


Publications
Last updated November 16th, 2011.
Year:
2011  2012,
2010  2011,
2009  2010,
2008  2009,
2007  2008,
2006  2007,
2005  2006,
2004  2005,
2003  2004,
2002  2003
Note: the names of all MITACS investigators are highlighted in bold,
the names of all MITACS students, postdoctoral fellows and research associates are underlined.
November 1, 2011  November 1, 2012
A. Refereed Contributions
1. Articles in refereed publications:
Published or accepted for publication:
M. Md. Ali, M. Moreno Maza and Y. Xie.
On the Factor Refinement Principle and its Implementation on Multicore Architectures.
J. of Physics: Conference Series, 385, 10 pages, 2012.
J.M. Borwein and A. Straub.
Mahler measures, short walks and logsine integrals.
To appear in Theoretical Computer Science,
Special issue on Symbolic and Numeric Computation. Elsevier.
C. Chen, J.H. Davenport, M. Moreno Maza, B. Xia and R. Xiao.
Computing with semialgebraic sets represented by triangular decomposition.
Accepted April 2012 for the J. Symbolic Comp. (25 pages)
Robert M. Corless
Pseudospectra of exponential matrix polynomials.
To appear in Theoretical Computer Science,
Special issue on Symbolic and Numeric Computation. Elsevier.
V. Dabbaghian, V.K. Mago, T. Wu, C. Fritz and A. Alimadad
Social interactions of eating behavior among high school students: A cellular automata approach.
BMC Journal of Public Health (2012), to appear.
J. Doliskani and É. Schost.
Taking Roots over High Extensions of Finite Fields.
To appear in Mathematics of Computation.
Hamradri Ganguli and J. Jankauskas.
On the equation f(g(x)) = f(x) h^m(x) for composite polynomials.
Accepted January 2007 for Journal of Australian Mathematical Society,
Special issue dedicated to Alf van der Poorten, (7 pages).
Mark Giesbrecht and Myung Sub Kim.
Computation of the Hermite form of a Matrix of Ore Polynomials.
arXiv.1109.3656v1 To appear in Journal of Algebra.
P. Giabbanelli, A. Alimadad, V. Dabbaghian and D. Fianegood.
Modeling the in uence of social networks and environment on energy balance and obesity.
J. Computational Science 3, 17–27, 2012.
Mark Giesbrecht, Daniel Roche and Hrushikesh Tilak.
Computing sparse multiples of polynomials.
Algorithmica. 64:3 pp.454–480, 2012.
S. Gupta, S. Sarkar, A. Storjohann, J. Valeriote.
Triangular xbasis decompositions and derandomization of linear algebra algorithms over K[x].
J. Symbolic Comp. special issue in honour of the
research and influence of Joachim von zur Gathen at 60
47(4), 422–453, 2012.
S. Haque and M. Moreno Maza.
Plain polynomial arithmetic on GPU.
J. of Physics: Conference Series, 385, 10 pages, 2012.
J. van der Hoeven and É. Schost.
Multipoint evaluation in higher dimensions.
To appear in Applicable Algebra in Engineering, Communication and Computing (14 pages).
J. Hu, Y. Hou, A.D. Rich, and D.J. Jeffrey.
Indefinite integration as term rewriting: integrals containing tangent.
To appear in
Programming and Computer Software, Springer, 2013.
P.W. Lawrence, R.M. Corless and D.J. Jeffrey.
Algorithm 917: Complex DoublePrecision Evaluation of the Wright ω Function.
ACM Transactions on Mathematical Software, 38(3), Article 20, 2012.
S. Maclean and G. Labahn
A new approach for
recognizing handwritten mathematics using relational grammars and fuzzy sets.
To appear in International Journal of Document Analysis and Recognition (27 pages).
V.K. Mago, R. Frank, A. Reid and V. Dabbaghian.
The strongest doesn't attract all but it does attract the most  evaluating
the criminal attractiveness of shopping malls using fuzzy logic.
J. Expert Systems, (2012), 13 pages, to appear.
V.K. Mago, L. Bakker, A. Alimadad, P. Borwein, V. Dabbaghian and E. Papageorgiou.
Fuzzy cognitive maps and cellular automata: An evolutionary approach for social system modeling.
J. Applied Soft Computing, 12 (2012), 3771–3784.
M. Moreno Maza, B. Xia and R. Xiao.
On solving parametric polynomial systems.
Accepted May 2012 for J. Mathematics in Computer Science (17 pages).
W. Ng, D.E. Chang and G. Labahn.
Energy Shaping for
Systems with Two Degrees of Underactuation and More than Three Degrees of Freedom.
To appear in SIAM Journal on Control and Optimization (25 pages).
A. Poteax and É. Schost.
On the complexity of computing with zerodimensional triangular sets.
To appear in J. Symbolic Computation (35 pages).
A. Poteax and É. Schost.
Modular Composition Modulo Triangular Sets and Applications.
To appear in Computational Complexity (39 pages).
V. Spicer, J. Ginther, A. A. Reid, H. Sei, and V. Dabbaghian
Bars on blocks: a cellular automata model of crime and liquor licensed establishment density.
Computers, Environment and Urban Systems, 36 (2012), 412–422.
W. Zhou and G. Labahn.
Algorithms for
Efficient Order Basis Computation.
J. Symbolic Comp., 47(7), 2012, 793–817.

Submitted for publication:

2. Other refereed contributions:
Papers in refereed conference proceedings:
A. Bostan, M. F. I. Chowdhury, R. Lebreton, B. Salvy and É. Schost.
Power Series Solutions of Singular (q)–Differential Equations
Proceedings of ISSAC 2012, ACM, 107&ndsash;114}, 2012.
Pavel Bourdykine and Stephen Watt.
Lightweight Abstraction for Mathematical Computation in Java.
Proceedings of CASC 2012, Springer–Verlag LNCS 7422, 2012.
C. Chen and M. Moreno Maza.
An Incremental Algorithm for Computing Cylindrical Algebraic Decompositions.
Electronic Proceedings of ASCM 2012, Beijing, China, October 26–28, 2012. (20 pages)
M. F. I. Chowdhury, C.P. Jeannerod, V. Neiger and É. Schost and G. Villard,
On the Complexity of Multivariate Interpolation with Multiplicities and of Simultaneous Polynomial Approximations.
Proceedings of ASCM 2012, Beijing, China, October 26–28, 2012.
M. Elsheikh, M. Giesbrecht, A. Novacin, B.D. Saunders.
Computation for Smith Forms of Sparse Matrices Over Local Rings.
Proceedings of ISSAC 2012, Grenoble, France, July 22–25, 2012.
M. Giesbrecht and N. Pham.
A Symbolic Computation Approach to the Projection Method.
Electronic Proceedings of ASCM 2012, Beijing, China, October 26–28, 2012.
E. Hubert and G. Labahn.
Rational
invariants of scalings from Hermite normal forms.
Proceedings of ISSAC 2012, Grenoble, France, July 22–25, (2012) 219–226
Riu Hu and Stephen Watt.
Optimization of Point Selection on Digital Ink Curves.
Proceedings of the 13th International Conference on Frontiers in Handwriting Recognition (ICFHR) 2012, IEEE Computer Society, 2012.
N. Iwanski, R. Frank, A. Reid and V. Dabbaghian.
A computational model for predicting the location of crime attractors on a road network.
European Intelligence and Security Informatics Conference (EISIC 2012), (2012), 60–67.
P. Jackson, A. Reid, N. Huitson, K. Wuschke and V. Dabbaghian
A cellular automata approach to modeling peer influence on binge drinking behavior.
Proceedings of the Cellular Automata Modeling for Urban and Spatial Systems (CAMUSS), (2012), to appear.
Piers W. Lawrence and Robert M. Corless
Numerical Stability of Barycentric Hermite Rootfinding.
Proceedings of the 2011 Internation Workshop on SymbolicNumeric Computation (SNC),
Marc Moreno Maza, editor, ACM, 147–148, 2011.
R. Lebreton and É. Schost.
Algorithms for the universal decomposition algebra.
Proceedings of ISSAC 2012, ACM, 234–241, 2012.
S. Marcus, M. Moreno Maza and P. Vrbik.
On Fulton's Algorithm for Computing Intersection Multiplicities.
Proceedings of CASC 2012, Springer–Verlag LNCS 7422 pp. 198–211, 2012.
Michael Monagan and Roman Pearce.
POLY: A new polynomial data structure for Maple.
Electronic Proceedings of ASCM 2012, Beijing, China, October 26–28, 2012.
Michael Monagan and Roman Pearce.
Sparse Polynomial Powering Using Heaps.
Proceedings of CASC 2012, Springer–Verlag LNCS 7422 pp. 236–247, 2012.
Michael Monagan.
A new edge selection heuristic for computing the Tutte polynomial of an undirected graph.
Proceedings of FPSAC 2012, Nagoya, Japan, July 30 – August 3, 2012.
To appear in Discrete Mathematics and Theoretical Computer Science, 2012, 849–860.
M. Moreno Maza, E. Schost and P. Vrbik.
Inversion Modulo ZeroDimensional Regular Chains,
Proceedings of CASC 2012, Springer–Verlag LNCS 7422 pp. 224–235, 2012.
M. Moreno Maza and R. Xiao.
Degree and dimension estimates for invariant ideals of Psolvable recurrences.
Electronic Proceedings of ASCM 2012, Beijing, China, October 26–28, 2012. (23 pages)
C. Pauderis and A. Storjohann.
Deterministic unimodularity certification.
Proceedings of ISSAC 2012, ACM Press, 281–283, 2012.
Stephen M. Watt
Computational Tools for Mathematical Collaboration.
Proceedings of the 13th International Symposium on Symbolic Numeric Algorithms
for Scientific Computing (SNASC 20122), IEEE Computer Society, 16–18, 2012.
W. Zhou, G. Labahn and A. Storjohann
Computing Minimal Nullspace Bases.
Proceedings of ISSAC 2012, Grenoble, France, July 22–25, (2012) 366–373.

Monographs, books, and book chapters:
Proceedings of the 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing.
Dongming Wang, Viorel Negru, Tetsuo Ida, Tudor Jebelean, Dana Petcu, Stephen Watt, Daniela Zaharie
(editors), IEEE Computer Society, 2012, ISBN 9780769546308.
Modelling and Simulation of Complex Social Systems.,
V. K. Mago and V. Dabbaghian (editors), Springer, 400 pages, in press.

Letters, notes, communications:
Government publications: none

B. Nonrefereed contributions:
1. Papers in nonrefereed conference proceedings: none
2. Theses:
Cory Ahn
Fast multiplication of polynomials over algebraic number fields.
MSc. Thesis, Department of Mathematics, Simon Fraser University, December 2011.
Supervisor: Michael Monagan
Md. Mohsin Ali
On the Factor Refinement Principle and it's Implementation on Multicore Architectures.
MSc. Thesis, Department of Computer Science, University of Western Ontario, December 2011.
Supervisor: Marc Moreno Maza
Samuel Johnson
Analytic combinatorics of planar lattice paths.
MSc. Thesis, Department of Mathematics, Simon Fraser University, June 2012.
Supervisor: Marni Mishna
Soo Go
Sparse Polynomial Interpolation and the Fast Euclidean Algorithm.
MSc. Thesis, Department of Mathematics, Simon Fraser University, July 2012.
Supervisor: Michael Monagan
Zunaid Haque
Multithreaded Real Root Isolation on Multicore Architectures.
MSc. Thesis, Department of Computer Science, University of Western Ontario, December April 20, 2012.
Supervisor: Marc Moreno Maza
Vincent Neiger
On the Computation of Small Modular Roots and the Specific Problem of Polynomial Reconstruction
MSc. Thesis, Computer Science, ENS Lyon, France, July 2012.
Supervisors: Gilles Villard, ClaudePierre Jeannerod and Eric Schost.
Wai Man Ng
Energy shaping for systems with two degrees of underactuation.
PhD Thesis, Applied Mathematics, University of Waterloo, December 2011.
Supervisors: Dong Eui Chang and George Labahn
Soumojit Sarkit
Computing Popov Forms of Polynomial Matrices.
MMath Thesis, School of Computing Science, University of Waterloo, December 5, 2011.
Supervisor: Arne Storjohann

3. Technical and internal reports: none
4. Industrial reports: none
C. Specialized Publications
1. Proprietary software packages:
James McCarron, Michael Monagan, and Asif Zaman.
Groups: A new software package for Maple 17 for computing in finite groups with a focus on
visualization tools and group isomorphism.
Michael Monagan.
GraphTheory: New software for Maple 17 for computing Tutte polynomials,
reliability polynomials, and testing graphs for isomorphism.
Marc Moreno Maza
Addition of the RealComprehensiveTriangularize command to the RegularChains library
for computing real solutions of parametric polynomial equations, inequations and inequalities.
The RealTriangularize command is being applied to optimization and control problems
through Maplesoft's industrial consulting projects.
Roman Pearce and Michael Monagan.
POLY: A new polynomial data structure for Maple 17 that automatically encodes
monomials in one machine word. Includes C code for Maple kernel routines,
external libraries, and conversions.


November 1, 2010  November 1, 2011
A. Refereed Contributions
1. Articles in refereed publications:
Published or accepted for publication:
Andrew Arnold and Michael Monagan.
Computing cyclotomic polynomials of very large height.
Mathematics of Computation, 80:276 (2011) 2359–2379.
D. H. Bailey and J. M. Borwein.
Exploratory Experimentation and Computation.
Notices of the AMS 58:10, 1410–1419, November 2011.
D. H. Bailey and J. M. Borwein.
High Precision Numerical Integration: Progress and Challenges.
J. Symbolic Computation, 46 (2011) 741–754.
M. Barkatou, C. El Bacha, G. Labahn and E. Pfluegel.
On Simultaneous Row and Column Reduction of HigherOrder
Linear Differential Systems.
J. Symbolic Computation 49(1) 2013, 45 – 64.
David Borwein, Jonathan Borwein and Armin Staub.
A sinc that sank. Accepted October 2011 for the Amer. Math. Monthly.
Jonathan M. Borwein and Armin Staub.
Logsine evluations of Mahler measures, Part I.
Accepted March 2011 for the Australian J. Maths.
Peter Borwein, Stephen Choi, and Michael Coons.
Completely Multiplicative Functions Taking Values in [1, 1].
Transactions of the AMS 362:12, December 2010, 6279–6291.
Peter Borwein, S. Choi, and J. Janauskas.
On a class of polynomials related to Barker sequences.
Accepted March 2011 for Proceedings of the AMS.
Peter Borwein, Stephen Choi, and Hamadri Ganguli.
Sign Changes of the Liouville Function on Quadratics.
arXiv:1109.3107. Accepted 2011 for Bull. Can. Math. Soc.
John C. Butcher, Robert M. Corless, Laureano Gonzalez–Vega and Azar Shakoori.
Polynomial algebra for Birkhoff interpolants.
Numerical Algorithms 56(3): 319–347 (2011).
Changbo Chen and M. Moreno Maza.
Algorithms for computing triangular decompositions of polynomial systems.
J. Symbolic Computation 47(6): 610–642, 2012.
Changbo Chen, Marc Moreno Maza and Yuzhen Xie.
Cache Complexity and Multicore Implementation for Univariate Real Root Isolation
To appear the in the Journal of Physics: Conference Series.
V. Dabbaghian, V. Spicer, S.K. Singh, P. Borwein and P.L. Brantingham.
The social impact in a highrisk community: a cellular automata model.
J. Computational Science 2 (2011), 238–246.
X. Dahan, A. Kadri and É. Schost.
Bitsize estimates for triangular sets in positive dimension.
To appear in J. Complexity, 37 pages.
C. É. Drevet, Md. N. Islam and É. Schost.
Optimization techniques for small matrix multiplication.
J. Theoretical Computer Science 412:22 (2011) 2219–2236.
L. de Feo and É. Schost.
Fast Arithmetics in ArtinSchreier Towers over Finite Fields.
To appear in J. Symbolic Computation, 28 pages.
R. Frank, V. Dabbaghian, A. Reid, S. Singh, J. Cinnamon and P. Brantingham.
Power of Criminal Attractors: Modeling the Pull of Activity Nodes.
J. Artificial Sciences and Social Simulation, 14:1 (2011), 27 pp.
P. Gaudry and É. Schost.
Genus 2 point counting over prime fields.
To apprear in J. Symbolic Computation, 46 pages.
Mark Giesbrecht and Daniel S. Roche.
Detecting lacunary perfect powers and computing their roots.
J. Symbolic Computation, 46:11 (2011) 1242–1259.
S. Gupta, S. Sarkar, A. Storjohann and J. Valeriote.
Triangular xbasis decompositions and derandomization of linear algebra algorithms over K[x].
To appear in J. Symbolic Computation.
Sardar Anisul Haque and Marc Moreno Maza.
Determinant Computation on the GPU using the Condensation Method.
To appear the in the Journal of Physics: Conference Series.
G.A. Kalugin and D.J. Jeffrey.
Unimodal sequences show Lambert W is Bernstein.
Mathematical Reports of the Academy of Sciences, 33(2) June 2011.
See also arXiv:1011.5940v1
G.A. Kalugin, D.J. Jeffrey, R.M. Corless and P.B. Borwein.
Stieltjes and other integral representations for functions of Lambert W.
Accepted August 2011 for J. Integral Transforms and Special Functions.
Appeared 23(8) 581–593, 2012.
G.A. Kalugin, D.J. Jeffrey and R.M. Corless.
Bernstein, Pick, Poisson and related integral expressions for Lambert W.
Accepted October 2011 for J. Integral Transforms and Special Functions.
Appeared 23(11) 817–829, 2012.
Francois Lemaire, Marc Moreno Maza, Wei Pan and Yuzhen Xie.
When does equal sat(T)?
J. Symbolic Computation 46:12 (2011) 1291–1305
Xin Li, Marc Moreno Maza, Raqeeb Rasheed and Éric Schost.
The modpn library: Bringing fast polynomial arithmetic into Maple.
J. Symbolic Computation 46:7 (2011) 841–858
S. Liang and D.J. Jeffrey.
An analytical approach for solving nonlinear boundary value problems in finite domains.
J. Numerical Algorithms, 56(1), 93–106, January 2011.
S. Maclean, G. Labahn, E. Lank, M. Marzouk and D. Tausky.
Grammarbased techniques for creating groundtruthed sketch corpora.
International Journal of Document Analysis and Recognition,
14:1 (2011) 65–74.
Michael Monagan and Roman Pearce.
Sparse Polynomial Pseudo Division using a Heap.
J. Symbolic Computation, 46:9 (2011) 805–822.
M. Moreno Maza and Wei Pan.
Solving Bivariate Polynomial Systems on a GPU
To appear the in the Journal of Physics: Conference Series.
M. Moreno Maza and Wei Pan.
Balanced Dense Polynomial Multiplication on MultiCores
Int. J. Found. Comput. Sci. 22:5 (2011) 1035–1055
Cosmin Oancea and Stephen M. Watt.
An Architecture for Generic Extensions.
J. Science of Computer Programming, 76:4, 258–277, April 2011, Elsevier.
Daniel S. Roche.
Chunky and equalspaced polynomial multiplication.
J. Symbolic Computation, 46:7 (2011), 791–806.
J. Tanguay, M. Gil, D.J. Jeffrey and S.R. Valluri.
Ddimensional Bose gases and the Lambert W function.
J. Math Phys. 51(12) 123303:1–14, December 2010.
W. Zhou and G. Labahn.
Efficient Computation of Order Bases.
To appear in J. Symbolic Computation (2011).

