Submitted
- S.A. Abramov, H.Q. Le, M. Petkovsek.
Polynomial ring automorphisms and rational
(w,sigma)-canonical forms
2005
- S.A. Abramov, H.Q. Le, Z. Li.
Univariate Ore polynomial rings in Computer Algebra.
Journal of Mathematical Sciences, 131, No.5, 5885--5903, Dec. 2005.
- S.A. Abramov, H.Q. Le.
On the order of the recurrence produced by the method of creative
telescoping.
Discrete Mathematics, 298, 2--17, Aug. 2005.
2004
- S.A. Abramov, J.J. Carette, K.O. Geddes, H.Q. Le.
Telescoping in the context of symbolic
summation in Maple.
Journal of Symbolic Computation, Volume 38, Issue 4, 1303--1326, Oct 2004.
- K.O. Geddes, H.Q. Le, Z. Li (2004).
Differential rational normal forms and
a reduction algorithm for hyperexponential functions.
In J. Gutierrez, editor,
Proceedings of the 2004 International
Symposium on Symbolic and Algebraic Computation, 183--190, 2004.
- S.A. Abramov, H.Q. Le (2004).
Utilizing relationships among linear systems generated
by Zeilberger's algorithm.
To appear in the Proceedings of the 2004
Formal Power Series and Algebraic
Combinatorics.
- H.Q. Le, Z. Li (2004).
Differential rational normal forms and representations of
hyperexponential functions.
In Proceedings of the Rhine Workshop on Computer Algebra 2004, pages 3--12,
Nijmegen, March 2004.
2003
- S.A. Abramov, H.Q. Le, M. Petkovsek (2003).
Rational canonical forms and
efficient representations of
hypergeometric terms.
In J.R. Sendra, editor, Proceedings of the 2003 International
Symposium on Symbolic and Algebraic Computation, 7--14.
- S.A. Abramov, H.Q. Le (2003).
The sequence of linear algebraic systems generated by Zeilberger's
algorithm.
Proceedings of the 2003 Formal Power Series and Algebraic
Combinatorics, 2003, on CD.
- H.Q. Le (2003).
A direct algorithm to construct the minimal Z-pairs
for rational functions.
Advances in Applied Mathematics, 30, 137--159.
- S.A. Abramov, H.Q. Le, Z. Li (2003).
OreTools: a computer algebra library for univariate Ore polynomial rings.
Technical Report CS-2003-12, School of Computer Science, University
of Waterloo.
- H.Q. Le (2003).
Algorithms for the construction of the minimal telescopers.
PhD thesis, School of Computer Science, University of Waterloo.
2002
- S.A. Abramov, H.Q. Le (2002).
A lower bound for the order of telescopers for a hypergeometric term.
Proceedings of the 2002 Formal Power Series and Algebraic
Combinatorics, 2003, on CD.
- H.Q. Le (2002).
Simplification of definite sums of rational functions
by creative symmetrizing method.
In T. Mora, editor,
Proceedings of the 2002 International
Symposium on Symbolic and Algebraic Computation, 161--167.
- S.A. Abramov, K.O. Geddes, H.Q. Le (2002).
Computer algebra library for the construction of the
minimal telescopers.
In N. Takayama, A.M. Cohen and X. Gao, editors, Proceedings of the
2002 International Congress of Mathematical Software, 319--329.
- K.O. Geddes, H.Q. Le (2002).
An algorithm to compute the
minimal telescopers for rational functions
(differential -- integral Case).
In N. Takayama, A.M. Cohen and X. Gao, editors, Proceedings of the
2002 International Congress of Mathematical Software, 453--463.
- S.A. Abramov, H.Q. Le (2002).
A criterion for the applicability of Zeilberger's algorithm to
rational functions.
Discrete Mathematics, 259:1--17, Dec 2002.
- S.A. Abramov, J.J. Carette, K.O. Geddes, H.Q. Le (2002).
Symbolic summation in Maple.
Technical Report CS-2002-32, School of Computer Science, University
of Waterloo, October 2002.
2001
- H.Q. Le (2001).
Computing the minimal telescoper for sums of hypergeometric terms.
SIGSAM Bulletin, v. 35, no. 3, September, 2--10.
- S.A. Abramov, K.O. Geddes, H.Q. Le (2001).
HypergeometricSum: a Maple
package for finding closed forms of indefinite and definite
sums of hypergeometric type.
Technical Report CS-2001-24,
Department of Computer Science, University of Waterloo,
Ontario, Canada.
- S.A. Abramov, K.O. Geddes, H.Q. Le (2001).
A direct algorithm to construct the minimal telescopers
for rational functions (q-difference case).
Technical Report CS-2001-25,
Department of Computer Science, University of Waterloo,
Ontario, Canada.
- H.Q. Le (2001).
A direct algorithm to construct Zeilberger's
recurrences for rational functions.
In H. Barcelo and V. Welker, editors, Proceedings of the 2001
Formal Power Series and Algebraic Combinatorics, 303--312
2000
- S.A. Abramov, H.Q. Le (2000).
Applicability of Zeilberger's algorithm to rational functions.
In A.A. Mikhalev, D. Krob and A.V. Mikhalev, editors, Proceedings
of the 2000 Formal Power Series and Algebraic Combinatorics, 91--102.
- H.Q. Le (2000).
On the q-analogue of Zeilberger's algorithm to rational functions,
Programming and Comput. Software (Programmirovanie) 27, 2001, 49--58.
- H.Q. Le (2000).
On the differential-integral analogue of Zeilberger's algorithm to
rational functions.
In D. Wang and X. Gao, editors, Proceedings of the 2000 Asian
Symposium on Computer Mathematics, 204--213.
- H.Q. Le (2000).
Mathematical graphical object representation.
Programming and Comput. Software (Programmirovanie), 26(6),
Nov-Dec 2000.
- H.Q. Le (2000).
Communication-oriented representation of
mathematical objects.
Programming and Comput. Software (Programmirovanie), Volume 26,
Number 1, Jan--Feb 2000.
1999
- H.Q. Le, C.R. Howlett (1999).
Client-server communication standards for mathematical computation.
In S. Dooley, editor, Proceedings of the 1999 International
Symposium on Symbolic and Algebraic Computation, 299--306.
- H.Q. Le (1999).
Client-server communication standards for mathematical computation.
Master's thesis, School of Computer Science, University of Waterloo, 1999.
I am the principal designer and developer of the following Maple packages which
get distributed in the official versions of Maple:
- SumTools: a package
for finding closed forms of
definite and indefinite sums.
- geom3d: a package in
three-dimensional Euclidean geometry. This package
includes tools for different types of regular polyhedra.
- geometry: a package in
two-dimensional Euclidean geometry.
- GaussInt: a package for doing
arithmetic in Gaussian integer domain.
Below is a list of interesting links.
- Work:
Centre for Experimental and Constructive Mathematics (CECM)
Department of Mathematics
Simon Fraser University
8888 University Dr., Burnaby, British Columbia CANADA V5A 1S6
E-mail: hle@cecm.sfu.ca
- Home:
-
104-1045 Haro Street, Vancouver, British Columbia, V6E 3Z8, Canada
Tel: 1 604 669 0289
-
79 Antigua Road, Mississauga, Ontario, L5B 2T8, Canada
Tel: 1 905 272 5768