My research area is known as computer algebra. I have worked on the Maple project since 1983. Maple is one of several computer algebra systems. It was developed at the University of Waterloo in the 1980s. I can supervise graduate students at Simon Fraser University who are interested in pursuing a graduate degree in computer algebra at the Ph.D. and Masters' level. Students need to have an interest for both mathematics and computer science and be interested in computer programming. Before you send me an application, please find out what computer algebra is, and in your letter, say why you are interested in doing computer algebra and what programming experience you have.
For details of my current research projects, please see my recent publications.
Graduate Students
- Archit Srivastava, MSc. in pure mathematics, in progress.
- Hyukho Kwon, MSc. in pure mathematics, in progress.
- Mahsa Ansari, Ph.D. in pure mathematics, in progress.
- Garrett Paluck, Ph.D. in pure mathematics, in progress.
- Tian Chen, Ph.D. student in applied mathematics, in progress.
- Sophie Hoare, MSc. in applied mathematics, April 2023.
- Ayool Jinadu, Ph.D. in pure mathematics, August 2023.
- Thesis: Solving parametric systems using Dixon resultants and sparse interpolationt tools.
- Kim Connolley, MSc. student in pure mathematics, August 22nd, 2020.
- Project: A Maple implementation of FFT-based algorithms for polynomial multipoint evaluation, interpolation, and solving transposed Vandermonde systems.
- Garrett Paluck, MSc. in mathematics, August 13th, 2019.
- Thesis: A new bivariate Hensel lifting algorithm for n factors.
- Jiaxiong (Lucas) Hu. Ph.D. in pure mathematics, August 2018.
- Thesis: Computing polynomial greatest common divisors using sparse interpolation.
- Justine Gauthier, MSc. in pure mathematics, August 2017.
- Project: Fast Multipoint Evaluation on n Arbitrary Points.
- John Kluesner, MSc. in pure mathematics, August 2017.
- Thesis: Resolving zero divisors of radical triangular sets using Hensel lifting and applications.
- Hao Ze. MSc. in pure mathematics, August 2017.
- Project: Fast power series inversion: Newton's iteration and the middle product optimization.
- Yusuf Baris Tuncer. Ph.D. in pure mathematics, August 2017.
- Thesis: Solving Multivariate Polynomial Diophantine Equations and their Role in Multivariate Polynomial Factorization.
- Marshall Law, MSc. in pure mathematics, April 2017.
- Thesis: Computing Characteristic Polynomials of Matrices of Structured Polynomials
- Soo Go. M. Sc. in pure mathematics, July 2012.
- Thesis: Sparse Polynomial Interpolation and the Fast Euclidean Algorithm.
- Steven Kieffer. M.Sc. in pure mathematics, April 2012.
- Thesis: Computability in Principle and in Practice in Algebraic Number Theory: Hensel to Zassenhaus.
- Cory Ahn. M.Sc. in pure mathematics, December 2011.
- Thesis: Fast polynomial multiplication over algebraic number fields.
- Andrew Arnold. M.Sc. in pure mathematics, January 2011.
- Thesis: Algorithms for Computing Cyclotomic Polynomials.
- Mahdi Javadi. Ph.D. in computing science, January 2011.
- Thesis: Efficient Algorithms for Calculations with Sparse Polynomials
- Chelsea Richards. M.Sc. in pure mathematics, August 2009.
- Project: Algorithms for Factoring Square-free Polynomials over Finite Fields.
- Suling Yang. M.Sc. in pure mathematics, April 2009.
- Project: Computing GCDs of Multivariate Polynomials over Finite Fields.
- Paul Vrbik. M.Sc. in pure mathematics, December 2008.
- Thesis: Delayed Polynomial Arithmetic and Applications.
- Liang Chen. M.Sc. in computer science, August 2007.
- Thesis: Solving Linear Systems over Cyclotomic Fields.
- Mahdi Javadi. M.Sc. in computer science, November 2006.
- Thesis: A Sparse Modular GCD Algorithm for Polynomials over Algebraic Function Fields.
- Aaron Bradford.
M.Sc. in pure mathematics, April 2006.
- Project: Computing Discrete Logarithms in GF(p).
- Sara Khodadad.
M.Sc. in computer science, November 2005.
- Thesis: Fast Rational Function Reconstruction.
- Roman Pearce. M.Sc. in pure mathematics, August 2005.
- Thesis: Rational Expression Simplification with Polynomial Side Relations.
- Allan Wittkopf. Ph.D. in applied and computational mathematics, October 2004.
- Thesis: Algorithms and Implementations for Differential Elimination.
- Stephen Tse. M.Sc. in computing science, July 2002.