Submitted for publication:
J. Adams, E. Freden, and M. Mishna.
From indexed grammars to generating functions.
(16 pages; arXiv:1102.1779) Submitted October 2011 to J. Theory of Computing, 2011.
Adrian Belshaw and Peter Borwein.
Chapernowne's Number, Strong Normality and the X Chromosome.
Submitted 2011 to Computational and Analytical Mathematics,
Spring Proceedings in Mathematics.
Changbo Chen, James H. Davenport, Marc Moreno Maza, Bican Xiz and Rong Xiao.
Computing with semialgebraic sets: effective boundaries and relaxation techniques.
Submitted to J. Symbolic Computation.
J. Doliskani and É. Schost.
Taking Roots over High Extensions of Finite Fields.
Submitted September 2011.
Mark Giesbrecht and Myung Sub Kim.
Computation of the Hermite form of a Matrix of Ore Polynomials.
arXiv.1109.3656v1 Submitted September 2011.
Mahdi Javadi and Michael Monagan.
Parallel Sparse Polynomial Interpolation over Finite Fields.
Submitted November 2010 to J. Symbolic Computation.
V.K. Mago, H.K. Morden, C. Fritz, T. Wu, S. Namazi, P. Geranmayeh, R. Chattopadhyay and V. Dabbaghian.
Analyzing the impact of social factors on homelessness: A fuzzy cognitive map approach.
Submitted to J. Intelligent systems, (2011), 32 pages.
V.K. Mago, R. Frank, A. Reid and V. Dabbaghian.
The strongest doesn't attract all but it does attract the most  evaluating
the criminal attractiveness of shopping malls using fuzzy logic.
Submitted to J. Expert Systems, (2011), 13 pages.
V.K. Mago, V. Dabbaghian, L. Bakker, A. Alimadad, P. Borwein and E. Papageorgiou.
Fuzzy cognitive maps and cellular automata: An evolutionary approach for social system modeling.
Submitted to J. Applied Soft Computing, (2011), 34 pages.
A. Poteax and É. Schost.
On the complexity of computing with zerodimensional triangular sets.
Submitted September 2011.


2. Other refereed contributions:
Papers in refereed conference proceedings:
A. Alimadad, V. Dabbaghian, S.K. Singh and H.H. Tsang.
Modeling HIV Spread through Sexual Contact Using a Cellular Automaton.
Proceedings of the IEEE Congress on Evolutionary Computation (2011) 2345–2350, New Orleans, June 5–8, 2011.
Jonathan M. Borwein and Armin Staub.
Special Values of Generalized Logsine Integrals.
Proceedings of ISSAC 2011, ACM Press, pp. 43–50, 2011.
Awarded best student paper prize.
Curtis Bright and Arne Storjohann.
Vector Rational Number Reconstruction.
Proceedings of ISSAC 2011, ACM Press, pp. 51–58, 2011.
Changbo Chen, James H. Davenport, Marc Moreno Maza, Bican Xia, and Rong Xiao.
Computing with semialgebraic sets represented by triangular decomposition.
Proceedings of ISSAC 2011, ACM Press, pp. 75–82, 2011.
Changbo Chen, James H. Davenport, Francois Lemaire, Marc Moreno Maza, Nalina Phisanbut, Bican Xia, and Rong Xiao and Yuzhen Xie.
Solving semialgebraic systems with the RegularChains library in Maple.
Proceedings of MACIS 2011, pp. 38–51, 2011.
Changbo Chen and Marc Moreno Maza.
Algorithms for computing triangular decompositions of polynomial systems.
Proceedings of ISSAC 2011, ACM Press, pp. 83–90, 2011.
Changbo Chen and Marc Moreno Maza.
Semialgebraic description of the equilibria of dynamical systems.
Proceedings of CASC 2011, Springer Verlag LNCS 6885, 2011.
Mark Giesbrecht, Daniel S. Roche and Hrushikesh Tilak.
Computing sparse multiples of polynomials.
Proceedings of the 2010 Int. Symp. on Algorithms and Computation (ISAAC 2010),
SpringerVerlag LNCS 6506, December 2010, pp. 266–278.
Mark Giesbrecht and Daniel Roche.
Diversification Improves Interpolation.
Proceedings of ISSAC 2011, ACM Press, pp. 123–131, 2011.
Somit Gupta and Arne Storjohann.
Computing Hermite Forms of Polynomial Matrices.
Proceedings of ISSAC 2011, ACM Press, pp. 155–162, 2011.
N. Iwanski, R. Frank, V. Dabbaghian, A. Reid and P. Brantingham.
Analyzing an Offender’s Journey to Crime: A Criminal Movement Model (CriMM)
Proceedings of the 2011 European Intelligence and Security Informatics Conference (EISIC 2011),
pp. 70–77, Athens, Greece, September 12–14, 2011.
Received Best Paper Award.
S. Maclean, D. Tausky, G. Labahn, E. Lank and M. Marzouk.
Is the iPad useful for sketch input? A comparison with the Tablet PC.
Proceedings of the International Symposium on SketchBased Interfaces and Modeling
(SBIM 2011). (2011)
Vadim Mazlov and Stephen Watt.
Polynomial Approximation in Handwriting Recognition.
Proceedings of SNC 2011, San Jose, California, June 7–9, 2011, ACM Press, pp. 3–7.
Vadim Mazlov and Stephen Watt.
Digital Ink Compression via Functional Approximation.
Proceedings of ICFHR 2010, Kokata, India, November 16–18, 2010,
IEEE Computer Society, pp. 688–694.
Marc Moreno Maza, Bican Xia and Rong Xioa.
On solving parametric polynomial systems.
Proceedings of MACIS 2011, pp. 205–215, 2011.
Soumojit Sarkar and Arne Storjohann.
Normalization of Row Reduced Matrices.
Proceedings of ISSAC 2011, ACM Press, pp. 297–304, 2011.
M.A. Tayebi, L. Bakker, U. Glasser and V. Dabbaghian.
Locating central actors in cooffending networks.
Proceedings of the 2011 conference on Advances in Social Networks Analysis and Mining (ASONAM 2011),
171–179, Kaohsiung, Taiwan, July 25–27, 2011.

Monographs, books, and book chapters:
Experimental and Computational Mathematics: Selected Writings.
Jonathan Borwein and Peter Borwein,
PSI press, December 2010. ISBN 978–1–935638–06–6.
Modern Mathematical Computation with Maple.
(preface)
Jonathan Borwein and Mathew Skeritt.
Springer Undergraduate Series in Mathematics and Technology (SUMAT), July 2011.
ISBN 978–1–4614–0121–6.
Milestones in Computer Algebra.
J. Symbolic Computation 46:7, July 2011.
Special issue in honour of Keith Geddes on his 60th birthday.
Mark Giesbrecht and Stephen Watt editors.
Proceedings of the 4th International Workshop on SymbolicNumeric Computation (SNC'11).
Marc Moreno Maza, editor.
ISBN: 9781450305150. ACM Press, 204 pages, New York, NY, USA, 2011.
Selected papers from ISSAC 2010..
J. Symbolic Computation special issue. To appear.
Wolfram Koepf and Stephen Watt editors.
SYNASC 2010: 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing.
Tetsuo Ida, Viorel Negru, Tudor Jebelean, Dana Petcu, Stephen Watt and Daniela Zaharie (editors).
IEEE Computer Society, 2011, ISBN 978–0–7695–4324–6.

Letters, notes, communications:
Michael Monagan and Roman Pearce.
Sparse Polynomial Multiplication and Division in Maple 14.
Communications of Computer Algebra, 44:4, 205–209, December, 2010.

Government publications: none

B. Nonrefereed contributions:
1. Papers in nonrefereed conference proceedings:
2. Theses:
Andrew Arnold
Algorithms for Computing Cyclotomic Polynomials.
MSc. Thesis, Department of Mathematics, Simon Fraser University, January 2011.
Supervisor: Michael Monagan
Changbo Chen
Solving polynomial systems via triangular decomposition.
Ph.D. Thesis, Department of Computer Science, University of Western Ontario, August 30th, 2011.
Supervisor: Marc Moreno Maza
Javad Doliskani
Point counting on genus 2 curves.
MSc. Thesis, Department of Computer Science, University of Western Ontario, April 2011.
Supervisor: É. Schost
David Fagnan
Computational Methods for Maximum Drawdown Options under JumpDiffusion.
MMath. Thesis, School of Computing Science, University of Waterloo, August 2011.
Supervisors: Peter Forsyth and George Labahn
Somit Gupta
Hermite Forms of Polynomial Matrices
Masters Thesis, School of Computing Science, University of Waterloo, 2011.
Supervisor: Arne Storjohann
Seyed Mohammad (Mahdi) Javadi
Efficient Algorithms for Computations with Sparse Polynomials.
Ph.D. Thesis, School of Computing Science, Simon Fraser University, January 2011.
Supervisor: Michael Monagan
Wei Pan
Algorithmic Contributions to the Theory of Regular Chains.
Ph.D. Thesis, Department of Comptuer Science, University of Western Ontario, January 25th, 2011.
Supervisor: Marc Moreno Maza
YunJung (Tristan) Kim
Algorithms for Kloosterman zeros.
MSc. Thesis, Department of Mathematics, Simon Fraser University, June 2011.
Supervisor: Petr Lisonek
Christopher Morley
Pricing CPPI Capital Guarantees: A Lagrangian Framework.
MSc. Thesis, Department of Applied Mathematics, University of Waterloo, August 2011.
Supervisors: Peter Forsyth and George Labahn
Daniel Roche
Efficient Computation with Sparse and Dense Polynomials.
Ph.D. Thesis, School of Computer Science, University of Waterloo, April 2011.
Supervisors: Mark Giesbrecht and Arne Storjohann.
Received the Outstanding Achievement in Graduate Studies award from the Faculty of Mathematics.
Jason Selby
Unconventional Applications of Compiler Analysis.
M.Math Thesis, School of Computer Science, University of Waterloo, August 2011.
Supervisor: Mark Giesbrecht
Fei Wang
Orthogonal Designs via Computational Algebra.
M.Math Thesis, School of Computer Science, University of Waterloo, August 2011.
Supervisors: Mark Giesbrecht and Ilias Kotsireas.

3. Technical and internal reports: none
4. Industrial reports: none
C. Specialized Publications
1. Proprietary software packages:
Jacques Carette, Alexandre Korobkine and Mark Lawford.
Software for the automatic verifiable synthesis of implementations from
mathematical models based on Newton's method.
See http://www.cas.mcmaster.ca/~carette/newtongen/
Changbo Chen and Marc Moreno Maza
Major new features for the RegularChains package for Maple 15 to
computing real solutions of any system of polynomial equations, inequations with
inequalities: ""RealTriangularize" produces formulas while "SamplePoints"
returns witness solutions. These two commands are meant
to cover the needs coming from Mathematics and Engineering.
Stephen Melczer, Michael Monagan and Roman Pearce.
A new algorithm for computing the prime decomposition of the radical
of an ideal for the nonzero dimensional case. Motivated by examples
with parameters from geometric theorem proving. Added to the PolynomialIdeals
package for Maple 16.
Roman Pearce and Michael Monagan.
Software for parallel polyomial division and space improvements to
software for parallel polynomial multiplication. Integrated into Maple 16, 2011.
The parallel division algorithm is described in the PASCO 2010 paper
Parallel Sparse Polyomial Division using Heaps.
Roman Pearce and Paul de Marco.
Development of a new polynomial data structure with ``immediate monomials''
for the Maple kernel. See subproject 3.1.2 Immediate Monomials in our
2008 project proposal.
Software includes support routines (coded in C) for polynomial addition, hashing,
evaluation, differentiation, change of monomial ordering, extracting coefficients, etc.

November 1, 2009  November 1, 2010
A. Refereed Contributions
1. Articles in refereed publications:
Published or accepted for publication:
Andrew Arnold and Michael Monagan.
Computing cyclotomic polynomials of very large height.
Accepted June 2010 for Mathematics of Computation.
David H. Bailey and Jonathan M. Borwein.
"Exploratory Experimentation and Computation."
Accepted February 2010 for Notices of the American Math. Soc.
David H. Bailey, Jonathan M. Borwein and Richard E. Crandall.
Advances in the theory of box integrals.
Mathematics of Computation, 79 (2010), 18391866.
A.C. Belanger, P.A. Forsyth and G. Labahn.
"Valuing the Guaranteed Minimum Death Benefit Clause with Partial Withdrawals."
Applied Mathematical Finance, 16:6 (2009) 451496.
Jonathan M. Borwein, OYeat Chan, and Richard Crandall.
"Higherdimensional box integrals."
Experimental Mathematics, 19:3 (2010) 431446.
Peter Borwein and Igor Pritsker.
The multivariate integer Chebyshev problem.
Constr. Approx. 30 (2009), 299310.
A. Bostan, M. F. I. Chowdhury, J. van der Hoven, and É. Schost.
Homotopy methods for multiplication modulo triangular sets.
To appear in J. Symbolic Computation, 2010.
M. BousquetMelou and M. Mishna.
Walks with small steps in the quarter plan.
Algorithmic Probability and Combinatorics,
Contemporary Mathematics series of the AMS, 520 (2010), 140.
Liang Chen and Michael Monagan.
Algorithms for Solving Linear Systems over Cyclotomic Fields.
J. Symbolic Computation, 45:9, 902917, September 2010.
V. Dabbaghian, P. Jackson, K. Wuschke and V. Spicer.
"A cellular automata model on residential migration in response
to neighbourhood social dynamics."
Math. Comput. Modelling, 52 (2010), 17521762.
V. Dabbaghian, J. D. Dixon.
"Computing matrix representations."
Math. Comp., 79 (2010), 18011810.
Luca De Feo and Éric Schost.
transalpyne: a language for automatic transposition.
Communications of Computer Algebra, 44:12, 5971, ACM Press, 2010.
R. Frank, V. Dabbaghian, A. Reid, S. Singh, J. Cinnamon and
P. Brantingham.
"Power of Criminal Attractors: Modeling the Pull of Activity Nodes."
Journal of Artificial Societies and Social Simulation,
to appear (2010), 32 pages.
Mark Giesbrecht and Daniel Roche.
Detecting lacunary perfect powers and computing their roots.
Accepted for the J. Symbolic Computation, 2010.
Mark Giesbrecht and Daniel Roche.
Interpolation of shiftedlacunary polynomials.
To appear in J. Computational Complexity, 2010.
Oleg Golubitsky and Stephen Watt.
DistanceBased Classification of Handwritten Symbols,
Int. J. of Document Analysis and Recognition, 13:2 133146, 2010.
David Jeffrey
LU factoring of noninvertible matrices.
Communications of Computer Algebra, 44:171, ACM Press, 18, 2010.
F. Lemaire, M. Moreno Maza, W. Pan and Y. Xie.
When does <T> equal sat(T)?
To appear, J. Symbolic Computation.
Songxin Liang and David Jeffrey.
"Approximate solutions to a parameterized sixth order boundary value problem."
Comp. Math. Applications, 59:1, 247253, 2010.
Songxin Liang and David Jeffrey.
"An analytical approach for solving nonlinear boundary value problems in finite domains."
To appear in Numerical Algorithms, 14 pp., 2010.
S. Maclean, G. Labahn, E. Lank, M. Marzouk, and D. Tausky.
"Grammarbased techniques for creating groundtruthed sketch corpora."
To appear in Int. Journal of Document Analysis and Recognition, 2010, 20 pages.
Marc Moreno Maza, Yuzhen Xie.
Balanced dense polynomial multiplication on multicores.
To appear in International Journal of Foundations of Computer Science, 2010, 20 pages.
Daniel Roche.
"Chunky and EqualSpaced Polynomial Multiplication."
To appear in J. Symbolic Computation, 2010.
M. J. Roy, D. M. Maijer, R. J. Klassen, J. T. Wood and É. Schost.
Analytical Solution of the Tooling/Workpiece Contact Interface Shape During a Flow Forming Operation.
To appear in Journal of Materials Processing Technology.
M. Safey el Din and É. Schost.
A baby steps/giant steps probabilistic algorithm for computing roadmaps in smooth bounded real hypersurface.
To appear in Journal of Discrete and Computational Geometry.

Submitted for publication:
A. Alimadad, V. Dabbaghian, P.J. Giabbanelli,
S.K. Singh and H.H. Tsang.
"Modeling HIV spread through sexual contact using a
cellular automaton", submitted (2010), 14 pages.
P. Borwein, S. Choi and C. Samuels.
Polynomials whose reducibility is related to the Goldbach conjecture.
Submitted to Journal of London Mathematical Society, 2010.
Peter Borwein and Michael Coons.
Transcendence of Gaussian Liouville Number and Relatives.
Submitted 2010.
V. Dabbaghian, V. Spicer, S.K. Singh, P. Borwein,
and P. Brantingham.
"The social impact on the drugcrime nexus: a cellular
automata model", submitted (2010), 18 pages.
X. Dahan, A. Kadri and É. Schost.
Bitsize estimates for triangular sets in positive dimension,
37 pages, submitted, 2010.
C. E. Drevet, Md. N. Islam and É. Schost.
Optimization techniques for small matrix multiplication, 32 pages, May 2010.
Mark Giesbrecht, Daniel Roche and Hrushikesh Tilak.
"Computing sparse multiples of polynomials", 26 pages, Submitted, 2010.
S. Gupta, S. Sarkar, A. Storjohann and J. Valeriote.
"Triangular xbasis decompositions and derandomization of linear
algebra algorithms over K[x]." Submitted to the Journal of Symbolic
Computation. October 2010. 33 pages.
J. van der Hoeven and É. Schost.
Multipoint evaluation in higher dimensions.
Submitted.
I. Huang, P. Forsyth and G. Labahn.
"Combined Fixed Point and Policy Iteration for HJB Equations in Finance"
Submitted October 2010 to SIAM Journal of Numerical Analysis.
Xin Li, Marc Moreno Maza and Wei Pan.
GCD Computations modulo regular chains.
Submitted to J. Symbolic Computation, 2010.
Michael Monagan and Roman Pearce.
Sparse Polynomial Multiplication and Division in Maple 14.
Submitted to Communications in Computer Algebra, 4 pages, 2010.
Marc Moreno Maza and Wei Pan
Fast polynomial multiplication on a GPU.
Submitted to the postconference proceedings of HighPerformance Computing Symposium 2010.
A. Poteax and É. Schost.
Modular Composition Modulo Triangular Sets and Applications.
Submitted October 2010.
Wei Zhou and George Labahn.
"Labahn, Efficient Computation of Order Bases"
Submitted to the Journal of Symbolic Computation, February 2010.


