Computational Algebra Group at SFU


Preprints

--------------- 2005 ---------------

Keld Bak, Stephan Sauer, Jens Oddershede, and John Ogilvie.
The vibrational g-factor of dihydrogen from theoretical calculation and analysis of vibrational-rotational spectr.
May 2005 [ PDF ]

Jeffrey B. Farr and Roman Pearce
Working with Multivariate Polynomials in Maple.
May 2005 [ PDF ] [ PostScript ]

S. Lo, M. Monagan, A. Wittkopf
A Modular Algorithm for Computing the Characteristic Polynomial of an Integer Matrix in Maple.
May 2005 [ PDF ] [ PostScript ] [ LaTeX ]
Maple code for computing strongly connected components: [ txt ]
The 72 by 72 matrix in Maple input format: [ txt ]
The 364 by 364 matrix in Maple input format: [ txt ]
The 1916 by 1916 matrix in Maple input format: [ txt ]

M. Ebrahimi, and M. Monagan
New options to visualize systems of differential equations in Maple.
May 2005 [ PDF ] [ PostScript ]

J. Farr, M. Khatirinejad, S. Khodadad, M. Monagan
A Graph Theory Package for Maple.
May 2005 [ PDF ] [ PostScript ]

Michael Monagan
Probabilistic Algorithms for Resultants
May 2005 [ PDF ] [ PostScript ]

Ha Le, Ziming Li
On a Set of Hyperexponential Elements and Fast Versions of Zeilberger's Algorithm.
January 2005 [ PDF ] [ PostScript ]

J. de Kleine, M. Monagan, A. Wittkopf
Algorithms for the Non-Monic Case of the Sparse Modular GCD Algorithm.
January 2005 [ PDF ] [ PostScript ]

--------------- 2004 ---------------

J. F. Ogilvie.
Teaching and Doing Mathematics with Symbolic Computation.
2004 [ PDF ]

J. van Stralen, L. Viischer and J. Ogilvie.
Theoretical and experminental evaluation of hte radial function for the electric dipole moment of hydrogen iodide.
May 2004 [ PDF ]

J. de Kleine, M. Monagan, A. Wittkopf
The Non-Monic Case in the Sparse Modular GCD Algorithm.
May 2004 [ PDF ] [ PostScript ]

M. Monagan, R. Pearce
The PolynomialIdeals Maple Package.
May 2004 [ PDF ] [ PostScript ]

Michael Monagan, Greg Fee
A Cryptographically Secure Random Number Generator for Maple
January 2003, July 2004 [ PostScript ] [ PDF ]

E. Cheb-Terrab
Solutions for the General, Confluent and Biconfluent Heun equations and their connection with Abel equations.
April 2004 (to the Journal of Physics A: Mathematical and General) [ PDF ]

E. Cheb-Terrab
A connection between Abel and pFq hypergeometric differential equations.
Feburary 2004 (to the European Journal of Applied Mathematics) [ PDF ] [ PostScript ]

L. Chan, E. Cheb-Terrab
Non-Liouvillian solutions for second order linear ODEs.
January 2004 [ PDF ] [ PostScript ]

Jeffrey B. Farr and Shuhong Gau
Computing Groebner Bases for Vanishing Ideals of Finite Sets of Points.
January 2004 [ PDF ] [ PostScript ]

A. D. Roche
A solution algorithm for the Abel Inverse Riccati ODE
January 2004 [ DVI ] [ PostScript ]

M. van Hoeij, M. B. Monagan
Algorithms for Polynomial GCD Computation over Algebraic Function Fields.
January 2004 [ DVI ] [ PostScript ] [ Maple Worksheet ]

--------------- 2003 ---------------

M. B. Monagan
Maximal Quotient Rational Reconstruction: An Almost Optimal Algorithm for Rational Reconstruction.
November 2003 [ DVI ] [ PostScript ]

J. Borwein, R. Crandall, G. Fee
On the Ramanujan AGM fraction.
June 2003 [ PDF ] [ PostScript ]

M. B. Monagan, S. C. Tse and A. D. Wittkopf
A Modular Resultant Algorithm for Number Fields.
January 2003 [ DVI ] [ PostScript ]

Greg Fee and Michael Monagan
Cryptography using Chebyshev Polynomials.
January 2003 [ PostScript ] [ PDF ]

--------------- 2002 ---------------

Peter Borwein, Kevin G. Hare and Alan Meichsner
Reverse Symbolic Computations: The IDENTIFY Function
July 2002 (MSW '02) [ PostScript ]

Jennifer de Kleine and Michael Monagan
A Modular Method for Computing Groebner Bases
July 2002 [ PostScript ]

Kevin G. Hare
Some Applications of the LLL Algorithm
July 2002 [ PostScript ]

G. J. Fee
Linear Least-Squares Data Fitting with Orthogonal Polynomials
July 2002 [ PostScript ]

Frank Wang and John F. Oglivie
Application of Maple to Lagrangian Mechanics
July 2002 [ PostScript ]

M.B. Monagan, S.C. Tse, and A.D. Wittkopf
Modular Algorithms for Resultants.
July 2002 [ PostScript ]

Edgardo Cheb-Terrab
The Function Wizard Project: Computer Algebra Handbook of Special Functions.
July 2002 [ PostScript ]

Edgardo Cheb-Terrab
ODE trends in computer algebra: Four linear and nonlinear challenges.
July 2002 [ PostScript ]

Michael Monagan
2D and 3D Graphics Routines for Teaching Linear Algebra.
March 2002 [ PostScript ] [ DVI ]

Mark van Hoeij and Michael Monagan
A Modular GCD Algorithm over Number Fields Presented with Multiple Extensions.
January 2002 [ PostScript ] [ DVI ]