- Thesis: Algorithms and Bounds for Resultants.
- Jennifer de Kleine. M.Sc. in computing science, 2001.
- Project: A Modular Design and Implementation of Buchberger's Algorithm.
- Laurent Bernardin. Ph.D. in computer science, ETH Zentrum, September 1999.
- Thesis: Factorization of Multivariate Polynomials over Finite Fields.
Undergraduate Students
- Khalil Shifji, Dixon Resultants, NSERC 2019.
- Khalil Shivji, Honors thesis, Fall 2019.
- A new algorithm for improved determinant computation with a view towards resultants.
- Robyn Hearn, Big Data, 2018.
- Roots of Polynomials.
- Robyn Hearn, Honors Research Project, Fall 2018.
- Irreducible Quadratics over Zn
- Ryan Mehregan, NSERC 2018.
- Hensel Lifting.
- Gabriel Henderson, NSERC 2017.
- Sparse Interpolation.
- Jesse Elliott, NSERC 2016.
- Sparse Interpolation.
- Jesse Elliott, Honors thesis, Fall 2016.
- Recovery of Exponents of Polynomials of High Degree
- Alex Fan, RA 2016.
- Sparse Interpolation.
- Alan Wong, Honors Research Project, Fall 2015.
- Heuristics and Identities for Computing the Tutte polynomial.
- Adriano Arce, VPR 2015.
- Discrete Logarithms.
- Hao Zhuang, USRA 2015.
- FFT over Finite Fields.
- Marshall Law, NSERC 2014.
- FFT multiplication mod p in parallel.
- Casie Bao, VPR 2014.
- Measuring river flow (discharge).
- Mathew Gibson, NSERC 2013.
- Algorithms for GCDs over finite fields.
- Alan Wong, NSERC 2013.
- Computing Tutte polynomials.
- Shraddha Ramesh, NSERC 2011.
- Algorithms for finite groups.
- Jaiganesh Balasundarum, MITACS Globalink 2011.
- Fast polynomial arithmetic.
- Stephen Melczer, NSERC 2010.
- Algebraic geometry.
- Julian Sahrasbuhde, NSERC 2009.
- Graph theory.
- Bill Bao, NSERC 2009.
- Scientific computing.
- Asif Zaman, NSERC 2008.
- Computational group theory.
- Andrew Arnold, NSERC 2007.
- Graph theory and number theory.
- Simon Lo, NSERC, 2006.
- Graph theory.
- Al Erickson, NSERC, 2006.
- Graph theory and polynomial factorization.
- Simon Lo, NSERC, 2005.
- Computer algebra.
- Mohammed Ebrahimi, NSERC, 2005.
- Scientific computing.
- Howard Liu, NSERC, 2005.
- Numerical integration and differentiation.
- Al Erickson, NSERC, 2005.
- Computer algebra.
- Simon Lo, NSERC, 2004.
- Computational linear algebra.
- Mohammed Ebrahimi, NSERC, 2004.
- Visualizations for differential equations in Maple.
- Scott Cowan, NSERC, 2003.
- Computational problems in cryptography and algebra.
- Aaron Bradford, NSERC, 2002.
- Evaluating definite integrals.
- Roman Pearce, NSERC, 2001.
- Groebner bases and ideal theoretic operations.
- George Zhang, NSERC, 2001.
- Algorithms for testing ideals for primality and maximality.
- Jamie Mulholland, NSERC, 2001
- Algorithms for trigonometric polynomials.
- Craig Pastro, NSERC, 2000.
- The Modular GCD algorithm over algebraic number fields.
- Michael Ludkovski, Directed Studies, 1999.
- Brown's and Zippel's modular GCD algorithms.
- Mark Siggers, Directed Studies, 1999
- Univariate Hensel lifting over Euclidean domains.
- Colin Percival, Career Prep, 1998.
- Polynomial GCDs over algebraic number fields.
- Rene Rodoni, Diplomarbeit, ETH Zurich, 1995.
- An Implementation of the Forward adn Reverse Mode in Maple.
- Roger Margot, Diplomarbeit, ETH Zurich, 1995.
- Univariate polynomial GCD's over Q(alpha).
- Igor Berchtold, Diplomarbeit, ETH Zurich, 1993.
- Sparse Matrix Determinants over Integral Domains.
- Laurent Bernardin, Diplomarbeit, ETH Zurich, 1993.
- Factorization of multivariate polynomials over a finite field.
- Walter Neuenschwander, Diplomarbeit, ETH Zurich, 1992.
- Algorithmische Differentiation.
- Stefan Schwendimann, Diplomarbeit, ETH Zurich, 1992.
- Ein Softwarepaket fuer die algebraische, projektive Geometrie.