2. Other refereed contributions:
Papers in refereed conference proceedings:
Andrew Arnold and Michael Monagan.
A highperformance algorithm for calculating cyclotomic polynomials.
Proceedings of PASCO '2010, ACM Press, pp. 112120, July 2010.
F. Boulier, C. Chen, F. Lemaire, and Marc Moreno Maza.
Real Root Isolation of Regular Chains
Proceedings of the Joint Conference of ASCM 2009 and MACIS 2009,
Fukuoka, Japan, December 1417, 2009.
MathforIndustry Lecture Notes Series, 22, 2009
Kyushu University. ISSN 18814042.
S. Burrill, M. Mishna and J. Post.
"On kcrossings and knestings of permutations".
Proceedings of FPSAC 2010, August 26, 2010.
Jacques Carette, Alan Sexton, Volker Sorge, and Stephen Watt.
Symbolic Domain Decomposition.
Proceedings of ASCI/MKM/Calculemus 2010, SpringerVerlag LNCS 6167, pp. 172188, 2010.
Changbo Chen, James H. Davenport, John P. May, Marc Moreno Maza, Bican Xia, Rong Xia.
Triangular decomposition of semialgebraic systems.
Proceedings of ISSAC '2010, ACM Press, pp. 187194, 2010.
Howard Cheng and George Labahn.
A Practical Implementation of a Modular Algorithm for Ore Polynomial Matrices.
Proceedings of the Joint Conference of ASCM 2009 and MACIS 2009.
MathforIndustry Lecture Notes Series, 22, Kyushu University, December 2009.
James Davenport and Jacques Carette.
The Sparsity Challenges.
Symbolic and Numeric Algorithms for Scientific Computing (SYNASC),
2009 11th International Symposium on, pp. 37, 2009.
Laurentiu Dragan and Stephen Watt.
"Type Specialization in Aldor",
To appear in Proceedings of the 12th International Workshop on
Computer Algebra in Scientific Computing, (CASC 2010),
September 512 2010, Tsakhkadzor, Armenia.
Joachim von zur Gathen, Mark Giesbrecht and Konstantin Ziegler.
Composition Collisions and Projective Polynomials,
Proceedings of ISSAC '2010, ACM Press, pp. 123130, 2010.
Mark Giesbrecht, George Labahn and Yang Zhang.
Computing Popov forms of matrices over PBW extensions.
Proceedings of the Joint Conference of ASCM 2009 and MACIS 2009,
Fukuoka, Japan, December 1417, 2009.
Oleg Golubitsky, Vadim Mazalov and Stephen M. Watt.
"Towards Affine Recognition of Handwritten Mathematical Characters",
Proc. International Workshop on Document Analysis Systems, (DAS 2010),
June 911 2010, Boston, ACM Press, pp. 3542, 2010.
Oleg Golubitsky, Vadim Mazalov and Stephen M. Watt.
"OrientationIndependent Recognition of Handwritten Characters
with Integral Invariants",
Proceedings of the Joint Conference of ASCM 2009 and MACIS 2009,
Fukuoka, Japan, December 1417, 2009.
MathforIndustry Lecture Notes Series, 22, 252261, 2009
Kyushu University. ISSN 18814042.
Sardar Anisul Haque, Shahadat Hossain and Marc Moreno Maza.
Cache friendly sparse matrixvector multiplication.
Proceedings of PASCO 2010, ACM Press, 175176, 2010.
David Harvey and Daniel Roche.
"An inplace truncated {F}ourier transform and applications to polynomial multiplication."
Proceedings of ISSAC '2010, ACM Press, pp. 325329, 2010.
Mahdi Javadi and Michael Monagan.
Inplace Arithmetic for Univariate Polynomials over an Algebraic Number Field.
Proceedings of the Joint Conference of ASCM 2009 and MACIS 2009,
Fukuoka, Japan, December 1417, 2009.
MathforIndustry Lecture Notes Series, 22, 330341, 2009, Kyushu University.
Mahdi Javadi and Michael Monagan.
Parallel Sparse Polynomial Interpolation over Finite Fields.
Proceedings of PASCO '2010, ACM Press, pp. 160168, July 2010.
D. J. Jeffrey and A. D. Rich.
"Reducing expression size using rulebased integration."
Intelligent Computer Mathematics, SpringerVerlag LNAI 4167, 234246, 2010.
G. A. Kalugin and D. J. Jeffrey.
"Series transformations to improve and extend convergence."
Proceedings of CASC 2010, Springer Verlag LNCS 6244, 134147, 2010.
Charles E. Leiserson, Liyun Li, Marc Moreno Maza and Yuzhen Xie.
Parallel computation of the minimal elements of a poset.
Proceedings of PASCO '2010, ACM Press, pp. 5362, 2010.
Charles E. Leiserson, Liyun Li, Marc Moreno Maza and Yuzhen Xie.
Efficient Evaluation of Large Polynomials.
Proceedings of the International Congress of Mathematical Software,
SpringerVerlag LNCS 6327, 2010.
Lingchua Meng, Yevgen Voronenko, Jeremy R. Johnson, Marc Moreno Maza, Franz Franchetti and Yuzhen Xie.
Spiralgenerated modular FFT algorithms.
Proceedings of PASCO '2010, ACM Press, pp. 169170, 2010.
Michael Monagan and Roman Pearce.
Parallel Sparse Polynomial Division using Heaps.
Proceedings of PASCO '2010, ACM Press, pp. 105111, July 2010.
Stephen Watt.
An Analytic Model for Colluding Processes,
To appear in Proceedings of the International Conference on Parallel Computer Algebra,
(PARCA 2010), June 29 to July 3, 2010, Tambov, Russia.
Stephen Watt.
On the Future of Computer Algebra Systems at the Threshold of 2010,
Proceedings of the Joint Conference of ASCM 2009 and MACIS 2009,
Fukuoka, Japan, December 1417, 2009.
MathforIndustry Lecture Notes Series, 22, Kyushu University, pp. 422430,
ISSN 18814042.

Monographs, books, and book chapters:
J. Borwein and P. Borwein.
"Experimental and Computational Mathematics: Selected Writings".
PSI, to appear, 2010.
Modelling in Healthcare.
The Complex Systems Modelling Group (CMSG), IRMACS, Simon Fraser University.
American Mathematical Society, 2010,
ISBN 978–0–8218–4969–9.
P. Borwein, P. Liljedahl, and H. Zhai.
Creativity in Mathematics, MAA Spectrum book series, to appear, 2010.
Marc Moreno Maza and Wei Pan.
Fast polynomial multiplication on a GPU.
Accepted in the postconference proceedings of
HighPerformance Computing Symposium 2010.
Proceedings of the 2010 International Workshop on Parallel and Symbolic Computation (PASCO 2010).
Marc Moreno Maza and JeanLouis Roch (ed.), ACM Press, 2010, 192 pages.
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation (ISSAC
2010), Stephen M. Watt (ed.), ACM Press, 2010, ISBN 9781450301503.
Proceedings of the 11th International Symposium on Symbolic and Numeric
Algorithms for Scientific Computing (SYNASC 2009),
Stephen Watt, Viorel Negru, Tetsuo Ida, Tudor Jebelean, Dana Petcu,
Daniela Zaharie (editors), IEEE Computer Society, 2010,
ISBN 9783642026133.

Letters, notes, communications: none
Government publications: none

B. Nonrefereed contributions:
1. Papers in nonrefereed conference proceedings: none
2. Theses:
Pavel Bourdykine
Type Safety without Objects in Java.
MSc. Thesis, Computing Science, University of Western Ontario, December 2009.
Supervisor: Stephen Watt
Mustafa Elsheik,
A Generative Approach to Meshing Geometry.
M.A.Sc. Thesis, Software Engineering, McMaster University, September 2010.
Supervisors: Jacques Carette and Spencer Smith.
Ruitong Huang,
Decomposition of Matrix Algebras over Fq(y).
M. Math Thesis, Computing Science, University of Waterloo, July 2010.
Mark Giesbrecht
Riu Hu,
Portable Implementation of Digital Ink: Collaboration and Calligraphy.
MSc. Thesis, Computing Science, University of Western Ontario, December 2009.
Supervisor: Stephen Watt
Liyun Li
Efficient Evaluation of Large Polynomials
MS Thesis: Computing Science, University of Western Ontario, August 2010.
Supervisor: Marc Moreno Maza
Songxin Liang,
Symbolic methods for analyzing polynomial and differential systems.
PhD. Thesis, Applied Mathematics, University of Western Ontario, May 2010.
Supervisor: David Jeffrey
Niloofar Mani,
Fast numeric geometric techniques for computer generated DAE models.
MSc. Thesis, Applied Mathematics, University of Western Ontario, August 2010.
Supervisor: Greg Reid
Vadim Mazalov,
Geometric Techniques for Digital Ink.
MSc. Thesis, Computing Science, University of Western Ontario, August 2010.
Supervisor: Stephen Watt
Jason Peasgood
A Method to Symbolically Compute Convolution Integrals
MMath Thesis, Computing Science, University of Waterloo, December 2009.
Supervisors: George Labahn and Keith Geddes
Mariolys Rivas
Dfinite Symmetric Functions
MSc. Thesis, Mathematics, Simon Fraser University, July, 2010.
Supervisor: Marni Mishna
Austin Roche,
A New Method for Functional Decomposition of Rational Invariants, and the Solution of Abel’s Differential Equation via the Equivalence Method.
PhD. Thesis, Mathematics, Simon Fraser University, August, 2010.
Supervisor: Peter Borwein
Nivedita Patil,
Interactive Computer Manipulation of Formal Sums.
MSc. Thesis, Computing Science, University of Western Ontario, July 2010.
Supervisor: Stephen Watt
Durgesh Saraph,
Wraparound error in Fourier Space Timestepping
MSc. Essay, Computational Mathematics, University of Waterloo, September 2010.
Supervisors: P. Forsyth and G. Labahn.
Hrushikesh Tilak,
Computing sparse multiples of polynomials.
M. Math Thesis, Computing Science, University of Waterloo, July 2010.
Mark Giesbrecht
Jonathan Valeriote,
Deterministic solution of rational linear systems of polynomials over abstract fields.
MSc. Project, Computational Mathematics, University of Waterloo, August, 2010.
Supervisor: Arne Storjohann
Maria Teresa InfanteVelazquez,
Metrics and Neatening of Handwritten Characters
MSc. Thesis, Computing Science, University of Western Ontario, July 2010.
Supervisor: Stephen Watt

3. Technical and internal reports: none
4. Industrial reports: none
C. Specialized Publications
1. Proprietary software packages:
Roman Pearce and Michael Monagan.
Software for polyomial division and parallel polynomial multiplication of
polynomials with integer coefficients. Integrated into Maple 14, 2010.
The parallel multiplication algorithm is described in the ISSAC 2009 paper
Parallel Sparse Polyomial Multiplication using Heaps.
The integration into Maple 14 is described in the report
Sparse Polynomial Multiplication and Division in Maple 14.
Ha Le and Marni Mishna. and Roman Pearce
Three new commands for the Maple 14 DEtools and LREtools packages, namely,
Closure, LocalClosure, and Desingularize.
Changbo Chen, James H. Davenport, John P. May, Marc Moreno Maza, Bican Xia, Rong Xiao.
Two new commands, RealTriangularize and SamplePoints, added to the RegularChains package.
RealTriangularize decomposes the input system of polynomial equations into regular semialgebraic systems,
the second generates at least one point per connected component. These are described in
the ISSAC 2010 paper
Triangular Decomposition of SemiAlgebra Systems. This is submitted to Maple 15.
Marc Moreno Maza and Wei Pan.
modpn++ : GPU support for the modpn library, providing FFTs and subresultant chain computations.
This work is described in the HPSC 2010 paper
Fast polynomial multiplication on a GPU.
Marc Moreno Maza and Wei Pan.
Integration of the solvers of the RegularChains library (these are based on
triangular set methods which are theoretically superior to Greobner bases methods) into
the Maple SolveTools package.

November 1, 2008  November 1, 2009
A. Refereed Contributions
1. Articles in refereed publications:
Published or accepted for publication:
D.H. Bailey and J.M. Borwein.
"HighPrecision Numerical Integration: Progress and Challenges."
J. Symbolic Computation, accepted July 2009.
David Bailey and Jonathan Borwein.
"Highly parallel, high precision integration."
International Journal of Computational Science and Engineering, 4 2009.
A.C. Belanger, P.A. Forsyth and G. Labahn.
"Valuing the Guaranteed Minimum Death Benefit Clause with Partial Withdrawals."
To appear in Applied Mathematical Finance, 2009.
J.M. Borwein and C. Hamilton.
"Symbolic Convex Analysis: Algorithms and Examples,"
Mathematical Programming, 116 (2009), 1735.
P. Borwein, S. Choi, M. Coons.
"Transcendence of power series for some number theoretic functions."
Proc. Amer. Math. Soc. 137(4) 13031305, 2009.
P. Borwein, S. Choi, M. Coons.
"Completely Multiplicative Functions Taking Values in [1,1]."
Accepted for Trans. Amer. Math. Soc, 2009.
A. Bostan and É. Schost
A simple and fast algorithm for computing exponentials of power series.
Information Processing Letters 109(13), 754756, 2009.
A. Bostan, B. Salvy and É. Schost
Fast conversion algorithms for orthogonal polynomials.
Linear Algebra and its Applications, to appear.
F. Boulier, F. Lemaire and M. Moreno Maza
Computing Differential Characteristic Sets by Change of Ordering.
J. Symbolic Computation 45(1), January 2010, Pages 124149.
Jacques Carette and Michael Kucera. "A Partial Evaluator for Maple."
Accepted for Science of Computer Programming.
L. Chen and M. Monagan.
"Algorithms for Solving Linear Systems over Cyclotomic Fields."
J. Symb. Comp., accepted May 2009.
X. Dahan, J. Wu and É. Schost
Evaluation properties of invariant polynomials.
J. Symbolic Computation, 44(11), 15921604, 2009.
S. Garg and É. Schost
Interpolation of polynomials given by straightline programs.
Theoretical Computer Science, 410(2729), 26592662, 2009.
Mark Giesbrecht and Daniel S. Roche.
"Interpolation of ShiftedLacunary Polynomials".
To appear, Computational Complexity.
M. Giesbrecht, G. Labahn and Ws Lee.
Symbolicnumeric Sparse Interpolation of Multivariate Polynomials.
J. Symbolic Computation, 44(8) (2009) 943959.
X. Li, M. Moreno Maza and É. Schost.
Fast Arithmetic for Triangular Sets: from Theory to Practice.
J. Symbolic Computation, 44(7) (2009), 891907.
S. Liang, J. Gerhard, D.J. Jeffrey and G. Moroz.
"A Package for Solving Parametric Polynomial Systems."
Communications in Computer Algebra, 43(3), pp 6172, ACM Press, September 2009.
S. Liang, D.J. Jeffrey.
"Approximate solutions to a parameterized sixth order boundary value problem".
Accepted for Computers and Mathematics with Applications.
S. Liang, D.J. Jeffrey.
"An efficient analytical approach for solving fourth order boundary value problems".
Computer Physics Communications Vol 180, issue 11, pp 20342040, 2009.
S. Liang, D.J.Jeffrey.
"New travelling wave solutions to modified CH and DP equations".
Computer Physics Communications. Vol 180, issue 9, pp 14291433, 2009.
S. Liang, D.J. Jeffrey.
"Comparison of homotopy analysis method and homotopy perturbation method through an evolution equation."
Communicatons Nonlinear Science Numerical Simulation, Vol 14, pp 40574064, 2009.
S. Liang, D.J. Jeffrey.
"Automatic computation of the complete root classification for a parametric polynomial."
J. Symbolic Computation, Vol 44, pp 14871501, 2009.
M. Mishna.
"Classifying lattice walks restricted to the quarter plane."
Journal of Combinatorial Theory, Series A 116:2 460477, February 2009.
M. Mishna and A. Rechnitzer.
"Two nonholonomic lattice walks in the quarter plane."
Theoretical Computer Science 410:3840, 36163630, September 2009.
M. Monagan and R. Pearce.
Sparse Polynomial Division Using a Heap.
J. Symb. Comp. special issue on on Milestones in Computer Algebra.
Accepted July 2009.
G.J. Reid and L. Zhi.
"Solving polynomial systems via symbolicnumeric reduction to geometric involutive form."
J. Symbolic Computation, 44(3) (March 2009), pp 280291.
R. Scott, G.J. Reid, W. Wu and L. Zhi.
"Geometric Involutive Bases and Applications to Approximate Commutative Algebra."
In Approximate Commutative Algebra, Edited by Lorenzo Robbiano and John Abbott,
Texts and Monographs in Symbolic Computation,
A Series of the Research Institute for Symbolic Computation (Springer), pp. 99124.
S.R. Valluri, M. Gil, D.J. Jeffrey, S. Basu.
"The LambertW function and Quantum statistics". Accepted J. Math. Phys.
W. Wu, G.J. Reid and S. Ilie.
"Implicit Riquier bases for PDAE and their semidiscretizations."
J. Symbolic Computation, 44(7) (July 2009), pp 923941.
W. Zhou, D.J. Jeffrey.
"Fractionfree matrix factors: new forms for LU and QR factors."
Frontiers in Computer Science in China, 2(1), pp 6780, 2008.

Submitted for publication:
C. Chen, F. Lemaire, L. Liyun, M. Moreno Maza,
W. Pan and Y. Xie.
Computing with Constructible Sets in Maple
Submitted to J. of Symbolic Computation, November 2008. Extended version of the MICA 2008
Proceedngs paper with the same title.
F. Lemaire, M. Moreno Maza, W. Pan and Y. Xie.
When does <T> equal sat(T)?
Submitted to J. of Symbolic Computation, November 2008.
Extended version of the ISSAC 2008 Proceedngs paper with the same title.
X. Li, M. Moreno Maza, R. Rasheed and É. Schost.
The Modpn Library: Bringing Fast Polynomial Arithmetic into Maple
Submitted to J. of Symbolic Computation, November 2008.
Extended version of the MICA 2008 Proceedngs paper with the same title.
A. Storjohann.
"On the complexity of inverting integer and polynomial matrices."
Submitted December 2008 to Computational Complexity.


