL;DR:
Using criteria for deciding whether a bivariate rational function in two variables can be written as a sum of two (q-)dierences of bivariaterational functions, it is shown how certain double sums can be evaluated in terms of single sums and in Terms of values of special functions.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

4. Quality Education
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2014 journal article

UNIPOTENT DIFFERENTIAL ALGEBRAIC GROUPS AS PARAMETERIZED DIFFERENTIAL GALOIS GROUPS

*JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU*, *13*(4), 671–700.

author keywords: differential algebraic groups; parameterized differential Galois theory; algorithms

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

9. Industry, Innovation and Infrastructure
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2013 journal article

Linear algebraic groups as parameterized Picard-Vessiot Galois groups

*JOURNAL OF ALGEBRA*, *373*, 153–161.

author keywords: Parameterized Picard-Vessiot theory; Linear algebraic groups; Inverse problem

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

9. Industry, Innovation and Infrastructure
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2013 journal article

PROJECTIVE ISOMONODROMY AND GALOIS GROUPS

*PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY*, *141*(2), 605–617.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

9. Industry, Innovation and Infrastructure
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2012 journal article

Monodromy groups of parameterized linear differential equations with regular singularities

*BULLETIN OF THE LONDON MATHEMATICAL SOCIETY*, *44*, 913–930.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

9. Industry, Innovation and Infrastructure
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2012 journal article

Residues and telescopers for bivariate rational functions

*ADVANCES IN APPLIED MATHEMATICS*, *49*(2), 111–133.

author keywords: Residues; Telescopers; Zeilberger's method

TL;DR:
This work gives necessary and sufficient conditions for the existence of telescopers for rational functions of two variables in the continuous, discrete and q-discrete settings and characterize which operators can occur as telescopers.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

4. Quality Education
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2011 journal article

A Jordan-Holder Theorem for differential algebraic groups

*JOURNAL OF ALGEBRA*, *328*(1), 190–217.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

9. Industry, Innovation and Infrastructure
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2010 journal article

An algorithm to compute Liouvillian solutions of prime order linear difference-differential equations

*Journal of Symbolic Computation*, *45*(3), 306–323.

UN Sustainable Development Goal Categories

4. Quality Education
(Web of Science)

Source: NC State University Libraries

Added: August 6, 2018

2010 journal article

Liouvillian solutions of linear difference-differential equations

*JOURNAL OF SYMBOLIC COMPUTATION*, *45*(3), 287–305.

author keywords: Linear difference-differential equations; Galois theory; Liouvillian sequences

TL;DR:
An algorithm for deciding if linear difference-differential systems of prime order have Liouvillian solutions is proposed and characterized in terms of the Galois group of the systems.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

9. Industry, Innovation and Infrastructure
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2008 journal article

Differential Galois theory of linear difference equations

*MATHEMATISCHE ANNALEN*, *342*(2), 333–377.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

9. Industry, Innovation and Infrastructure
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2007 journal article

Model theory of partial differential fields: From commuting to noncommuting derivations

*PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY*, *135*(6), 1929–1934.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

9. Industry, Innovation and Infrastructure
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2005 journal article

On the constructive inverse problem in differential Galois theory

*COMMUNICATIONS IN ALGEBRA*, *33*(10), 3639–3665.

author keywords: Galois theory; inverse problem; linear differential equations; Picard-Vessiot

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

9. Industry, Innovation and Infrastructure
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2002 article

Linear differential operators for polynomial equations

Cormier, O., Singer, M. F., Trager, B. M., & Ulmer, F. (2002, November). *JOURNAL OF SYMBOLIC COMPUTATION*, Vol. 34, pp. 355–398.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

9. Industry, Innovation and Infrastructure
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2001 article

Effective methods in algebraic geometry

Singer, M. F. (2001, October 24). *JOURNAL OF PURE AND APPLIED ALGEBRA*, Vol. 164, pp. 1–2.

Source: Web Of Science

Added: August 6, 2018

1999 article

Calculating the Galois group of L-1(L-2(y))=0, L-1,L-2 completely reducible operators

Berman, P. H., & Singer, M. F. (1999, June 17). *JOURNAL OF PURE AND APPLIED ALGEBRA*, Vol. 139, pp. 3–23.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

9. Industry, Innovation and Infrastructure
(Web of Science)

16. Peace, Justice and Strong Institutions
(OpenAlex)

Source: Web Of Science

Added: August 6, 2018

1999 journal article

Computing Galois groups of completely reducible differential equations

*JOURNAL OF SYMBOLIC COMPUTATION*, *28*(4-5), 473–494.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

9. Industry, Innovation and Infrastructure
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

1999 journal article

Solving difference equations in finite terms

*JOURNAL OF SYMBOLIC COMPUTATION*, *27*(3), 239–259.

UN Sustainable Development Goal Categories

4. Quality Education
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

1997 article

Linear differential equations and products of linear forms

Singer, M. F., & Ulmer, F. (1997, May). *JOURNAL OF PURE AND APPLIED ALGEBRA*, Vol. 117, pp. 549–563.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

9. Industry, Innovation and Infrastructure
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

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