An algorithm for computing an integral basis in an algebraic
function field. J. Symb. Comput., 18, 353-363 (1994). Recent additions are marked in yellow.
An algorithm for computing an integral basis in an algebraic
function field. J. Symb. Comput., 18, 353-363 (1994).
Computing parametrizations of rational algebraic curves.
ISSAC '94 Proceedings, 187-190 (1994).
An algorithm for computing the Weierstrass normal form.
ISSAC '95 Proceedings, 90-95 (1995).
See also the same problem for the hyperelliptic case.
Rational Parametrizations of Algebraic Curves using a Canonical Divisor.
J. Symb. Comput., 23, 209-227 (1997).
Computing Riemann matrices of algebraic curves.
Joint work with Bernard Deconinck.
PhysicaD, 152, 28-46 (2001).
Towards Factoring Bivariate Approximate Polynomials.
Rob Corless, Mark Giesbrecht, Mark van Hoeij,
Ilias Kotsireas and Stephen Watt,
ISSAC '01 proceedings, 85-92 (2001)
ps file.
Computing Riemann Theta Functions.
Bernard Deconinck, Matthias Heil, Alexander Bobenko, Mark van Hoeij and Markus Schmies.
Math. Comp. 73, 1417-1442 (2004).
Solving conics over function fields. Joint work
with John Cremona.
Journal de Theorie des Nombres de Bordeaux, 18, p. 595-606 (2006).
Rational Solutions of Linear Difference Equations.
ISSAC '98 Proceedings, 120-123 (1998).
Finite Singularities and Hypergeometric Solutions of Linear Recurrence
Equations.
J. Pure Appl. Algebra, 139, 109-131 (1999).
Desingularization of
linear difference operators with polynomial
coefficients. Joint work with
S.A. Abramov.
ISSAC '99 Proceedings, 269-275 (1999) dvi file.
Related results can be found in the next paper:
Set of Poles of Solutions of Linear Difference Equations with Polynomial Coefficients.
Joint work with S.A. Abramov.
Computational Mathematics and Mathematical Physics, Vol. 43,
No. 1, p. 57--62 (2003) dvi file.
A conjecture in the problem of rational
definite summation. See also the preliminary
SumRat implementation. (2002).
Computing Hypergeometric
Solutions of Linear Recurrence Equations. Joint work with
Thomas Cluzeau.
AAECC, Vol. 17, 83-115 (2006).
Apparent Singularities
of Linear Difference Equations with Polynomial Coefficients. Joint work
with S.A. Abramov and M. A. Barkatou.
AAECC, Vol. 17, 117-133 (2006).
Slides on
"Factorization and hypergeometric solutions of linear recurrence systems"
at Manuel Bronstein's conference (July 2006).
Formal Solutions and Factorization of Differential Operators
with Power Series Coefficients.
J. Symb. Comput., 24, 1-30 (1997).
Factorization of Differential Operators with Rational Functions Coefficients.
J. Symb. Comput., 24, 537-561 (1997).
An algorithm for computing invariants of differential Galois groups.
Joint work with
J.A. Weil.
J. Pure Appl. Algebra, 117&118, 353-379 (1997).
Rational Solutions of the Mixed Differential Equation
and its Application to Factorization of Differential Operators.
ISSAC '96 Proceedings, 219-225 (1996).
Note: the 4 papers above are also included in
my Ph.D thesis
postscript file,
pdf file
(1996, written in English with a short
summary in Dutch). Here is the list of errata.
It is a custom in the Netherlands to include a
number of statements, ``stellingen'', with
the thesis (some of these are in English, some in Dutch).
Here is my masters thesis (1992,
an integral basis algorithm, written in Dutch).
A method for the Integration of Solutions of Ore Equations.
Joint work with S.A. Abramov.
ISSAC '97 Proceedings, 172-175 (1997).
Note: there is now a newer version
of this paper which has appeared as
Integration of Solutions of Linear Functional Equations
in: Integral Transforms and Special Functions, 1999, Vol.8, No 1-2, pp. 3-12.
Liouvillian solutions of linear differential equations of order three and higher.
Joint work with Jean-Francois Ragot,
Felix Ulmer and
Jacques-Arthur Weil. J. Symb. Comput., 28, 589-609 (1999).
The Minimum Polynomial of an Algebraic Solution of Abel's problem.
Preprint FSU00-02.
Decomposing a 4'th order linear differential equation as a symmetric
product. Banach Center Publications, 58, 89-96, (2002).
abstract.
Closed Form Solutions of Linear Odes having Elliptic Function Coefficients.
Joint work with Reinhold Burger and
George Labahn.
ISSAC'04 Proceedings, 58-64, (2004).
Descent for differential modules and skew fields. Joint
work with Marius van der Put.
Journal of Algebra, 296, pp. 18-55 (2006).
A Modular Algorithm to Compute the Exponential Solutions
of a Linear Differential Operator. Joint
work with Thomas Cluzeau.
J. Symb. Comput., 38, 1043-1076 (2004).
dvi file.
Solving Second Order Linear Differential Equations with Klein's Theorem.
Joint work with Jacques-Arthur Weil.
ISSAC'05 Proceedings, 340-347, (2005).
draft implementation,
slides of the talk.
The Fourth-Order Type
Linear Ordinary Differential Equations. Joint work with W. N. Everitt
and D. J. Smith. Preprint (not submitted for publication) (2006).
Solving Third Order Linear Differential
Equations in Terms of Second Order Equations,
ISSAC'07 Proceedings, 355-360, (2007).
slides of the ISSAC'2007 talk.
A longer version of this talk was
presented at the DART workshop
(DART slides).
Closed Form Solutions for Linear Differential and
Difference Equations, Project Description for NSF grant 0728853 (submitted Feb 2007, awarded
Sept. 2007 - 2010).
Solving Differential Equations in Terms of Bessel Functions,
Joint work with R. Debeerst and W. Koepf. Accepted for ISSAC'2008.
Factoring polynomials and the knapsack problem.
Journal of Number Theory, 95, 167-189, (2002).
ps file.
Additional information can be found in the source code of the
implementation
and in this summary
(proceedings of CaLC'2001,
Lect. Notes in Comp. Science, 2146, p. 45-50).
Some sample inputs, many of which could
not be factored before, e.g. M12.
A Modular GCD algorithm over Number Fields presented with Multiple Extensions.
Joint work with Michael Monagan.
ISSAC'02 proceedings, 109-116, (2002).
Algorithms for Polynomial GCD Computation over Algebraic Function Fields. Some
comments.
Joint work with Michael Monagan,
ISSAC'04 proceedings, 297-304, (2004).
ps file.
Factoring polynomials over global fields.
Joint work with K. Belabas, J. Klueners, and A. Steel. Preprint
arXiv:math/0409510v1
Generating Subfields,
Joint work with J. Klueners. Abstract of a talk at
Oberwolfach,
July 22, 2005.
Approximate Bivariate Factorization, a Geometric Viewpoint,
Joint work with A. Galligo,
SNC'2007 Proceedings, p. 1-10 (2007).
Complexity of factoring polynomials with rational number coefficients,
slides at a plenary talk at Journees Arithmetique, July 2-6,
Edinburgh. See also the poster at ISSAC'2007
and the poster at ECCAD'2008.