2. Other refereed contributions:
Papers in refereed conference proceedings:
B. Beckermann and G. Labahn.
FractionFree Computation of Simultaneous Pade Approximants.,
Proceedings of ISSAC'09, ACM Press, 1522, 2009.
J.M. Borwein.
"Digitallyassisted discovery and proof."
Pages I.3I.11, Proceedings of ICMI Study 19 Workshop "On Proof and Proving,"
National University of Taiwan, May 1015, 2009.
A. Bostan and É. Schost
Fast algorithms for differential equations in positive characteristic.
Proceedings ISSAC'09, pp. 4754, ACM Press, 2009.
Jacques Carette and William M. Farmer.
A Review of Mathematical Knowledge Management.
Proceedings of Conferences on Intelligent Computer Mathematics,
LNAI 5625, pp. 233246, SpringerVerlag, 2009.
C. Chen, M. Moreno Maza, B. Xia, L. Yang.
Computing Cylindrical Algebraic Decomposition via Triangular Decomposition
Proceedings of ISSAC 2009, pages 95102, ACM Press, 2009.
C. Chen, J. H. Davenport, J. May, M. Moreno Maza, B. Xia, R. Xiao and Y. Xie.
User Interface Design for Geometrical Decomposition Algorithms in Maple.
Proceedings of Mathematical UserInterface, 12 pages, 2009.
L. Ding and É. Schost
Code generation for polynomial multiplication.
Proceedings CASC'09, pp. 6678, Springer, 2009.
L. De Feo and É. Schost
Fast arithmetics in ArtinSchreier towers over finite fields.
Proceedings ISSAC'09, pp. 127134, ACM Press, 2009.
Mark Giesbrecht and Myung Sub Kim.
"On Computing the Hermite Form of a Matrix of Differential Polynomials."
Proceedings of CASC '09, Springer Verlag, LNCS 5743 118129, 2009.
Oleg Golubitsky and Stephen M. Watt.
"Online Recognition of MultiStroke Symbols with Orthogonal Series,"
Proc. 10th International Conference on Document Analysis and Recognition,
(ICDAR 2009), IEEE Computer Society, pp. 12651269, 2009.
A. Hariri and É. Schost
Trinomial bases and Chinese remaindering for modular polynomial multiplication.
Proceedings SAC'08, pp. 361372, Springer, 2009.
Mahdi Javadi and Michael Monagan.
On Factorization of Multivariate
Polynomials over Algebraic Number and Function Fields.
Proceedings of ISSAC '09, ACM Press, 199206, 2009.
D.J. Jeffrey. "Watch out for discontinuous integrals."
Computer Algebra in Education, edited by Michael J. Wester and Michel
Beaudin, Aulonna Press, White Lake. ISBN 9780975454196. pp. 7180, 2008.
X. Li, M. Moreno Maza, W. Pan.
Computations Modulo Regular Chains
Proceedings of ISSAC 2009, ACM Press, pages 239246, 2009.
S. MacLean, D. Tausky, G. Labahn, E. Lank and M. Marzouk.
"Tools for the efficient generation of handdrawn corpora based on contextfree grammars."
Proceedings of the Eurographics Symposium on SketchBased Interfaces and Modeling (SBIM 2009). 125132, 2009.
Michael Monagan and Roman Pearce.
Parallel Sparse Polyomial Multiplication using Heaps.
Proceedings of ISSAC '09, ACM Press, 263269, 2009.
Michael Monagan and Paul Vrbik.
Lazy and Forgetful Polynomial Arithmetic and Applications.
Proceedings of CASC '09, Springer Verlag, LNCS 5743 226239, 2009.
M. Moreno Maza and Y. Xie.
Balanced Dense Polynomial Multiplication on Multicores
Proceedings of Parallel and Distributed Computing, Applications and
Technologies (PDCAT), IEEE Press, 9 pages, 2009.
Amit Regmi and Stephen M. Watt.
"A Collaborative Interface for Multimodal Ink and Audio Documents,"
Proc. 10th International Conference on Document Analysis and Recognition,
(ICDAR 2009), IEEE Computer Society, pp. 901905, 2009.
A.D. Rich, D.J. Jeffrey: "A knowledge repository for indefinite
integration based on transformation rules." Proceedings of MKM 2009,
SpringerVerlag LNAI 5625, 480485, 2009.
Daniel S. Roche. "Space and TimeEfficient Polynomial Multiplication."
Proceedings of ISSAC '09, ACM Press, pp 295302, 2009.
Alan P. Sexton, Volker Sorge and Stephen M. Watt.
"Computing with Abstract Matrix Structures,"
Proceedings of ISSAC '09, ACM Press, pp. 325332, 2009.
Alan P. Sexton, Volker Sorge and Stephen M. Watt.
"Reasoning with Generic Cases in the Arithmetic of Abstract Matrices",
Proc. Conferences on Intelligent Computer Mathematics 2009,
Springer Verlag LNAI 5625, pp. 138153, 2009.
A. Storjohann. "Integer matrix rank certification".
Proceedings of ISSAC '09, ACM Press, pp. 333340, 2009.
Stephen M. Watt.
"Algorithms for the Functional Decomposition of Laurent Polynomials,"
Proc. Conferences on Intelligent Computer Mathematics 2009,
Springer Verlag LNAI 5625, pp. 186200, 2009.
W. Zhou and G. Labahn.
"Efficient Computation of Order Bases",
Proceedings of ISSAC'09, ACM Press, 375382, 2009.

Monographs, books, and book chapters:
Azadeh Alimadad, Peter Borwein, Vahdi Dabbaghian,
Ron Ferguson, Yuri Gusev, Warren Hare, Michael Hayes, Michel Joffres,
Crystal Linkletter, Snezana MitovicMinic, Sandy Rutherford,
Krisztina Vasarhelyi, and Les Vertesi.
Mathematical Modelling in Health Care.
Accepted by the American Mathematical Society, August 2009.
M. Moreno Maza and Y. Xie.
FFTbased Dense Polynomial Arithmetic on Multicores.
To appear in the High Performance Computing Symposium, Edited by Doug Mewhart,
Springer, Lecture Notes in Computer Science, 22 pages, 2009.
Conferences on Intelligent Computer Mathematics 2009:
16th Symposium on the Integration of Symbolic Computation and
Mechanized Reasoning and 8th International Conference on Mathematical
Knowledge Management, Jacques Carette, Lucas Dixon,
Claudio Sacerdoti Coen and Stephen M. Watt (editors),
Springer Verlag LNAI 5625, 2009.

Letters, notes, communications:
Government publications: none

B. Nonrefereed contributions:
1. Papers in nonrefereed conference proceedings: none
2. Theses:
Jonathan AquanAssee,
Boundary Conditions For MeanReverting Square Root Process.
Masters Project, Computational Mathematics, Waterloo, August 2009.
Supervisor: George Labahn.
Curtis Bright,
Vector Rational Number Reconstruction.
Masters Project, Computational Mathematics, Waterloo, August 2009.
Supervisor: Arne Storjohann.
Sophie Burrill
Crossings and nestings in four combinatorial families.
MSc. Thesis, Mathematics, Simon Fraser University, July 2009.
Supervisor: Marni Mishna
Muhummad Chowdhury,
Homotopy techniques for multiplication modulo triangular sets.
Masters Thesis, Computer Science, Western, April 2009.
Supervisor: Éric Schost
Michael Coons,
Multiplicative Functions.
PhD. Thesis, Mathematics, Simon Fraser University, August 2009.
Supervisor: Peter Borwein
Hui Ding,
Computation of Lambert W in C^{nxn}.
PhD. Thesis, Applied Mathematics, Western, April 2009.
Supervisors: Robert Corless and David Jeffrey.
Ling Ding,
Highperformance code generation for polynomials and power series.
Masters Thesis, Computer Science, Western, April 2009.
Supervisor: Éric Schost
Nazrul Islam,
Optimization Techniques For Matrix Multiplication.
Masters Thesis, Computer Science, Western, April 2009.
Supervisor: Éric Schost
Myung Sub Kim,
Hermite form computation of matrices of differential polynomials.
Masters Thesis, Computer Science, Waterloo, August 2009.
Supervisor: Mark Giesbrecht.
Benoit Lacelle,
Towards an efficient implementation for the resolution of structured linear systems.
Masters Thesis, Computer Science, University of Paris 7, April 2009.
Supervisor: Éric Schost
Xin Li,
Toward Highperformance Polynomial System Solvers Based on Triangular Decompositions.
PhD. Thesis, Computer Science, Western, April 2009.
Supervisor: Marc Moreno Maza, Stephen Watt
Scott Maclean,
Theory and practice in mathematical data corpus creation.
Masters Thesis, Computer Science, Waterloo, September 2009.
Supervisor: George Labahn.
Alan Meichsner,
The Integer Chebyshev Problem.
PhD. Thesis, Mathematics, Simon Fraser University, August 2009.
Supervisor: Peter Borwein
Amit Regmi,
Supporting Multimodal Collaboration with Digital Ink and Audio.
Masters Thesis, Computer Science, Western, February 2009.
Supervisor: Stephen M. Watt
Lisa Theng,
Representation of Calligraphy.
Bachelor's Thesis, Computer Science, Western, April 2009.
Supervisor: Stephen M. Watt
Paul Vrbik,
Delayed Polynomial Arithmetic and Applications.
Masters Thesis, Mathematics, Simon Fraser University, December 2008.
Supervisor: Michael Monagan
Suling Yang,
Computing GCDs of Multivariate Polynomials over Finite Fields.
Masters Project, Mathematics, Simon Fraser University, April 2009.
Supervisor: Michael Monagan

3. Technical and internal reports:
D.H. Bailey and J.M. Borwein.
"PSLQ: an Algorithm to Discover to Integer Relations", Computeralgebra Rundbrief,
October 2009.
Jacques Carette.
A partial evaluator for Maple.
Oleg Golubitsky and Stephen M. Watt.
"TieBreaking for Curve Multiclassifiers",
Ontario Research Centre for Computer Algebra (ORCCA),
University of Western Ontario Research Report TR0902 (8 pages), 2009.
Oleg Golubitsky and Stephen M. Watt,
"Improved Character Recognition through Subclassing and Runoff Elections",
Ontario Research Centre for Computer Algebra (ORCCA),
University of Western Ontario, Research Report TR0901 (9 pages), 2009.
Michael Monagan and Roman Pearce,
Sparse Polynomial Multiplication and Divison in Maple 14.
MITACS project research report, October 2009.

4. Industrial reports: none
C. Specialized Publications
1. Proprietary software packages:
Andrew Arnold.
A sparse powerseries algorithm for computing cyclotomic polynomials.
Integrated by Roman Pearce into Maple 14. July 2009.
Mohammad Ghebleh, Mahdad KhatarinjadFard and Michael Monagan.
Improvements to Maple's GraphTheory package for
planar graph drawing, bipartite matching, and network flows.
Accepted for Maple 14, July 2009
Mahdi Javadi and Michael Monagan. A C library of routines for univariate polynomial arithmetic
(multiplication, division, and gcd) modulo a triangular set modulo a machine prime p.
Integrated into RECDEN for Maple 14, September 2009.
George Labahn..
Indefinite symbolic integration of Ei, Si and Ci.
Integrated by George Labahn. into Maple 13. November 2008.
Roman Pearce.
sdmp: a C library of algorithms for sparse distributed multiplication and
exact division over Z and Zp. Available from http://www.cecm.sfu.ca/~rpearcea.
Package integrated into expand and divide for Maple 14, August 2009.
C. Chen, F. Lemaire, M. Moreno Maza, B. Xia, R. Xiao and Y. Xie.
The SemiAlgebraicSetTools Module of the RegularChains Library.
In Maple 13, Maplesoft, Canada, 2009.
X. Li, M. Moreno Maza and W. Pan.
The Modpn Library
In Maple 13, Maplesoft, Canada, 2009.
X. Li, M. Moreno Maza, W. Pan and Y. Xie.
The FastArithmeticTools Module of the RegularChains Library
In Maple 13, Maplesoft, Canada, 2009.

November 1, 2007  November 1, 2008
A. Refereed Contributions
1. Articles in refereed publications:
Published or accepted for publication:
A. Amiraslani, P. Lancaster and R.M. Corless.
Linearization of Matrix Polynomials Expressed in Polynomial Bases.
IMA J. Numer Anal, 10.1093/imanum/drm051 online April 2008.
D. H. Bailey, J. M. Borwein, D. M. Broadhurst and L. Glasser.
Elliptic integral representation of Bessel moments.
J. Phys. A: Math. Theory, 41 (2008), 52035231.
D. Borwein, J. M. Borwein and O'Yeat Chan.
Functions via ExpArc Integrals,
J. Math. Analalysis and Applications, 341 (2008) 478500.
J. M. Borwein, C. Hamilton.
Symbolic Complex Analysis: Algorithms and Examples.
Mathematical Programming, 116 (2009), 1735.
J. M. Borwein and Bruno Salvy.
A proof of a recursion for Bessel moments.
Experimental Mathematics, 17 (2008) 223230.
Jon Borwein, Neil Calkin and Dante Manna.
Euler and Boole summation revisited.
Accepted November 2007, American Math Monthly, 16 pages.
P. Borwein, T. Erdelyi, R. Ferguson and R. Lockhart.
On the zeros of cosine polynomials: solution of an an old problem of Littlewood.
Annals of Math (2) 167 (2008), no. 3, 11091117.
P. Borwein, E. Kaltofen, and M. Mossinghof.
Irreducible polynomials and Barker sequences.
Accepted Nov. 2007 for Communications in Computer Algebra, ACM Press.
A. Bostan, B. Salvy and É. Schost.
Fast conversion algorithms for orthogonal polynomials.
Accepted 2008 for Linear Algebra and its Applications.
A. Bostan, C.P. Jeannerod, and É. Schost.
Solving structured linear systems with large displacement rank.
In press, Theoretical Computer Science, 2008.
M. Bronstein, R.M. Corless, J.H. Davenport and D.J. Jeffrey.
Algebraic Properties of the Lambert W Function from a result of Rosenlicht and of Liouville.
Integral Transforms and Special Functions 19, 709712, October 2008.
J. Carette and R. Janicki.
Computing properties of numerical imperative programs by symbolic computation.
Fundamenta Informaticae, 80 13 (2007), 125146.
J. Carette and O. Kiselyov.
Multistage programming with Functors and Monads: eliminating abstraction overhead from generic code.
In press, Science of Computer Programming, 2008.
J. Carette and O. Kiselyov and C. Shan.
Finally tagless, partially evaluated.
Accepted for Journal of Functional Programming, 2008
C. Chen, F. Lemaire, M. Moreno Maza, W. Pan and Y. Xie.
On the verification of polynomial system solvers.
Frontiers of Computer Science in China 2(1): 5566 (2008).
R.M. Corless and Silvana Ilie.
Polynomial cost for solving highindex DAE.
BIT Numerical Mathematics (2008) 48 2949.
R.M. Corless, A. Shakoori, D.A. Aruliah, and L. GonzalezVega.
Barycentric Hermite Interpolants for Event Location in InitialValue Problems.
J. Numer. Anal. Indust. Appl. Math. 3, no. 12, pp. 116, 2008.
X. Dahan, X. Jin, M. Moreno Maza and É. Schost.
Change of ordering for regular chains in positive dimension.
Theor. Comput. Sci. 392(13), pp. 3765, 2008.
P. Forsyth and G. Labahn.
Numerical Methods for Controlled HamiltonJacobiBellman PDEs in Finance,
Journal of Computational Finance (2008) 11(2) 144.
M. Giesbrecht, G. Labahn, and WS. Lee.
Symbolicnumeric sparse interpolation of multivariate polynomials.
To appear, J. Symbolic Computation, 2008.
O. Golubitsky, M. Kondratieva, M. Moreno Maza, and A. Ovchinnikov.
A bound for the RosenfeldGroebner algorithm.
J. Symb. Comput., 43 (8) 582610, 2007.
O. Golubitsky, M. Kondratieva and A. Ovchinnikov.
Algebraic transformation of differential characteristic decompositions from one ranking to another.
To appear in J. Symb. Comput., 2008.
O. Golubitsky, M. Kondratieva and A. Ovchinnikov.
Canonical characteristic sets of characterizable differential ideals.
Moscow University Mathematics Bulletin, 63 (2): pp. 7981 (2008).
O. Golubitsky.
Universal characteristic decomposition of radical differential ideals,
J. Symb. Comput., 43 (1): pp. 2745 (2008).
X. Li, M. Moreno Maza and É. Schost.
Fast Arithmetic for triangular sets: from theory to practice.
In press, J. Symbolic Computation, 2008.
S. Liang, D.J. Jeffrey.
"Automatic computation of the travelling wave solutions to nonlinear PDEs."
Computer Physics Communications, Vol 178, issue 9, pp 700712, May 2008.
G. J. Reid and L. Zhi.
Solving polynomial systems via symbolicnumeric reduction to geometric involutive form.
To appear in J. Symbolic Computation.
R. Scott, G. J. Reid and L. Zhi.
Geometric Involutive Bases and Applications to Approximate Commutative Algebra,
Accepted May 2008, RISC Series on Symbolic Computation.
G Soederlind, S. Ilie, and R.M. Corless.
Adaptivity and Computational Complexity in the Numerical Solution of ODEs,
J. Complexity 24 (3) 341361, 2008.
W. Wu, G. J. Reid and S. Ilie.
Implicit Riquier bases for PDAE and their semidiscretizations.
Accepted April 2008, Journal of Symbolic Computation.
W. Zhou and D. Jeffrey.
Fractionfree matrix factors: new forms for LU and QR factors.
Frontiers in Computer Science in China, 2 (1), 6780, 2008.

Submitted for publication:
A. Arnold and M. Monagan.
Computing cyclotomic polynomials of large height.
Submitted October 2008 to Mathematics of Computation.
P. Borwein and Michael Coons.
Transcendence of power series for some number theoretic functions.
Submitted June 2008 to Proceedings of the American Mathematical Society.
J. Carette and Michael Kucera, A Partial Evaluator for Maple.
Submitted 2008 to Science of Computer Programming.
X. Dahan, É. Schost and J. Wu.
Evaluation properties of invariant polynomials.
Submitted 2008.
M. Giesbrecht and D. Roche.
Interpolation of ShiftedLacunary Polynomials.
Submitted to J. Computational Complexity
S. Liang and D. J. Jeffrey.
An algorithm for computing the complete root classification of a parametric polynomial.
Submitted 2008 to J. Symbolic Computation.
M. Monagan and R. Pearce.
Sparse Polynomial Division Using a Heap.
Submitted September 2008 to the J. Symb. Comp. special issue on
on Milestones in Computer Algebra.
L. Chen and M. Monagan.
Algorithms for Solving Linear Systems over Cyclotomic Fields.
Submitted February 2008 to the J. Symbolic Computation.