--------------- 2001 ---------------

Jennifer de Kleine and Michael Monagan
A Modular Design and Implementation of Buchberger's Algorithm.
November 2001 [ PostScript ]

Jamie Mulholland and Michael Monagan
Algorithms for Trigonometric Polynomials.
April 2001 [ PostScript ] [ DVI ]

Jonathan M. Borwein and Peter B. Borwein,
Challenges in Mathematical Computing,
February 2001 [ PostScript ] [ PDF ]

Peter Borwein and Kevin G. Hare,
Non-trivial quadratic approximation to zero of a family of cubic Pisot numbers.
February 2001 [ PostScript ] [ PDF ]

Peter Borwein and Kevin G. Hare,
General forms for minimal spectral values for a class of quadratic Pisot numbers.
February 2001 [ PostScript ] [ PDF ]

Erich Kaltofen, Michael Monagan, Allan Wittkopf
On the Modular Polynomial GCD Algorithm over the Integers, Finite Fields, and Number Fields.
January 2001 [ PostScript ] [ DVI ]

--------------- 2000 ---------------

E. Cheb-Terrab
Algorithms for Computing Exact Solutions for Ordinary and Partial Differential Equations,
November 2000 MITACS Research Report [ PostScript ]

Michael Monagan, Petr Lisonek, Hans Bauck,
Simplification of Algebraic Expressions,
November 2000 MITACS Research Report [ PostScript ]

Michael Monagan, Jamie Mulholland, Petr Lisonek
Theory and Algorithms for Trigonometric Polynomials,
November 2000 MITACS Research Report [ PostScript ]

M. Monagan, J. Ales, J. de Kleine, C. Pastro, A. Wittkop,
Data Structures and Algorithms for Polynomials,
November 2000 MITACS Research Report [ PostScript ]

Peter Borwein and Kevin G. Hare,
Some Computations on Pisot and Salem Numbers,
September 2000 [ PostScript ] [ PDF ]

Peter Borwein and Loki Jorgenson,
Visible Structures in Number theory
[ PostScript ] [ PDF ]

C. Percival,
Rapid Multiplication Modulo the Sum and Difference of Highly Composite Numbers.
[ PostScript ]

J. Mullholland and M. Monagan,
Algorithms for Trigonometric Polynomials. [ PostScript ] [ DVI ]

G. J. Reid and A. D. Wittkopf,
Determination of Maximal Symmetry Groups of Classes of Differential Equations.
January 2000 [ PostScript ]

M. Monagan and A. Wittkopf,
On the Design and Implementation of Brown's Algorithm over the Integers and Number Fields.
January 2000 [ DVI ] [ PostScript ]

P. Lisonek and R. Israel,
Metric Invariants of Tetrahedra via Polynomial Elimination.
January 2000 [ DVI ] [ PostScript ]

E. S. Cheb-Terrab and A. D. Roche,
An Abel ODE Class Generalizing Known Integrable Classes.
[ DVI ] [ PostScript ]

E. S. Cheb-Terrab and T. Kolokolnikov,
Solving First Order ODEs using Linear Transformations.
[ PostScript ]

E. S. Cheb-Terrab and A. D. Roche,
Abel ODEs: Equivalence and Integrable Classes.
[ DVI ] [ PostScript ]

----------- Before 2000 ------------

K. Hare,
Rapid Computation of Bernoulli and Related Numbers.
(ISSAC '99, poster session)
[ PostScript (abstract) | PostScript (poster) ]

G. Fee,
Gauss-Legendre Quadrature.
(ISSAC '99, poster session)
[ PostScript (abstract) | PostScript (poster) ]

K. Hare,
Some Applications of the LLL Algorithm.
[ PostScript ]

M. B. Monagan and M. A. Slawinski,
The Sensitivity of Traveltime Inversion for an Anisotropic Parameter in Seismology.
[ PostScript ]

M. B. Monagan and J. F. Ogilvie,
The Diatomic Anharmonic Oscillator according to Matrix Mechanics.
Mathematics and Computers in Simulation 49 (1999), 221-234.
[ PostScript ]

J. M. Borwein, D. M. Bradley, D. J. Broadhurst and P. Lisonek,
Combinatorial Aspects of Multiple Zeta Values.
The Electronic Journal of Combinatorics 5(1) (1998), R38.
[ DVI | PostScript ]

J. M. Borwein, D. M. Bradley, D. J. Broadhurst and P. Lisonek,
Special Values of Multiple Polylogarithms.
Transactions of the American Mathematical Society (in print).
[ DVI | PostScript ]

J. M. Borwein and P. Lisonek,
Applications of Integer Relation Algorithms.
Discrete Mathematics 217 (2000), 65-82.
[ DVI | PostScript ]

J. M. Borwein, P. Lisonek and J. A. Macdonald,
Arithmetic-Geometric Means Revisited.
MapleTech 4 (1997), 20-27.
[ DVI | PostScript ]

E. Kaltofen and M. Monagan,
On the Genericity of the Modular Polynomial GCD Algorithm.
January 1999 (to ISSAC '99)
[ DVI | PostScript ]

D. Villard and M. B. Monagan,
Automatic Differentiation: An Implementation in Maple.
(ISSAC '98, poster session)
[ DVI | PostScript ]

M. B. Monagan and G. M. Monagan,
A Toolbox for Program Manipulation and Efficient Code Generation with an Application to a Problem in Computer Vision.
January 1997 (to ISSAC '97)
[ DVI | PostScript ]

M. Monagan and R. Margot,
On Computing Univariate GCDs over Number Fields.
June 1997 (to SODA '98)
CECM Preprint 96:066
[ DVI | PostScript ]

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