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Works (30)
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
arxiv.org (repository)
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.
author keywords: Linear differential equations; linear difference equations; linear q-difference equations; Mahler equations; consistent systems
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.
author keywords: Differential Galois theory of difference equations; Linear differential algebraic groups; Hypertranscendence; Difference algebra; Differential algebra
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.
author keywords: Differential algebra; Differential algebraic groups; Jordan-Holder Theorem; Linear partial differential equations
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.
TL;DR:
A normal form is given for integrable linear difference-differential equations which is irreducible over C(x,t) and solvable in terms of Liouvillian solutions, and an algorithm is devised to compute all LiouVillian solutions.
(via Semantic Scholar)
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.
TL;DR:
A linear differential operator is constructed that allows one to calculate the genus of the complex curve defined by P= 0, the absolute factorization of P over the algebraic closure of k0, and information concerning the Galois group ofP over ___ k0(x) as well as overk0 (x).
(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
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.
TL;DR:
An algorithm is given to calculate a presentation of the Picard?Vessiot extension associated to a completely reducible linear differential equation that shows how to compute the Galois group of such an equation as well as properties of theGalois groups of general equations.
(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
1999 journal article
Solving difference equations in finite terms
JOURNAL OF SYMBOLIC COMPUTATION, 27(3), 239–259.
TL;DR:
It is shown that the solution space of a difference equation with rational function coefficients has a basis of Liouvillian sequences iff the Galois group of the equation is solvable.
(via Semantic Scholar)
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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