2. Other refereed contributions:
Papers in refereed conference proceedings:
D.H. Bailey and J.M. Borwein.
High Precision Numerical Integration: Progress and Challenges.
Electronic proceedings of MICA '08, 2008.
A. Bostan, B. Salvy and É. Schost.
Power Series Composition and Change of Basis,
Proc. of ISSAC '08, ACM Press, 269276, 2008.
J. Carette, W. Farmer.
High Level Theories.
Proc. Calculemus '08, 2008.
J. Carette, S. Smith, J. McCutchan, C. Anand, and A. Korobkine.
Case Studies in Model Manipulation for Scientific Computing.
Proc. AISC '08, 2008.
C. Chen, F. Lemaire, L. Li, M. Moreno Maza, W. Pan and Y. Xie.
The ConstructibleSetTools and ParametricSystemsTools modules of the RegularChains library in Maple,
Proc. of the International Conference on Computational Science and Applications,
IEEE Computer Society, pp. 342352, 2008.
C. Chen, L. Li, M. Moreno Maza, W. Pan and Y. Xie.
On the representation of constructible sets.
Proc. of Milestones in Computer Algebra, pp. 7260, 2008.
P. Davies, H. Cheng, G. Labahn.
Computing Popov Form of General Ore Polynomial Matrices.
Electronic proceedings of MICA '08, pp. 149156, 2008.
M. Giesbrecht and D. Roche.
On Lacunary Polynomial Perfect Powers.
Proceedings of ISSAC '08, ACM Press, pp. 103110, 2008.
M. Giesbrecht and D. Roche.
Interpolation of ShiftedLacunary Polynomials.
Mathematical Aspects of Computer and Information Sciences, December 2007.
O. Golubitsky and S.M. Watt.
Online Stroke Modeling for Handwriting Recognition.
Proceedings of the 18th Annual International Conference on Computer Science and
Software Engineering (CASCON 2008), IBM Canada, ISSN 17057345, pp. 7280, October 2008.
L. GonzalezVega, R.M. Corless, J. Butcher, D.A. Arulia and A. Shakoori.
Barycentric Birkhoff Interpolation,
Electronic proceedings of MICA '08, 2008.
B. Keshari and S.M. Watt.
Online Mathematical Symbol Recognition using SVMs with Features from Functional Approximation.
Proc. Mathematical UserInterfaces Workshop (MathUI 08), July 2008.
X. Li, M. Moreno Maza, R. Rasheed and É. Schost.
The Modpn library: Bringing Fast Polynomial Arithmetic into Maple.
Proceedings of MICA '08, pp. 103108, 2008.
X. Li, M. Moreno Maza, R. Rasheed and É. Schost,
HighPerformance Symbolic Computation in a Hybrid CompiledInterpreted Program.ing Environment.
International Conference on Computational Sciences and Its Applications,
IEEE Computer Soc., pp. 331341, 2008.
F. Lemaire, M. Moreno Maza, W. Pan and Y. Xie.
When does (T) equal Sat(T) ?
Proc. ISSAC '08, ACM Press, pp. 207214, 2008.
S. Liang, D. J. Jeffrey and M. Moreno Maza.
The complete root classification of a parametric polynomial on an interval.
Proceedings of ISSAC 2008, ACM Press, pp. 189196, 2008.
S. Liang and D. J. Jeffrey.
Unconstrained parametric minimization of a polynomial: approximate and exact.
Proceedings of the 2007 Asian Symposium on Computing and Mathematics,
Springer Verlag LNAI, 5081, pp. 2231, 2007.
A.P. Sexton, V. Sorge, and S.M. Watt.
Abstract Matrix Arithmetic.
Proc. 10th International Symposium on Symbolic and Numeric Algorithms for
Scientific Computing, (SYNASC 2008), September, 2008.
S.M. Watt.
Functional Decomposition of Symbolic Polynomials.
Proc. International Conference on Computatioanl Sciences and its Applications
(ICCSA 2008), July 3 2008, IEEE Computer Society, pp. 353362.
S.M. Watt.
Symbolic Polynomials with Sparse Exponents.
Proceedings of MICA '08, pp. 9197, May 2008.

Monographs, books, and book chapters:
D.H. Bailey and J.M. Borwein.
Experimental Discovery and Proof of Identities, pp. 2152 in
Tappas in Experimental Mathematics, Contemporary Matematics, 457, 2008.
J.M. Borwein and D.H. Bailey.
The Computer as Crucible: an Introduction to Experimental Mathematics.
A.K. Peters, November 2008.
J.M. Borwein and D.H. Bailey.
Mathematics by Experiment: Plausible Reasoning in the 21st Century.
A.K. Peters, second edition, September 2008.
J. Borwein, V. Jungic, D. Langstroth, M. Macklem and S. Wilson.
The Coast to Coast Seminar, in Communicating Mathematics in the Digital Era,
A.K. Peters, October 2008.
P. Borwein, S. Choi, B. Rooney and A. Weirathmueller.
The Riemann Hypothesis, Springer Verlag, to appear, 2008.
D.J. Jeffrey and R.M. Corless.
Chapter 72 Linear Algebra in Maple in Handbook of Linear Algebra,
Leslie Hogben ed., CRC, 2007.
M. Moreno Maza, G.J. Reid, R. Scott, W. Wu.
On Approximate Linearized Triangular Decompositions.
In SymbolicNumeric Computation, edited by Dongming Wang and Lihong Zhi,
Birkhauser, pp. 279298, 2007.
M. Moreno Maza and S.M. Watt editors.
Proceedings of Milestones in Computer Algebra MICA 2008:
A conference in honour of Keith Geddes' 60th birthday
ISBN 9781595937445, 2008.

Letters, notes, communications: none
Government publications: none

B. Nonrefereed contributions:
1. Papers in nonrefereed conference proceedings: none
2. Theses:
Ksenija Garaschuk, On Binary and Ternary Kloosterman Sums.
MSc. Thesis, Mathematics, Simon Fraser University, November 2007.
Supervisor: P. Lisonek
Birendra Keshari,
Techniques for Transformation and Exchange of Standardized Digital Ink.
M.Sc. Thesis, Computer Science, University of Western Ontario, April 2008.
Supervisor: S.M. Watt
Mahdad KhatarinjardFard, Regular Structures of Lines in Complex Spaces.
Ph.D. Thesis, Mathematics, Simon Fraser University, October 2008.
Supervisor: P. Lisonek
Mathew Malenfant,
A Comparison of Two Families of Algorithms for Symbolic Polynomials.
M.Sc. Thesis, Computer Science, University of Western Ontario, December 2007.
Supervisor: S.M. Watt
Azar Shakoori, Bivariate Polynomial Solver by Values.
Ph.D. Thesis, Applied Mathematics, University of Western Ontario, December 2007.
Supervisor: R.M. Corless
Xiang (Sophy) Wang, Generating Numerical Evaluation Routines for Bivariate
Routines for Bivariate Functions via Tensor Product Series.
M.Math Thesis, School of Computer Science, University of Waterloo, September 2008.
Supervisor: K.O. Geddes

3. Technical and internal reports:
Peter Borwein, Kevin G. Hare and Alan Meichsner.
Reverse Symbolic Computations, The identify Function.
MITACS project research report, July 2008.
M. Javadi and M. Monagan.
Computing Polynomial Greatest Common Divisors over Algebraic Number and Function Fields.
MITACS project research report, August 2008.
M. Monagan and R. Pearce.
Polynomial Multiplication and Division using a Heap
MITACS project research report, September 2008.
C. Pernet and A. Storjohann.
Frobenius form in expected matrix multiplication time over sufficiently large fields.
November 30, 2007, 27pp.
A. Storjohann.
On the complexity of inverting integer and polynomial matrices. July 22, 2008, 24 pp.
W. Wu, G. Reid and O. Golubitsky.
Towards geometric completion of differential systems by points.
Research Institute for Symbolic Computation (RISC) Series, 2008.

4. Industrial reports: none
C. Specialized Publications
1. Proprietary software packages:
J. Borwein,
Continual upgrading of the inverse symbolic calculator at
http://ddrive.cs.dal.ca/~isc
which now has a stable python based multithreaded version at Dalhousie.
C. Chen, F. Lemaire, M. Moreno Maza, W. Pan, B. Xia, and Y. Xie.
The SemiAlgebraicSetTools module of the RegularChains library in Maple.
Together with the command ParametricSystemTools:RealRootClassification,
it amounts to 25,000 lines of Maple code (Submitted to Maple).
This provides a variety of tools for studying the real solutions
of polynomial systems, including real root isloation and acounting,
partial cylindrical decomposition, real root classification.
Most of the underlying algorithms are new and remain to be published.
M. Ghebleh, M. Monagan and A. Wittkopf,
Additions to Maple's GraphTheory package including
a graph isomorphism test, a routine for generating nonisomorphic
graphs, etc. Integrated into Maple 13, August 2008.
M. Javadi and M. Monagan,
A new sparse modular GCD algorithm for computing GCDs of multivariate
polynomials over algebraic functions fields given by multiple field
extensions. Submitted to Maple 13, August 2008.
G. Labahn,
Maple code for the integration of expressions involving the Ci, Si, erf, Fresnel C and S functions.
Submitted to Maple 13, August 2008.
X. Li and M. Moreno Maza (developers) and É. Schost and W. Pan (contributors).
The Modpn library. Submitted to Maple 13.
Modpn is a C and Maple library dedicated to fast arithmetic for
multivariate polynomials modulo a prime.
Modpn amounts to 35,000 lines of C code and 10,000 lines of Maple code.
X. Li and M. Moreno Maza.
The FastArithmeticTools module of the RegularChains library in Maple.
5,000 lines of Maple code. Submitted to Maple 13.
This package provides modular methods, with fast arithmetic support
from he Modpn library, for the core operations of the RegularChains library.
The current version works in prime characteristic only.
The characteristic zero case is work in progress for the next release.
M. Monagan and R. Pearce,
A C implemementation of algorithms for multiplication and division
of polynomials over the integers modulo n using chained heaps.
Integrated into Maple 13, August 2008.
M. Monagan
A modular algorithm for solving Ax=b over cyclotomic fields.
Integrated into Maple 13, August 2008.
C. Pernet.
fflasffpack: a new inplace reduction to matrix multiplication for the computation of
an inverse of a square matrix over a finite field. Implemented and included in the
LinBox library by C, December 2007.

November 1, 2006  November 1, 2007
A. Refereed Contributions
1. Articles in refereed publications:
Published or accepted for publication:
A. Amiraslani, D. Aruliah, R. Corless.
Block LU Factors of Generalized Companion Matrix Pencils,
Theoretical Computer Science, accepted June 2007.
D.H. Bailey and J. M. Borwein.
Experimental Discovery and Proof of Identities.
Accepted for Contemporary Mathematics, November, 2007.
B. Beckermann, H. Cheng and G. Labahn.
Fractionfree Row Reduction of Matrices of Ore Polynomials, Journal of Symbolic Computation
41(5) (2006) 513543.
B. Beckermann, G. Golub and G. Labahn.
On the numerical condition of a generalized Hankel eigenvalue problem,
Numerische Mathematik 106(1) (2007) 4168
B. Beckermann, G. Labahn and G. Villard.
Normal Forms for General Polynomial Matrices,
Journal of Symbolic Computation, 41(6) (2006) 708737.
J. M. Borwein and C. Hamilton.
Symbolic Convex Analysis: Algorithms and Examples.
In press, Auslander Special Volume of Mathematical Programming, 2007.
P. Borwein and S. Choi.
The average norm of polynomials of fixed height,
Trans. Amer. Math. Soc. 359 (2007), no. 2, 923936.
P. Borwein, S. Choi, I. Mercer.
Expected norms of zeroone polynomials,
Canad. Math. Bull. (Accepted Feb 2007)
P. Borwein, S. Choi, B. Rooney and A. Weirathmueller.
The Riemann Hypothesis, SpringerVerlag, New York, to appear 2007.
P. Borwein, E. Dobrowolski and M. Mossinghoff.
,
Annals of Math, 166, (2007), no. 2, 347366
P. Borwein and T. Erdélyi.
On the zeros of polynomials with coefficients from a finite set : a question of Littlewood,
Acta Arithemica. 128 (2007), no. 4, 377384.
P. Borwein, T. Erdélyi, R. Ferguson and R. Lockhart.
On the zeros of cosine polynomials: solution of an an old problem of Littlewood,
Annals of Math, (Accepted Mar. 2007).
P. Borwein, G. Fee, R. Ferguson and A. van der Waall.
Zeros of partial sums of the Riemann zetafunction,
Experiment. Math. 16 (2007), no. 1, 2139.
P. Borwein, R. Ferguson and J. Knauer.
The merit factor problem (Bristol: Accepted Jan. 2007).
P. Borwein, R. Ferguson and M. Mossinghoff.
Sign changes in sums of the Liouville Lambda Function,
Math. Comp. (Accepted Jan. 2007).
P. Borwein and M. Mossinghoff.
Barker sequences and flat polynomials,
(Bristol: Accepted Jan. 2007).
P. Borwein, M. Mossinghoff and J. Vaaler.
The L_{1} norm of polynomials,
Proc. Amer. Math. Soc. 135 (2007), no. 1, 253261.
A. Bostan, P. Gaudry, É. Schost.
Linear Recurrences with Polynomial Coefficients and Application to Integer Factorization and CartierManin Operator
SIAM J. Comput., 36 (2007) no. 6 17771806.
A. Bostan, F. Morain, B. Salvy, É. Schost.
Fast algorithms for computing isogenies between elliptic curves,
Mathematics of Computation, to appear.
M. Bronstein, R. Corless, J. H. Davenport, D. Jeffrey.
Algebraic Properties of the Lambert W Function,
Integral Transforms and Special Functions, accepted May 2006.
H. Cheng and G. Labahn.
Outputsensitive Modular Algorithms for Polynomial Matrix Normal Forms,
Journal of Symbolic Computation,42(7) (2007) 733750.
R. Corless, N. Rezvani, A. Amiraslani.
Pseudospectra of matrix polynomials expressed in alternative bases,
Mathematics and Computer Science, Accepted June 2007.
X. Dahan, X. Jin, M. Moreno Maza, É. Schost.
Change of order for regular chains in positive dimension.
To appear in Theoretical Computer Science, 2007.
G. C. Essex, S. Ilie, R. Corless.
Broken Symmetry and LongTerm Forecasting,
Journal of Geophysical Research  Atmospheres, accepted July 2007.
J.B. Farr and P. Lisonek.
Large caps with free pairs in dimensions five and six. Innovations in Incidence Geometry 4 (2006), 6988.
P. Forsyth and G. Labahn.
Numerical Methods for Controlled HamiltonJacobiBellman PDEs in Finance,
To appear in Journal of Computational Finance (2007) 44 pages.
M. Ghebleh and M. Khatirinejad.
Planarity of iterated line graphs. Discrete Mathematics. 5 pages (to appear, 2006).
O. Golubitsky.
Universal characteristic decomposition of radical differential ideals,
Journal of Symbolic Computation (2007, accepted).
O. Golubitsky, M. Kondratieva, A. Ovchinnikov.
Canonical characteristic sets of characterizable differential ideals,
Moscow University Mathematics Bulletin (2008, to appear)
M. Khatirinejad.
On WeylHeisenberg orbits of equiangular lines. Journal of Algebraic Combinatorics. 21 pages (to appear, 2007).
M. Khatirinejad and P. Lisonek.
Linear codes for high payload steganography. Discrete Applied Mathematics. 17 pages (accepted subject to revisions, May 2007)
I.G. Lisle, G.J. Reid.
Symmetry classification using invariant differential operators,
Foundations of Computational Mathematics (2006), 353386.
S. Lo, M. Monagan, A. Wittkopf.
Strongly Connected Graph Components and Computing Characteristic Polynomials of Integer Matrices in Maple.
Accepted March 2007 for Communications in Computer Algebra.
M. Mishna.
Automatic enumeration of regular objects,
Journal of Integer Sequences, Vol. 10 (2007), Article 07.5.5
M. Mishna.
Kronecker product identities from Dfinite symmetric functions,
Accepted by Séminaire Lotharingien de Combinatoire.
M. Moreno Maza, G. J. Reid, R. Scott and W. Wu.
On Approximate Triangular Decompositions in Dimension Zero,
Journal of Symbolic Computation. 42(7), (2007) 693716.
G. Söderlind, S. Ilie, R. Corless.
Adaptivity and Computational Complexity in the Numerical Solution of ODEs,
J. Complexity accepted September 2007.
J. Zhao, M. Davison, R. Corless.
Compact finite difference method for American option pricing,
Journal of Compuational and Applied Mathematics, Volume 206, pp. 306321 (2007).

Submitted for publication:
A. Bostan, C.P. Jeannerod, É. Schost.
Solving structured linear systems with large displacement rank. Submitted 2007.
M. Coons and P. Vrbik,
On the density of integers birepresentable as the sum of two cubes.
Submitted to the Journal of Experimental Mathematics.
J.G. Dumas, C. Pernet, and W. Zhou.
Memory efficient scheduling of StrassenWinograd's matrix multiplication algorithm, Submitted to SIAM Journal of Matrix Analysis, September 2007.
M. Giesbrecht, G. Labahn and Ws Lee.
Symbolicnumeric Sparse Interpolation of Multivariate Polynomials,
Submitted to Journal of Symbolic Computation (2007)
S. Ilie, R. Corless, G. C. Essex.
The computational complexity of extrapolation methods,
submitted October 2006.


