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ORCIDMichael F. Singer
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- affiliation: North Carolina State University, Department of Mathematics, Raleigh, NC, USA
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Books and Theses
- 1991
[b1]Michael F. Singer:
Differential equations and computer algebra. Computational mathematics and applications, Academic Press 1991, ISBN 978-0-12-645950-0, pp. I-VI, 1-228
Journal Articles
- 2022
- [j23]Evelyne Hubert, Michael F. Singer:
Sparse Interpolation in Terms of Multivariate Chebyshev Polynomials. Found. Comput. Math. 22(6): 1801-1862 (2022) - 2020
- [j22]Antonio Jiménez-Pastor
, Veronika Pillwein, Michael F. Singer:
Some structural results on Dn-finite functions. Adv. Appl. Math. 117: 102027 (2020) - [j21]Thomas Dreyfus, Charlotte Hardouin, Julien Roques, Michael F. Singer:
Walks in the quarter plane: Genus zero case. J. Comb. Theory, Ser. A 174: 105251 (2020) - 2016
- [j20]Shaoshi Chen, Manuel Kauers, Michael F. Singer:
Desingularization of Ore operators. J. Symb. Comput. 74: 617-626 (2016) - 2012
- [j19]Shaoshi Chen, Michael F. Singer:
Residues and telescopers for bivariate rational functions. Adv. Appl. Math. 49(2): 111-133 (2012) - 2010
- [j18]Ruyong Feng, Michael F. Singer, Min Wu:
Liouvillian solutions of linear difference-differential equations. J. Symb. Comput. 45(3): 287-305 (2010) - [j17]Ruyong Feng, Michael F. Singer, Min Wu:
An algorithm to compute Liouvillian solutions of prime order linear difference-differential equations. J. Symb. Comput. 45(3): 306-323 (2010) - 2002
- [j16]Olivier Cormier, Michael F. Singer, Barry M. Trager, Felix Ulmer:
Linear Differential Operators for Polynomial Equations. J. Symb. Comput. 34(5): 355-398 (2002) - 1999
- [j15]Hoon Hong, Erich L. Kaltofen, Michael F. Singer:
East Coast Computer Algebra Day '99 (April 24, 1999): abstracts of invited talks and presented posters. SIGSAM Bull. 33(2): 43-52 (1999) - [j14]P. A. Hendricks, Michael F. Singer:
Solving Difference Equations in Finite Terms. J. Symb. Comput. 27(3): 239-259 (1999) - [j13]Elie Compoint, Michael F. Singer:
Computing Galois Groups of Completely Reducible Differential Equations. J. Symb. Comput. 28(4-5): 473-494 (1999) - 1996
- [j12]Michael F. Singer:
Testing reducibility of linear differential operators: A group theoretic perspective. Appl. Algebra Eng. Commun. Comput. 7(2): 77-104 (1996) - 1995
- [j11]Michael F. Singer, Felix Ulmer:
Necessary conditions for liouvillian solutions of (third order) linear differential equations. Appl. Algebra Eng. Commun. Comput. 6: 1-22 (1995) - [j10]Dima Grigoriev, Michael F. Singer, Andrew Chi-Chih Yao:
On Computing Algebraic Functions Using Logarithms and Exponentials. SIAM J. Comput. 24(2): 242-246 (1995) - 1994
- [j9]Dima Grigoriev, Marek Karpinski, Michael F. Singer:
Computational Complexity of Sparse Rational Interpolation. SIAM J. Comput. 23(1): 1-11 (1994) - 1993
- [j8]Michael F. Singer, Felix Ulmer:
Galois Groups of Second and Third Order Linear Differential Equations. J. Symb. Comput. 16(1): 9-36 (1993) - [j7]Michael F. Singer, Felix Ulmer:
Liouvillian and Algebraic Solutions of Second and Third Order Linear Differential Equations. J. Symb. Comput. 16(1): 37-73 (1993) - 1991
- [j6]Michael F. Singer:
Liouvillian Solutions of Linear Differential Equations with Liouvillian Coefficients. J. Symb. Comput. 11(3): 251-273 (1991) - 1990
- [j5]Michael F. Singer:
Formal Solutions of Differential Equations. J. Symb. Comput. 10(1): 59-94 (1990) - [j4]Dima Grigoriev, Marek Karpinski, Michael F. Singer:
Fast Parallel Algorithms for Sparse Multivariate Polynomial Interpolation over Finite Fields. SIAM J. Comput. 19(6): 1059-1063 (1990) - 1986
- [j3]James H. Davenport, Michael F. Singer:
Elementary and Liouvillian Solutions of Linear Differential Equations. J. Symb. Comput. 2(3): 237-260 (1986) - 1985
- [j2]Michael F. Singer, B. David Saunders, Bob F. Caviness:
An Extension of Liouville's Theorem on Integration in Finite Terms. SIAM J. Comput. 14(4): 966-990 (1985) - 1978
- [j1]Michael F. Singer:
The Model Theory of Ordered Differential Fields. J. Symb. Log. 43(1): 82-91 (1978)