2. Other refereed contributions:
Papers in refereed conference proceedings:
D. A. Aruliah, R. Corless, L. GonzalezVega and A. Shakoori.
Geometric applications of the Bezout matrix in the Lagrange basis,
Proceedings of the 2007 international workshop on Symbolicnumeric computation (SNC '07),
pp. 5564. ACM 2007.
D. A. Aruliah, R. Corless, A. Shakoori, L. GonzalezVega and I. F. Rua.
Computing the topology of a real algebraic plane curve whose equation is not directly available,
Proceedings of the 2007 international workshop on Symbolicnumeric computation (SNC '07),
pp. 4654. ACM 2007.
T. Ashby, A. Kennedy and S. Watt
Generation and Optimization of Code using Coxeter Lattice Paths (Invited),
pp. 110, Proc. Parallel Symbolic Computation (PASCO'07),
July 2728 2007, Waterloo, Canada, ACM Press.
A. Bostan, F. Chyzak, G. Lecerf, B. Salvy, É. Schost.
Differential equations for algebraic functions,
In ISSAC'07, pages 2532. ACM Press, 2007.
A. Bostan, F. Chyzak, F. Ollivier, B. Salvy, É. Schost, A. Sedoglavic.
Fast computation of power series solutions of systems of differential equations,
In SODA'07, pages 2007 10121021. ACM Press, 2007.
A. Bostan, C.P. Jeannerod, É. Schost.
Solving Toeplitz and Vandermondelike linear systems with large displacement rank,
In ISSAC'07, pages 3340. ACM Press, 2007.
F. Boulier, C. Chen, O. Golubitsky, F. Lemaire, M. Moreno Maza, and W. Pan.
Comprehensive Triangular Decomposition,
Proc. 10th International Workshop on Computer Algebra in Scientific Computing (CASC),
Bonn, Germany. Lecture Notes in Computer Science, vol. 4770, pp. 73101 (2007).
M. Bronstein, M. Moreno Maza and S. Watt.
Generic Programming Techniques in Aldor,
Proc. Fifth Asian Workshop on Foundations of Software, (AWFS),
June 13 2007, Xiamen, China, (accepted).
C. Chen, F. Lemaire, M. Moreno Maza, W. Pan and Y. Xie.
Efficient Computations of Irredundant Triangular Decompositions with the RegularChains Library.
In proc. Computer Algebra Systems and Their Applications (ICCS'07),
SpringerVerlag LNCS 4488, pp. 268271, 2007.
C. Chen, M. Moreno Maza, W. Pan and Y. Xie.
On the verification of polynomial system solvers.
In proc. of the Fifth Asian Workshop on Foundations of Software,
pages 116144, University of Xiamen, China, 2007.
C. Chen, F. Lemaire, O. Golubitsky, M. Moreno Maza, and W. Pan..
Comprehensive Triangular Decomposition.
Proc. of Computer Algebra in Scientific Computing 2007 (CASC '07).
SpringerVerlag LNCS 4770, pp. 73101, 2007.
H. Cheng and G. Labahn.
Modular Computation for Matrices of Ore Polynomials,
Proceedings of WSPC (In Honor of 60th birthday of Sergei Abramov),
4366 (2007)
H. Cheng, G. Hanrot, E. Thomé, E. Zima, P. Zimmermann.
Time and SpaceEfficient Evaluation of Some Hypergeometric Constants.
Proceedings of ISSAC '07, pages 8591, 2007.
Y. Chicha and S. Watt.
A Localized Tracing Scheme applied to Garbage Collection,
pp. 323339, Proc. The Fourth Asian Symposium on Programming Languages and Systems, (APLAS 2006),
November 810 2006, Sydney, Australia, Springer Verlag LNCS 4279.
R. M. Corless and D. Assefa.
JefferyHamel flow with maple: a case study of integration of elliptic functions in a CAS,
Proceedings of ISSAC '07, ACM Press, pp. 108115, July 2007.
R. M. Corless, H. Ding, D. J. Jeffrey and N. J. Higham.
The solution of S exp(S) = A is not always the Lambert W function of A,
Proceedings of ISSAC '07, ACM Press, pp. 116121, July 2007.
R. M. Corless and N. Rezvani.
The nearest polynomial of lower degree,
SNC '07: Proceedings of the 2007 international workshop on Symbolicnumeric computation,
pp. 199200, ACM 2007.
W. Eberly, M. Giesbrecht, P. Giorgi, A. Storjohann and G. Villard.
Faster inversion and other black box matrix computations using efficient block projections.
ACM International Symposium on Symbolic and Algebraic
Computation (ISSAC), pp. 143150, 2007.
O. Golubitsky, M. Kondratieva, M. Moreno Maza and A. Ovchinnikov.
Bounds and algebraic algorithms in differential algebra: the ordinary case.
In Proc. of the 9th International Conf. on Intelligent Systems and Computer Science,
pp. 711, 2006.
M. Javadi and M. Monagan.
A Sparse Modular GCD Algorithm for Polynomial GCD Computation over Algebraic Function Fields.
Proceedings of ISSAC '07, ACM Press, pp. 187194, July 2007.
F Lemaire, M. Moreno Maza and Y. Xie.
Making a Sophisticated Symbolic Solver Available to Different Communities of Users.
In the Proceedings of the Asian Technology Conference in Mathematics (ATCM '06)
Polytechnic University of Hong Kong, December 2006.
X. Li, M. Moreno Maza, É. Schost.
Fast arithmetic for triangular sets: from theory to practice,
In ISSAC'07, pages 269276. ACM Press, 2007.
X. Li, M. Moreno Maza, É. Schost.
On the virtues of generic programming for symbolic computation.
In ICCS'07, pages 251258 of SpringerVerlag LNCS 4488, 2007.
X. Li, M. Moreno Maza.
Multithreaded parallel implementation of arithmetic operations modulo a triangular set.
Proc. Parallel Symbolic Computation '07 (PASCO'07), ACM Press, pp. 5359, 2007.
S.Liang, D.J. Jeffrey.
Rulebased simplification in vectorproduct spaces,
Calculemus 2007, LNAI 4573, pp 116127, Springer 2007.
M. Malenfant and S. Watt
Sparse Exponents in Symbolic Polynomials,
Proc. Symposium on Algebraic Geometry and Its Applications:
in honor of the 60th birthday of Gilles Lachaud, (SAGA 2007),
May 711 2007, Papeete, Tahiti.
P. Mihailescu, F. Morain, É. Schost.
Computing the eigenvalue in the SchoofElkiesAtkin algorithm using Abelian lifts,
In ISSAC'07, pages 285292. ACM Press, 2007.
M. Monagan and R. Pearce.
Polynomial Division using Dynamic Arrays, Heaps, and Packed Exponent Vectors.
Proceedings of Computer Algebra in Scientific Computing (CASC '07),
SpringerVerlag LNCS 4770, pp. 295315, 2007.
M. Moreno Maza, G. J. Reid, R. Scott and W. Wu.
On Approximate Linearized Triangular Decompositions,
In SymbolicNumeric Computation, edited by Dongming Wang and Lihong Zhi,
(Birkhauser, Basel, Boston) 2006, in press.
M. Moreno Maza and Y. Xie.
Componentlevel parallelization of triangular decomposition.
Proc. Parallel Symbolic Computation '07 (PASCO'07), ACM Press, pp. 6977, 2007.
M. Moreno Maza, B. Stephenson, S. Watt and Y. Xie
Multiprocessed Parallelism Support in ALDOR on SMPs and Multicores,
pp. 6068, Proc. Parallel Symbolic Computation, (PASCO'07),
July 2728 2007, Waterloo, Canada, ACM Press.
Z. Olesh and A. Storjohann.
The vector rational function reconstruction problem,
Proceedings of the Waterloo Workshop on Computer Algebra:
devoted to the 60th birthday of Sergei Abramov (WWCA), World Scientific, 2007, pp. 137149.
C. Pernet and A. Storjohann.
Faster algorithms for the characteristic polynomial,
In ISSAC'07, 8pp. ACM Press, 2007.
J. Selby, F. Ruffell, M. Giesbrecht and M. Godfrey,
Recovering maintainability effort in the presence of global
data usage. 14th Working Conference on Reverse Engineering
(WCRE), to appear, October 2007.
D. Tausky, G. Labahn, E. Lank and M. Marzouk.
Managing Ambiguity in Mathematical Matrices,
Proc. of Eurographics Workshop on SketchBased Interfaces and Modelling.
S. Watt.
Two Families of Algorithms for Symbolic Polynomials.
pp. 193210, in Computer Algebra 2006: Latest Advances in Symbolic Algorithms 
Proceedings of the Waterloo Workshop I. Kotsireas, E. Zima (editors) , World Scientific 2007.
S. Watt.
What Happened to Languages for Symbolic Mathematical Computation?,
pp. 8190, Proc. Programming Languages for Mechanized Mathematics, (PLMMS),
June 2930 2007, Hagenberg, Austria, J. Carette and F. Wiedijk (editors), RISCLinz.
G. Wozniak, M. Daley and S. Watt.
Dynamic ADTs: a "Don't Ask, Don't Tell" Policy for Data Abstraction,
pp. 209220, Proc. International Lisp Conference, (ILC),
April 14 2007, Cambridge UK, Association of Lisp Users.
W. Wu and G. Reid.
Symbolicnumeric Computation of Implicit Riquier Bases for PDE,
In ISSAC'07, pages 377386. ACM Press, 2007.
W. Zhou, D. J. Jeffrey.
Completely Fraction Free matrix factorization and Applications,
Proceedings of the Fifth Asian Workshop on Foundations of Software, 160164, 2007.
W. Zhou, D. J. Jeffrey, G. J. Reid.
Symbolic computation sequences and numerical analytic geometry applied to multibody dynamical systems,
SymbolicNumeric Computation, 335347, Birkhauser Verlag Basel / Switzerland, 2007.

Monographs, books, and book chapters:
M. Moreno Maza and S. Watt (editors).
Proceedings of the 2007 International Workshop on Parallel Numeric Computation (PASCO'07),
ACM Press New York, 2007, ISBN 9781595937414.
J. Verschelde and S. Watt (editors).
Proceedings of the 2007 International Workshop on SymbolicNumeric Computation (SNC'07),
ACM Press New York, 2007, ISBN 9781595937445.

Letters, notes, communications: none
Government publications: none

B. Nonrefereed contributions:
1. Papers in nonrefereed conference proceedings:
A. Arnold.
Generating Random Fullerenes.
Mitacs industrial math summer school report, August 17th, 2007.
M. Khatirinejad.
Extended Abstract and Poster: Equiangular lines in complex spaces and their application in quantum information theory.
Presented at the Combinatorics & Optimization at 40 Conference 2007 (International conference).

2. Theses:
J. Chen, Generating Numerical Evaluation Routines for Bivariate
Functions via Tensor Product Series.
M.Math research paper, School of Computer Science, University of Waterloo, May 2007.
Supervisor: K.O. Geddes
Liang Chen, Solving Linear Systems over Cyclotomic Fields.
MSc. Thesis, School of Computing Science, Simon Fraser University, August 7th, 2007.
Supervisor: M. Monagan
Laurentiu Dragon,
On Measuring and Optimizing the Performance of Parametric Polymorphism.
PhD Thesis, Dept. of Computer Science, University of Western Ontario, September 4th, 2007.
Supervisor: S. Watt.
Mahdi Javadi, A Sparse Modular GCD Algorithm for Polynomials
over Algebraic Function Fields.
MSc. Thesis, School of Computing Science, Simon Fraser University, November 22nd, 2006.
Supervisor: M. Monagan
M.J. Hinek, On the security of some variants of RSA.
Ph.D. Thesis, School of Computer Science, University of Waterloo, May 2007.
Supervisors: M. Giesbrecht, D. Stinson
C. Li, Compression of Polynomial Matrices.
M. Math Thesis, School of Computer Science, University of Waterloo, May 2007.
Supervisors: M. Giesbrecht, A. Storjohann
Raqueeb Rasheed, Modular Methods for Solving Polynomual Systems.
MSc. Thesis, Dept. of Computer Science, University of Western Ontario,
August 23rd, 2007. Supervisor: M. Moreno Maza.
Wenyuan Wu, Geometric SymbolicNumeric Methods for Differential
and Algebraic Systems. Ph.D. Thesis,
Dept. of Applied Mathematics, University of Western Ontario, August 2007.
Supervisor: G. Reid
Yuzhen Xie, Fast Algorithms, Modular Methods, Parallel Approaches
and Software Engineering for Solving Polynomial Systems Symbolically.
Ph.D. Thesis, Dept. of Computer Science, University of Western Ontario,
September 4th, 2007. Supervisors: M. Moreno Maza, S. Watt.
Wengin Zhou, Symbolic Computation Techniques for Solving
Large Expression Problems from Mathematics and Engineering.
Ph.D. Thesis, Dept. of Applied Mathematics, University of Western Ontario,
April, 2007. Supervisors: D. Jeffrey and G. Reid.

3. Technical and internal reports:
4. Industrial reports: none
C. Specialized Publications
1. Proprietary software packages:
C. Chen, M. Moreno Maza, W. Pan, Y. Xie.
The ComprehensiveTriangularDecomposition module is a package for
decomposing a triangular set with parameters over a field into irreducible
components where each component has the same geometry for different
values of the parameters. October 2007.
C. Chen, F. Lemaire, L. Li, M. Moreno Maza, W. Pan, Y. Xie.
The ConstructibleSetTools module of the RegularChains library in Maple 12.
This package provides an extensive set of commands to compute
with constructible sets, parametric or not, in characteristic zero or not.
In particular, it provides an algorithmic realization of
Chevalley's Theorem: the image (or preimage) of a constructible set
by a rational map is alse a constructible set.
C. Chen, F. Lemaire, L. Li, M. Moreno Maza, W. Pan, Y. Xie.
The ParametricSystemTools module of the RegularChains library in Maple 12.
This package provides an implementation of Comprehensive Triangular Decomposition a parametric constructible set.
As an application, the command ComplexRootClassification determines the possible numbers of
(complex) solutions of an input parametric system together with the correspoding conditions on the parameters.
C. Chen, F. Lemaire, L. Li, M. Moreno Maza, W. Pan, Y. Xie.
LinBox. LinBox is a C++ template library for exact,
highperformance linear algebra computation with dense, sparse,
and structured matrices over the integers and over finite fields.
Release of LinBox 1.1.4 (October 27, 2007)
Release of LinBox 1.1 (January 31, 2007)
G. Fee, V. DhabbigianAbdoly, and M. Monagan.
FiniteGroups, a Maple package. Includes a database of all small finite groups.
L. Chen and M. Monagan.
A modular algorithm for solving linear systems over cyclotomic fields.
C. Percival, P. Borwein, M. Monagan.
A GMP implementation of a self initializing quadratic sieve integer factorization algorithm for Maple.
N. Rezvani
NPGZ  Nearest Polynomial with a Given Zero (including "lower degree") in the SNAP package.

November 1, 2005  November 1, 2006
A. Refereed Contributions
1. Articles in refereed publications:
Published or accepted for publication:
S. Abramov, H. Q. Le, Z. Li.
Univariate Ore polynomial rings in Computer Algebra.
Journal of Mathematical Sciences 131(5), (2005), pp. 58855903.
B. Beckermann, G. Labahn and G. Villard.
Normal Forms for General Polynomial Matrices.
Journal of Symbolic Computation, 41(6) (2006) 708737.
B. Beckermann, H. Cheng, G. Labahn.
Fractionfree Row Reduction of Matrices of Ore Polynomials.
Journal of Symbolic Computation 41(5) (2006) 513543.
J. Borwein, C. Hamilton.
Symbolic Convex Analysis: Algorithms and Examples.
Auslander Special Volume of Mathematical Programming, accepted April 2006.
P. Borwein, S. Choi and F. Chu.
An old conjecture of ErdosTuran on additive bases.
Math Comp. 75(253) (2006) 475484.
P. Borwein, E. Dobrowolski and M. Mossinghoff.
Lehmer's problem for polynomials with odd coefficients.
Annals of Math, (accepted October 2006). 166, (2007), no. 1.
R. Brent, C. Percival, and P. Zimmermann.
Error bounds on complex floatingpoint multiplication.
To appear in Math Comp.
M. Bronstein, R. Corless, J. Davenport, and D. Jeffrey.
Alebraic Properties of the Lambert W Function.
Accepted May 2006 for Integral Transforms and Special Functions.
H. Cheng and G. Labahn.
Outputsensitive Modular Algorithms for Polynomial Matrix Normal Forms.
To appear in the Journal of Symbolic Computation (25 pages).
V. Dabbaghian.
On constructing representations of the symmetric groups",
Bull. Korean Math. Soc. 43 (2006), 119  123.
V. Dabbaghian.
Constructing representations of higher degrees of finite simple groups and covers.
To appear in Math. Comp. (2006), (8 pages).
V. Dabbaghian.
Characters of some finite groups of Lie type with a restriction containing a linear character once.
Accepted for the Journal of Algebra (19 pages).
S. Ilie, R. Corless and G. Reid.
The numerical solution of index1 differential algebraic equations is of polynomial cost
in the number of bits requested.
Numerical Algorithms 41, (2006) 161171.
I. Lisle and G. Reid.
Symmetry classification using invariant differential operators.
Foundations of Computational Mathematics (2006), 353386.
M. Moreno Maza, G. Reid, R. Scott, and W. Wu.
On Approximate Triangular Decompositions in Dimension Zero.
Accepted November 2, 2006, for the Journal of Symbolic Computation.
Jichao Zhao and Robert M. Corless. Compact Finite Difference Method for
IntegroDifferential Equations. Accepted November 2005 for Applied Mathematics and
Computation.

Submitted for publication:
D. Bailey and Jonathan Borwein,
Highly parallel, high precision integration.
Submitted June 2006 to the International Journal of Computational Science and Engineering.
P. Borwein, R. Ferguson, M. Mossinghoff.
Sign changes in sums of the Liouville function.
Submitted July 2006 to Math. Comp.
P. Borwein, T. Erdelyi, R. Ferguson, R. Lockhart.
On the zeros of cosine polynomials: solution of an an old problem of Littlewood.
Submitted September 2006 to ACTA.
V. Dabbaghian.
On the restriction of characters of SteinbergTits triality Group ^3D_4(q) on unipotent classes.
Submitted 2006 to the Journal of Group Theory.
V. Dabbaghian. Values of the nonunipotent characters of the Chevalley group of
type F4(2^f) at unipotent elements. (5 pages).
Submitted 2006 to the Journal of Lie Theory.
O. Golubitsky and M. Kondratieva, M. Moreno Maza and A. Ovchinnikov.
Bounds for algorithms in differential algebra.
Submitted 2006 to the Journal of Symbolic Computation.


2. Other refereed contributions:
Papers in refereed conference proceedings:
J. Borwein, C. Hamilton.
Symbolic Computation of Multidimensional Fenchel Conjugates.
Proceedings of ISSAC '06, 2330. ACM Press, 2006.
P. Borwein and M. Mossingoff.
Barker Sequences and Flat Polynomials.
Submitted October 2006 to the Proceedings of Number Theory and
Polynomials Conference, Bristol, 37 April 2006.
F. Boulier, F. Lemaire, and M. MorenoMaza.
Well known theorems on triangular systems and the D5 principle.
To appear in Proceedings of Transgressive Computing 2006, Granada, Spain.
J. Carette, W. Zhou, D. Jeffrey, and M Monagan.
Hierarchical representations with signatures for large expression management.
Proceedings of AISC '06, SpringerVerlag LNAI 4120 (2006) 254268.
F. W. Chapman, K. O. Geddes, An improved algorithm for the automatic
derivation and proof of tensor product identities via computer algebra.
Proceedings of Calculemus 2006 (Genoa, Italy, July 2006),
Electronic Notes in Theoretical Computer Science, Elsevier B.V., Amsterdam, 2006.
H. Cheng and G. Labahn, On Computing Polynomial GCD in Alternate Bases.
Proceedings of ISSAC '06, 4754. ACM Press, 2006.
R. Corless, S. Ilie, and G. Reid.
Computational complexity of numerical solution of polynomial systems.
Proceedings of Transgressive Computing 2006, Granada, Spain (2006) 405408.
R. Corless.
On a Generalized Companion Matrix Pencil for Matrix Polynomials Expressed
in the Lagrange Basis.
Proceedings of SymbolicNumeric Computaton (SNC '06), Xi'an, China, 118, 2005.
X. Dahan, X. Jin, M. MorenoMaza and E. Schost.
Change of Ordering for Regular Chains in Positive Dimension.
Proceedings of Algebraic Geometry and Geometric Modelling '06. Barcelona, Spain. 4953, 2006.
W. Eberly, M. Giesbrecht, P. Giorgi, A. Storjohann, G. Villard.
Solving sparse rational linear systems.
Proceedings of ISSAC '06, 6370. ACM Press, 2006.
A. Filatei, X. Li, M. MorenoMaza and E. Schost.
Implementation Techniques for Fast Polynomial Arithmetic in a Highlevel Programming Environment.
Proceedings of ISSAC '06, 108115. ACM Press, 2006.
M. Giesbrecht, G. Labahn, and W. Lee.
Symbolicnumeric Sparse Interpolation of Multivariate Polynomials.
Proceedings of ISSAC '06, 116123. ACM Press, 2006.
J. Hefferman and R. Corless
Solving some delay differential equations using computer algebra.
To appear in the Mathematical Scientist, 31(1) June 2006.
S. Khodadad, M. Monagan.
Fast Rational Function Reconstruction.
Proceedings of ISSAC '06, 184190. ACM Press, 2006.
S. Ling, D. Jeffrey, S. Watt.
ComponentFree Vector Algebra in Aldor.
Proceedings of Transgressive Computing 2006. pp. 415418.
M. Monagan, R. Pearce.
Rational Simplification Modulo a Polynomial Ideal.
Proceedings of ISSAC '06, 239245. ACM Press, 2006.
M. Moreno Maza and Y. Xie.
Parallelization of Triangular Decompositions.
Proceedings of Algebraic Geometry and Geometric Modelling '06. Barcelona, Spain. 99100, 2006.
M. Moreno Maza and Y. Xie.
An Implementation Report for Parallel Triangular Decompositions on a Shared Memory Multiprocessor.
Proceedings of Symposium on Parallelism in Algorithms and Architectures '06. ACM Press, 2006.
M. Moreno Maza and Y. Xie.
Solving polynomial systems symbolically and in parallel.
Submitted to IPDPS '07, 2006.
S. Watt. Pivot Free Block Matrix Inversion.
To appear in the Proceedings of the 2006 Symbolic and Numerical Algorithms
in Scientific Computing Symposium (SYNASC '06), September 2006, Timisoara, Romania.
S. Watt. A Technique for Generic Iteration and Its Optimization.
Proc. ACM SIGPLAN Workshop on Generic Programming 2006 (WGP '06),
September 16, 2006, Portland Oregon. ACM Press, pp. 7686, 2006.
Wenyan Wu and Greg Reid.
Application of Numerical Linear Algebra and Numerical Algebraic Geometry to PDE.
Proceedings of ISSAC '06, 345352. ACM Press, 2006.
J. Zhao, Y. Lin, L. Ma, R. Corless
A highly efficient and accurate algorithm for solving the partial
differential equation in cardiac tissue models. Accepted for WSEAS, 2006.

Monographs, books, and book chapters:
P. Borwein, S. Choi, B. Rooney, A. Weirathmueller
The Riemann Hypothesis, SpringerVerlag, New York, To Appear in 2007
D. Jeffrey and R. Corless
Book chapter: Linear Alegbra in Maple.
To appear in the CRC Handbook of Linear Algebra, 2006.
M. Moreno Maza, G. Reid, R. Scott and W. Wu.
Book chapter: On Approximate Linearized Triangular Decompositions.
In Advances on SymbolicNumeric Computation, Springer, (2007), 268287.

Letters, notes, communications: none
Government publications: none

B. Nonrefereed contributions:
1. Papers in nonrefereed conference proceedings:
A. Bradford, C. Percival, M. Monagan.
Integer Factorization and Computing Discrete Logarithms in Maple.
Maple Conference 2006 Proceedings, 213. ISBN 1897310137.
J. Carette, Wenqin Zhou, D.J. Jeffrey, M.B. Monagan.
Linear Algebra using Maple's Maple's LargeExpressions Package.
Maple Conference 2006 Proceedings, 1425. ISBN 1897310137.
X. Dahan, X. Jin, M. MorenoMaza, E. Shost.
Change of Ordering for Regular Chains in Positive Dimension.
Maple Conference 2006 Proceedings, 2634. ISBN 1897310137.
L. Dragan and S. M. Watt.
On the Performance of Parametric Polymorphism in Maple.
Maple Conference 2006 Proceedings, 3542. ISBN 1897310137.
M. Ebrahimi, M. Ghebleh, M. Javadi, M. Monagan, A. Wittkopf.
A Graph Theory Package for Maple, Part II: Graph Coloring, Graph Drawing,
Support Tools, and Networks.
Maple Conference 2006 Proceedings, 99112. ISBN 1897310137.
S. Lo, M. Monagan, R. Pearce.
Generic Linear Algebra and Quotient Rings.
Maple Conference 2006 Proceedings, 179188. ISBN 1897310137.
S. Watt.
Making Computer Algebra More Symbolic.
Proceedings of Transgressive Computing 2006, Granada, Spain, April 2006. pp. 4349.

2. Theses:
A. Amiraslani, New Algorithms for Matrices, Polynomials and Matrix Polynomials.
Ph.D., May 2006. Supervisors: R. Corless and D. Aruliah.
A. Filatei, Implementation of Fast Polynomial Arithmetic in Aldor.
M.Sc., March 2006. Supervisor: M. Moreno Maza.
M. GagnePortelance, Computerassisted calculation in quantum field theory.
Ph.D., February 2006. Supervisors: R. Corless and D. McKeon.
S. Ilie, Computational Complexity of Numerical Solutions of IVP for DAE.
Ph.D., November 2005. Supervisors: R. Corless and G. Reid
S. Khodadad, Fast Rational Function Reconstruction.
M.Sc., November 2, 2005. Supervisor: M. Monagan.
S. Liang, A RuleBased ComponentFree Vector Algebra Package.
M.Sc. Thesis, April 2006. Supervisor: S. Watt.
N. Rezvani, Automated Generation of Numerical Evaluation Routines.
M.Sc., December 2005. Supervisors: R. Corless and D. Aruliah.
R. Scott, Approximate Grobner Bases  a Backwards Approach.
M.Sc., August 2006. Supervisor: G. Reid.
J. Zhao, A Highly Accurate Compact Finite Difference Method
and its Applications in Financial Mathematics and Computational Biology.
Ph.D., August 2006. Supervisors R. Corless and D. Aruliah.

3. Technical and internal reports: none
4. Industrial reports: none
C. Specialized Publications
1. Proprietary software packages:
A. Bradford and M. Monagan
A Maple implementation of the index calculus algorithm for computing discrete logarithms
in the integers modulo p.
In Maple 11.
Robert Corless
Matrix polynomial support for the Bernstein basis and the Lagrange basis.
Strong linearizations implemented in
CompanionMatrix allow nonlinear eigenvalue problems to be solved by
converting them to generalized eigenvalue problems. The linearization
for the Lagrange basis is new. Numerical evaluation uses the
barycentric form. The de Casteljau algorithm was implemented for
evaluation in the Bernstein case. In Maple 11.
R. Corless and N. Rezvani (2006)
Nearest polynomial with a given zero. This routine in the SNAP package
uses the witness vector from Holder's inequality to find the nearest
polynomial (in any pnorm on the vector of coefficients, in any of
several polynomial bases) with a given zero. The zero may be at
infinity. Linear constraints may be supplied, allowing structured
problems to be solved.
M. Ebrahimi and M. Monagan
DEplot[interactive]: A Maple GUI for visualizing first order systems of DEs which
contains a database of known systems, e.g., the Kermack McKendrick SIR model.
In Maple 11.
M. Ebrahimi, J. Farr, M. Ghebleh, L. Goddyn, S. Javadi,
M. KhatarinejardFard, S. Khodadad, P. Lisonek,
S. Lo, M. Monagan, and A. Wittkopf
GraphTheory: A Maple package for Graph drawing and Graph theoretic algorithms.
Includes facilities for drawing graphs in 2D and 3D, generating random graphs,
exporting and importing graphs, and a library of known special graphs.
In Maple 11.
S. Lo, M. Monagan and A. Wittkopf
StronglyConnectedBlocks: A Maple procedure for finding the block structure of a matrix.
Used to compute determinants and characteristics polynomials of sparse matrices.
In Maple 11.
M. Monagan and R. Pearce
QuotientRings: A Maple package for computations in quotient rings.
C. Percival and P. Borwein
An implementation of a self initializing quadratic sieve algorithm for
factoring integers.

November 1, 2004  November 1, 2005
A. Refereed Contributions
1. Articles in refereed publications:
Published or accepted for publication:
S. Abramov, H. Q. Le.
On the order of the recurrence produced by the method of creative telescoping.
Discrete Mathematics, vol. 298, (2005), 217.
D. H. Bailey and J. M. Borwein.,
Experimental Mathematics: Examples, Methods and Implications.
Notices of the Amer. Math. Soc., 52(5) (2005), 502514.
P. Borwein, T. Erdelyi, and F. Littman.
Polynomials with Coefficients from a finite set.
Accepted June 2005 for Transactions of the American Mathematical Society.
P. Borwein, S. Choi, R. Ferguson.
Norms of cyclotomic Littlewood polynomials.
Math. Proc. Cambridge Philos. Soc. 138 (2), 315326, 2005.
P. Borwein, A. Cuyt and P. Zhou.
Explicit construction of general multivariate Pade approximants to an Appell function.
Adv. Comput. Math. 22 (2005) 249273.
P. Borwein, G. Fee, R. Ferguson and A. van der Waall.
Zeros of partial sums of the Riemann zetafunction.
Accepted August 2005 for Experimental Math.
Y. A. Brychkov and K. O. Geddes.
On the derivatives of the Bessel and Struve functions with respect to the order.
ITSF, 16(3), (2005), 187198.
Y. d'Halluin, P.A. Forsyth and G. Labahn. A SemiLagrangian approach for
American Asian Options under jump diffusion, To appear in SIAM Journal of Scientific Computing, 32 pages.
Jane M. Heffernan and Robert M. Corless. Solving some delay differential
equations with computer algebra, The Mathematical Scientist, accepted Feb
2005, to appear in Vol 31, no 1, June 2006.
Silvana Ilie, Robert M. Corless and G. J. Reid. The numerical solution of
index1 differential algebraic equations is of polynomial cost, accepted to Numerical Algorithms summer 2005.
A. Storjohann. The modulo extended gcd problem and space efficient algorithms
for integer matrices. To appear in Journal of Algorithms, 25 pages.
A. Storjohann. The shifted number system for fast linear algebra on integer
matrices. Journal of Complexity, 21(4) (2005) 609650.

Submitted for publication: none.

2. Other refereed contributions:
Papers in refereed conference proceedings:
B. Botting, M. Giesbrecht and J. May.
Using the Riemannian SVD for Problems in Approximate Algebra.
Proc. SymbolicNumeric Computation (SNC '05), Xi'an, China, (2005) 209219.
P. Borwein, R. Ferguson.
Polyphase sequences with low autocorrelation.
IEEE Transactions. IT 51(4) 2005, 15641567.
J. Carette, O. Kiselyov. Multistage programming with {F}unctors and {M}onads:
eliminating abstraction overhead from generic code.
Generative Programming and Componentbased Engineering, 256274, 2005.
O.A. Carvajal, F.W. Chapman, K.O. Geddes.
Hybrid SymbolicNumeric Integration
in Multiple Dimensions via TensorProduct Series,
Proceedings of ISSAC '05, Beijing, China, ACM Press, 2005, pp. 8491.
Z. Chen and A. Storjohann. A BLAS Based C Library for Exact Linear Algebra
on Integer Matrices, Proceedings of ISSAC05, Beijing China, (2005) 9299.
Robert M. Corless. On a generalized companion matrix pencil for matrix
polynomials expressed in the Lagrange basis,
Proc. SymbolicNumeric
Computation (SNC 2005) Xi'an, China, D. Wang & L. Zhi, eds, 118.
X Dahan, M. MorenoMaza, E. Schost, W. Wu and Y. Xie.
Lifting techniques for triangular decompositions. (Won the best student paper award.)
Proceedings of ISSAC 2005, Beijing China, ACM Press, (2005) 108115.
M. Giesbrecht, G. Labahn and Y. Zhang. Computing Valuation Popov Forms,
Workshop on Computer Algebra Systems and their Applications (CASA'05), May
2005.
M. Giesbrecht and J.P. May. New algorithms for exact and approximate
polynomial decomposition.
International Workshop on SymbolicNumeric
Computation (SNC'05). pp. 297307. July 2005. Extended version submitted to
edited volume.
J. de Kleine, M. Monagan, A. Wittkopf.
Algorithms for the Nonmonic case of the Sparse Modular GCD Algorithm.
Proceedings of ISSAC '2005, ACM Press, pp. 124131, 2005.
M. Moreno Maza, G. Reid, R. Scott and W. Wu.
On Approximate Triangular Decompositions I. Dimension Zero.
Proceedings of SymbolicNumeric Computation '05, Xi'an, China, (2005) 250275.
M. Moreno Maza, G. Reid, R. Scott and W. Wu.
On Approximate Triangular Decompositions II. Linear Systems.
Proceedings of SymbolicNumeric Computation '05, Xi'an, China, (2005) 276296.
M. B. Monagan, Probabilistic Algorithms for Resultants.
Proceedings of ISSAC '2005, ACM Press, (2005) 245252.
C. Oancea, J. Selby, M. Giesbrecht and S. Watt.
Distributed Models of ThreadLevel Speculation. International Conference on Parallel and
Distributed Processing Techniques and Applications (PDPTA), June 2005.
C. Onacea, C. So, S. Watt.
Domains and Expressions: An interface between two approaches to computer algebra.
Proceedings of ISSAC '2005, ACM Press, (2005) 261268.
G. Reid, Jan Verchelde, A. Wittkopf and W. Wu.
SymbolicNumeric Completion of Differential Systems by Homotopy Continuation.
Proceedings of ISSAC '2005, ACM Press, (2005) 269276.
G. Reid, J. Tang, J. Yu, L. Zhi.
Hybrid method for solving new pose estimation equation system.
Proceedings IWMMGIAE 2004, SpringerVerlag LNCS 3519, (2005) 4455.
A. Storjohann and G. Villard, Computing the Rank and Nullspace Basis of a
Polynomial Basis. Proceedings of ISSAC '2005, Beijing China, (2005) 309316.
Jichao Zhao, Robert M. Corless, and Matt Davison, Financial Applications
of Symbolically Generated Compact Finite Difference Formulae.
Proc. SymbolicNumeric Computation (SNC 2005) Xi'an, China, D. Wang & L. Zhi, eds, 220234.
W. Zhou, D. Jeffrey and G. Reid
Symbolic preprocessing for the numerical simulation of multibody dynamic systems.
Proc. SymbolicNumeric Computation (SNC 2005) Xi'an, China, (2005) 220234.
W. Zhou, D. Jeffrey, G. Reid
An algebraic method for analyzing openloop dynamic systems.
Proceedings of CASA '05, SpringerVerlag LNCS 3516, (2005) 586593.
W. Zhou, D. Jeffrey, G. Reid, C. Schmitke and J. McPhee.
Implicit reduced involutive forms and their application to engineering multibody systems.
Proceedings IWMMGIAE 2004, SpringerVerlag LNCS 3519, (2005) 3143.

Monographs, books, and book chapters: none.
Letters, notes, communications: none.
Government publications: none.

B. Nonrefereed contributions:
1. Papers in nonrefereed conference proceedings:
M. Ebrahimi, M. Monagan,
New Options to Visualize Systems of Differential Equations in Maple,
Proceedings of the 2005 Maple Conference, 439450, Maplesoft, 2005.
J. Farr and R. Pearce,
Working With Multivariate Polynomials in Maple.
Proceedings of 2005 Maple Conference, 272281, Maplesoft, 2005.
J. Farr, M. Khatarinejad, S. Khodadad, M. Monagan,
A Graph Theory Package for Maple,
Proceedings of the 2005 Maple Conference, 260271, Maplesoft, 2005.
G. Labahn, T. Humphries,
Symbolic Interation of Jacobian Elliptic Functions in Maple.
Proceedings of the 2005 Maple Conference, 331339, Maplesoft, 2005.
F. Lemaire, M. MorenoMaza and Y. Xie,
The Regular Chains Library.
Proceedings of the 2005 Maple Conference, 355368, Maplesoft, 2005.
Simon Lo, Michael Monagan and Allan Wittkopf,
A Modular Algorithm for Computing the Characteristic Polynomial of an
Integer Matrix in Maple,
Proceedings of the 2005 Maple Conference, 369376, Maplesoft, 2005.
Ashley Pitcher and Robert M. Corless, Quasipolynomial rootfinding: A
numerical homotopy method, Electronic proceedings of the Canadian
Undergraduate Mathematics Conference, Queen's University, August 2005.
Tom Robinson and Keith Geddes,
Automated Generation of Numerical Evaluation Routines.
Proceedings of the 2005 Maple Conference, 383398, Maplesoft, 2005.

2. Theses:
Chris Hamilton, Symbolic convex analysis.
M.Sc., March 29, 2005. Supervisor: J. Borwein
Xin Li, Efficient Management of Symbolic Computations with Polynomials.
M.Sc., August 2005. Supervisor: M. Moreno Maza.
Roman Pearce, Rational Expression Simplification with Polynomial Side Relations
M.Sc., August 4, 2005. Supervisor: M. Monagan.
Tom Robinson, Automated Generation of Numerical Evaluation Routines.
M.Math., May 2005. Supervisor: K. Geddes

3. Technical and internal reports:
Nargol Rezvani and Robert M. Corless, The Nearest Polynomial with a Given
Zero, Revisited, SIGSAM Bulletin (Communications in Computer Algebra),
134(3) pp. 7176, September 2005.