Conference and Workshop Papers
- 2021
- [c14]Shaoshi Chen, Ruyong Feng, Pingchuan Ma, Michael F. Singer:
Separability Problems in Creative Telescoping. ISSAC 2021: 83-90 - 2014
- [c13]Shaoshi Chen, Ruyong Feng, Ziming Li, Michael F. Singer:
Parallel telescoping and parameterized Picard-Vessiot theory. ISSAC 2014: 99-106 - 2013
- [c12]Shaoshi Chen, Maximilian Jaroschek, Manuel Kauers, Michael F. Singer:
Desingularization explains order-degree curves for ore operators. ISSAC 2013: 157-164 - 2012
- [c11]Shaoshi Chen, Manuel Kauers, Michael F. Singer:
Telescopers for rational and algebraic functions via residues. ISSAC 2012: 130-137 - 2006
- [c10]Ziming Li, Michael F. Singer, Min Wu, Dabin Zheng:
A recursive method for determining the one-dimensional submodules of Laurent-Ore modules. ISSAC 2006: 220-227 - 2000
- [c9]Olivier Cormier, Michael F. Singer, Felix Ulmer:
Computing the Galois group of a polynomial using linear differential equations. ISSAC 2000: 78-85 - 1993
- [c8]Michael F. Singer, Felix Ulmer:
On a Third Order Differential Equation whose Differential Galois Group is the Simple Group of 168 Elements. AAECC 1993: 316-324 - 1992
- [c7]Michael F. Singer, Felix Ulmer:
Liouvillian Solutions of Third Order Linear Differential Equations: New Bounds and Necessary Conditions. ISSAC 1992: 57-62 - 1990
- [c6]Dima Grigoriev, Marek Karpinski, Michael F. Singer:
Interpolation of Sparse Rational Functions Without Knowing Bounds on Exponents. FOCS 1990: 840-846 - 1989
- [c5]Michael F. Singer:
Liouvillian Solutions of Linear Differential Equations with Liouvillian Coefficients. Computers and Mathematics 1989: 182-191 - 1988
- [c4]Michael F. Singer:
Liouvillian First Integrals of Differential Equations. ISSAC 1988: 57-63 - 1985
- [c3]Michael F. Singer, James H. Davenport:
Elementary and Liouvillian Solutions of Linear Differential Equations. European Conference on Computer Algebra (2) 1985: 595-596 - 1981
- [c2]Michael F. Singer, B. David Saunders, Bob F. Caviness:
An extension of Liouville's theorem on integration in finite terms. SYMSACC 1981: 23-24 - [c1]Myra Jean Prelle, Michael F. Singer:
Elementary first integrals of differential equations. SYMSACC 1981: 30-35
Informal and Other Publications
- 2021
- [i13]Shaoshi Chen, Ruyong Feng, Ziming Li, Michael F. Singer, Stephen M. Watt:
Telescopers for differential forms with one parameter. CoRR abs/2101.06576 (2021) - [i12]Shaoshi Chen, Ruyong Feng, Pingchuan Ma, Michael F. Singer:
Separability Problems in Creative Telescoping. CoRR abs/2102.03693 (2021) - 2020
- [i11]Evelyne Hubert, Michael F. Singer:
Sparse Interpolation in Terms of Multivariate Chebyshev Polynomials. CoRR abs/2001.09144 (2020) - [i10]Charlotte Hardouin, Michael F. Singer:
On Differentially Algebraic Generating Series for Walks in the Quarter Plane. CoRR abs/2010.00963 (2020) - 2014
- [i9]Shaoshi Chen, Ruyong Feng, Ziming Li, Michael F. Singer:
Parallel Telescoping and Parameterized Picard-Vessiot Theory. CoRR abs/1401.4666 (2014) - [i8]Shaoshi Chen, Manuel Kauers, Michael F. Singer:
Desingularization of Ore Operators. CoRR abs/1408.5512 (2014) - 2013
- [i7]Shaoshi Chen, Maximilian Jaroschek, Manuel Kauers, Michael F. Singer:
Desingularization Explains Order-Degree Curves for Ore Operators. CoRR abs/1301.0917 (2013) - 2012
- [i6]Shaoshi Chen, Manuel Kauers, Michael F. Singer:
Telescopers for Rational and Algebraic Functions via Residues. CoRR abs/1201.1954 (2012) - [i5]Shaoshi Chen, Michael F. Singer:
Residues and Telescopers for Rational Functions. CoRR abs/1203.4200 (2012) - [i4]Shaoshi Chen, Michael F. Singer:
On the Summability of Bivariate Rational Functions. CoRR abs/1210.6366 (2012) - 2008
- [i3]Ruyong Feng, Michael F. Singer, Min Wu:
Liouvillian Solutions of Difference-Differential Equations. CoRR abs/0810.1574 (2008) - 2007
- [i2]Michael F. Singer:
Introduction to the Galois Theory of Linear Differential Equations. CoRR abs/0712.4124 (2007) - 2006
- [i1]Ziming Li, Michael F. Singer, Min Wu, Dabin Zheng:
A Recursive Method for Determining the One-Dimensional Submodules of Laurent-Ore Modules. CoRR abs/cs/0604084 (2006)
Coauthor Index
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