4. Industrial reports: none.
C. Specialized Publications
1. Proprietary software packages:
J. Borwein and C. Hamilton
SCAT (Symbolic Convex Analysis Toolkit): A Maple package for
computing symbolic subdifferentials and (Fenchel) conjugates for real
valued functions in one or more dimensions.
Available from http://ddrive.cs.dal.ca/projects/scat
Y. Brychkov, E. ChebTerrab, and K. Geddes.
Differentiation of Bessel and Struve functions wrt a parameter. In Maple 10.
E. ChebTerrab
Maple code for the solution of ODEs of Heun type and support
for the numerical evaluation, differentiation, series expansion, and simplification
of the family of Heun functions. In Maple 10.
R. Corless and D. Jeffrey
Maple code the numerical evaluation, power series expansion, and simplifications of
the WrightOmega function. Numerical evaluation is nontrivial near the branch cuts.
In Maple 10.
R. Corless, M. Benghorbal, R. Morris, E. ChebTerrab
Maple code for fractionalorder differentiation. In Maple 10.
R. Corless and E. ChebTerrab
Maple code for symbolic order differentiation. In Maple 10.
M. Ebrahimi, M. Monagan, A. Wittkopf
DEplot: Maple and C code for visualizing the direction field of a first order system
system of differential equations with randomly placed little fish. In Maple 11.
Jeff Farr
A Maple package for multivariate polynomial and rational function
interpolation and multivariate Pade approximation.
The algorithms generalize Newton interpolation using ideas from
the theory of Groebner bases.
J. Farr, M. KhatarinejardFard, S. Khodadad,
P. Lisonek, S. Lo, M. Monagan
The development of a graph theory package for Maple which supports
algorithms for graph drawing, planarity testing, NPcomplete problems,
bounds, exact computation of spanning polynomials.
F. Lemaire, M. Moreno Maza, Y. Xie with contributions
from X Jin, E. Schost, and W. Wu
RegularChains: A Maple package of 50 routines for solving systems of algebraic
equations using triangular decomposition techniques and for studying properties
of the solutions. Provides automatic case discussion and case recombination
using a new lifting technique, and facilties for linear algebra over a direct
product of fields. In Maple 10.
S. Lo and M. Monagan
A package of "generic" Maple routines for doing linear algebra over
arbitrary commutative rings, integral domains, Euclidean domains and fields.
Provides a simple mechanism for coding generic algorithms in Maple.
S. Lo, M. Monagan, and A. Wittkopf
A Maple implementation of a modular algorithm for computing the characteristic
polynomial of an integer matrix using 25 bit floating point primes. In Maple 11.
Michael Monagan
Maple code for computing the GCD of two univariate polynomials
over an algebraic function field with one or more parameters.
Uses the dense modular algorithm of Monagan and van Hoeij.
M. Monagan and R. Pearce
Maple code for simplifying a fraction in a quotient ring,
i.e., simplifying fractions modulo polynomial side relations. In Maple 11.
Roman Pearce.
A Maple implementation of the ``F4 algorithm'' for computing Groebner
bases with rational coefficients using modular linear algebra. In Maple 10.

2003  2004
A. Refereed Contributions
1. Articles in refereed publications:
Published or accepted for publication:
S.A. Abramov, J.J. Carette, K.O. Geddes, and H.Q. Le, Telescoping in the context
of symbolic summation in Maple,
Journal of Symbolic Computation, 38 (4), Oct 2004, pp. 13031326.
D.A. Aruliah, R.M. Corless,
Numerical parameterizatin of affine varieties using ODEs, ISSAC, University of
Cantabria, Santander Spain, (2004), 1218.
M.M. Benghorbal,
The MittagLeffler theorem and integer order symbolic derivative formulas of meromorphic
functions, Int'l Comp. and Num. Anal. and App. (accepted September 2004).
M. Benghorbal, Robert M. Corless,
A unified formula for arbitrary order symbolic derivatives and integrals of a
rational polynomial, Int'l. J. Pure and Applied Mathematics (Accepted June 2004).
M. Benghorbal and Robert M. Corless, Power series solutions of fractional
differential equations, Int' J. Pure & Applied Maths, 15, no. 3 (2004) 333352.
P. Borwein, S. Choi and R. Ferguson,
Norms of cyclotomic littlewood polynomials, Proc. Cambridge Phil. Soc.
(accepted January 2004).
P. Borwein and R. Ferguson, Polyphase sequences with low autocorrelation. IEEE
Trans. IT (accepted September 2004).
Borwein, Peter; Hare, Kevin G.; Mossinghoff, Michael J., The Mahler measure of polynomials with odd
coefficients, Bull. London Math. Soc. 36 (2004), no. 3, 332338.
J. Cai, M. Moreno Maza, S. Watt, M. Dunstan,
Debugging A HighLevel Language via a Unified Interpreter and
Compiler Runtime Environment.
pp 119124 in Actas de los Encuentros de Algebra Computacional y Aplicaciones
2004, Universitad de Candabria 2004, ISBN 84688698804.
R.M. Corless,
Generalized companion matrices in the Lagrange basis, EACA, Santander, Spain, 2004, 317322.
Robert M. Corless, Stephen M. Watt, and Lihong Zhi, QR factoring to
compute the GCD of univariate approximate polynomial. IEEE Trans. Signal
Processing 52, no. 12, December 2004, 33943402.
E.S. ChebTerrab, A connection between Abel and pFq hypergeometric differential equations,
Accepted for publication in the European Journal of Applied Mathematics (submitted: February 2004. Revised version
accepted: September 2004; in print).
E.S. ChebTerrab,
Solutions for the General, Confluent and BiConfluent Heun equations and their connection with
Abel equations, Journal of Physics A: Mathematical and General 37 99239949 (2004).
W. Eberly and M. Giesbrecht,
Efficient decomposition of separable algebras. Journal of Symbolic Computation.
Volume 37, Issue 1, 2004, pp. 3518.
Y. d'Halluin, P.A. Forsyth, G. Labahn, A penalty method for American options
with jump diffusion processes, Numerische Matematik, 97:2 (2004) 321352.
T. Mulders and A. Storjohann,
Certified dense linear system solving, Journal of Symbolic Computation, 37(4):485
510, 2004.
C. Oancea, S. Watt,
A Framework for Using Aldor Libraries with Maple, pp 219224 in Actas de los Encuentros de
Algebra Computacional y Aplicaciones 2004, Universitad de Candabria 2004, ISBN 84688698804.
D. Saunders, A. Storjohann and G. Villard,
Matrix rank certification, Electronic Journal of Linear Algebra, 11:1623, 2004.

Submitted for publication:
P. Borwein, S. Choi and F. Chu, An Old Conjecture of ErdossTurán on Additive
Bases. To Math. Comp. (submitted October 2004).
R. Corless, D. Jeffrey,
Computer Algebra Support for the Wright omega function.
To TOMS. (submitted September 2004).
R. Corless, D. Jeffrey,
Complex numerical values of the Wright omega function.
To TOMS. (submitted September 2004).


2. Other refereed contributions:
Review articles: none.
Papers in refereed conference proceedings:
J. Cai, M. Moreno Maza, S. Watt, M. Dunstan,
Debugging A HighLevel Language via a Unified Interpreter and
Compiler Runtime Environment, pp 125138, ACA 2004,
Proc the Tenth International Conference on Applications
of Computer Algebra, Lamar University 2004, ISBN 0975994603.
Y. Chicha, M. Lloyd, C. Oancea, S. Watt,
Parametric Polymorphism for Computer Algebra Software Components,
pp 119130 in SYNASC 2004, 6th International Symposium on
Symbolic and Numeric Algorithms for Scientific
Computation, MITRON (Timisoara) 2004, ISBN 9736614417.
R.M. Corless, S.M. Watt,
Bernstein Bases are Optimal, but, sometimes, Lagrange Bases are Better, pp 141152 in
SYNASC 2004, 6th International Symposium on Symbolic and Numeric Algorithms for Scientific Computation,
MITRON (Timisoara) 2004, D. Peteu, V. Negru, D Zaharie, T. Jebelean, eds, ISBN 9736614417.
J. Carette, Understanding Expression Simplification,
Proceedings of ISSAC '2004, ACM Press, pp. 7279, 2004.
L.Chan, E.S. ChebTerrab, Non Liouvillian solutions for second order linear ODEs,
Proceedings of ISSAC, Santander, Spain, 2004.
K.O. Geddes, H.Q. Le and Z. Li, Differential rational normal forms and a reduction algorithm for
hyperexponential functions, Proceedings of ISSAC'04 (International Symposium on Symbolic and Algebraic
Computation, J. Gutierrez (ed.), ACM Press, New York, 2004, pp. 183190.
M. Giesbrecht, G. Labahn, W.s. Lee,
Symbolicnumeric sparse interpolation of multivariate polynomials,
Proc. 9th Rhine Workshop on Computer Algebra, 2004.
M. Giesbrecht, G. Labahn and W.s. Lee,
SymbolicNumeric Sparse Polynomial Interpolation in Chebyshev Basis
and Trigonometric Interpolation,
Proc. Workshop on Computer Algebra in Scientific Computation, 2004.
M. van Hoeij, M. B. Monagan, Algorithms for Polynomial
GCD Computation over Algebraic Function Fields,
Proceedings of ISSAC '04, ACM Press, pp. 297304, 2004.
G. Labahn and Ziming Li,
Hyperexponential Solutions of Finiterank Ideals in Uncoupled Ore Algebras,
Proceedings of ISSAC'04, Santander, Spain, ACM Press, (2004) 213220.
M. B. Monagan, Maximal Quotient Rational Reconstruction:
An Almost Optimal Algorithm for Rational Reconstruction,
Proceedings of ISSAC '2004, ACM Press, pp. 243249, 2004.

Monographs, books, and book chapters:
C. So, E. Smirnova, S. Watt, An Architecture for Distributed Mathematical Web Services, pp 363377 in LNCS
3119 "Mathematical Knowledge Management, Springer Verlag 2004, ISBN 3540230297.

Letters, notes, communications: none.
Government publications: none.

B. Nonrefereed contributions:
1. Papers in nonrefereed conference proceedings:
J. de Kleine, M. Monagan, S. Wittkopf, The NonMonic Case of the Sparse Modular GCD Algorithm, Proceedings
of the Maple 2004 Summer Workshop (on CD), 2004.
R. Pearce, M. Monagan, The Polynomial Ideals Maple Package, Proceedings of the Maple 2004 Summer Workshop
(on CD), 2004.
M. B. Monagan, G. J. Fee, A Cryptographically Secure Random Number Generator for Maple, Proceedings of the
Maple 2004 Summer Workshop (on CD), 2004.

2. Theses:
Mhenni Benghorbal, Ph.D. Power Series for Fractional Differential Equations, PhD Thesis, University of Western Ontario, 2004.
(Supervisor: R. Corless)
Brad Botting. M.Math. (Computer Science, Waterloo), Structured Total Least Squares for Approximate Polynomial
Operations, 2004. (Supervisor: M. Giesbrecht)
Jinlong Cai, Debugging a High Level Language via a Unified Interpreter and Compiler Runtime Environment, MSc thesis,
Department of Computer Science, U Western Ontario, 2004.
(Supervisor: M. Moreno Maza)
O.A. Carvajal, A Hybrid SymbolicNumeric Method for Multiple Integration Based on TensorProduct Series
Approximations, Master's Thesis, Department of Computer Science, University of Waterloo, 2004. (Supervisors: K.O. Geddes
and F.W. Chapman)
Bradford Hovinen, M.Math (Computer Science, Waterloo), Blocked Lanczosstyle
Algorithms over Small Finite Fields,
2004. (Supervisor: M. Giesbrecht)
Ivo Moravec, M.Math (Computer Science, Waterloo, 2004). Thesis title: Fast Arithmetic and Code Generation for Univariate
Functions. 2004. (Supervisor: M. Giesbrecht)
A. Wittkopf, Algorithms and Implementations for Differential Elimination, Ph.D. Thesis, SFU, 2004. (Supervisor: M. Monagan)
Yang Zhang, Ph.D. (Applied Mathematics, UWO). Thesis title: Algorithms for NonCommutative Differential Operators.
2004. (Supervisor: M. Giesbrecht)

3. Technical and internal reports: none.
4. Industrial reports: none.
C. Specialized Publications
1. Proprietary software packages: See 2002  2003.
2002  2003
A. Refereed Contributions
1. Articles in refereed publications:
Published or accepted for publication:
B. Beckermann, G. Labahn and G. Villard, Normal Forms for General Polynomial Matrices, To appear in Journal
of Symbolic Computation, 25 pages.
P. Borwein and T. Erdélyi, Lower bounds for the merit factors of trigonometric polynomials
from Littlewood classes,
J. Approx. Theory, vol 125, 2003, 190197.
P. Borwein and R. Ferguson, A Complete Description of Golay Pairs for Lengths up to
100, Math. Comp., vol 73,
2003, 967985.
P. Borwein and K.G. Hare, General forms for minimal spectral values for a class of
quadratic Pisot numbers, Bull.
London Math. Soc., vol 35, 2003, 4754.
P. Borwein and K.G. Hare, Nontrivial quadratic approximations to zero of a family of cubic
Pisot numbers,
Trans. Amer. Math. Soc. 355 (2003), no. 12, 47674779.
P. Borwein, K.G. Hare and M. Mossinghoff, The L1 norm of polynomials, Proc. Amer. Math. Soc. (accepted June
2003).
P. Borwein, P. Lisonek and C. Percival, Computational investigations of the
ProuhetTarryEscott problem, Math.
Comp., vol 72, 2003, 20632070.
P. Borwein and M. Mossinghoff, Newman polynomials with prescribed vanishing and integer sets with distinct
subset sums, Math. Comp., vol 72, 2003, 787800.
P. Borwein, C.G. Pinner, and I.E. Pritsker, Monic integer Chebyshev problem. Math. Comp. 72 (2003), no. 244,
19011916.
R. Corless, S. Watt, L. Zhi, QR Factoring to Compute the GCD of Univariate Approximate, Accepted to IEEE
Transactions on Signal Processing.
J. Gerhard, M. Giesbrecht, A. Storjohann, E. Zima, Shiftless decomposition and polynomialtime rational
summation, ACM International Symposium on Symbolic and Algebraic Computation (ISSAC), 2003, pp. 119126.
M. Giesbrecht, E. Kaltofen, W.s. Lee, Algorithms for Computing Sparsest Shifts of Polynomials in Standard,
Chebyshev, and Pochhammer Bases, Journal of Symbolic Computation. Volume 36, Issues 34, 2003, pp. 287683.
A. Storjohann, Highorder lifting and integrality certification, Journal of Symbolic Computation, 36(34):613648,
2003.
A. Storjohann, The shifted number system for fast linear algebra on integer
matrices, Journal of Complexity, approx.
40 pages, to appear.

Submitted for publication:
P. Borwein, S. Choi and J. Jedwab, Binary sequences with merit factors greater than 6.34, IEEE (submitted June
2003).
P. Borwein, A. Cuyt and P. Zhou, Explicit Construction of General Multivariate Padé Approximants to An Appell
Function, Math. Comp.
P. Borwein, G. Fee, R. Ferguson and A. van der Waall, Zeros of partial sums of
the Riemann zetafunction,
(submitted November 2003).
P. Borwein, E. Dobrowolski and M. Mossinghoff, Lehmer's Problem for polynomials with odd
coefficients, Annals
of Math (submitted Annals September 2003).


2. Other refereed contributions:
Review articles: none.
Papers in refereed conference proceedings:
E.S. ChebTerrab, Second order Linear ODEs: Two NonLiouvillian approaches, Proceedings of the Workshop on
Group Theory and Numerical Analysis, CRM2003, Montreal, Canada (printed during 2004).
K.O. Geddes and H.Q. Le, An algorithm to compute the minimal telescopers for rational functions
(Differential  integral case), International Congress of Mathematical Software, A.M. Cohen, X. Gao, N. Takayama
(eds.), World Scientific, 2002, pp. 453463.
K.O. Geddes and W.W. Zheng, Exploiting fast hardware floating point in high
precision computation, Proceedings
of ISSAC'03 (International Symposium on Symbolic and Algebraic Computation), J.R.~Sendra (ed.), ACM Press,
New York, 2003, pp. 111118.
M. Giesbrecht, Y. Zhang, Factoring and
Decomposing Ore Polynomials over Fq(t), ACM International Symposium
on Symbolic and Algebraic Computation (ISSAC), 2003, pp. 127134.

Monographs, books, and book chapters:
R.M. Corless, E.L. Kaltofen, S.M. Watt, Hybrid Methods, pp. 112125 in Handbook of Computer Algebra, J.
Grabmeier, E. Kaltofen, V. Weispfenning (eds).
M. Giesbrecht, A. Storjohann and G. Villard, Algorithms for matrix canonical
forms, Invited Submission.
Computer Algebra Handbook. Foundations, Applications, Systems. Springer Verlag, 2003, pp. 3841.
S. Watt, MathML, pp. 154160 in Handbook of Computer Algebra, J. Grabmeier, E. Kaltofen, V. Weispfenning
(eds), Springer Verlag, Heidelberg 2003, ISBN 3540654666.

Letters, notes, communications: none.
Government publications: none.

B. Nonrefereed contributions:
1. Papers in nonrefereed conference proceedings: none.
2. Theses:
Justin Wozniak, A Control Systems package for Maple, MMath, School of Computer Science, University of Waterloo (2003)
(Supervisor: George Labahn)

3. Technical and internal reports: none.
4. Industrial reports: none.
C. Specialized Publications
1. Proprietary software packages:
E.S. ChebTerrab
The algorithms for computing nonLiouvillian (that is, special function) solutions for second order linear ODEs
presented in [2] and [3] were coded in the Maple language and are now the main algorithms in the Maple computer
algebra system for computing this type of solutions. The special cases of the Heun functions are being coded in this
moment. The classification of Abel equations mappable into linear equations is core theoretical work, not coded yet,
but at the base of upcomming software for solving this problem.
M. Ebrahimi, M. Monagan
Development of improved visuals for visualizing a direction field. Incorporated into DEplot, a tool for studying
systems of DEs.
G. Fee, M. Monagan
A package of Maple routines for pseudo random number generation using the BlumBlumShub generator.
G. Labahn
Maple code for solving odes having elliptic functions as coefficients. Functionality can be used in standalone form
(in DEtools package : DEtools[dperiodic_sols]) or as part of Maple's differential equation solver.
Maple code for solving odes having nested exponential functions as coefficients. Functionality is currently used in
standalone form (in DEtools package : DEtools[expcoeff_sols]).
S. Lo, M. Monagan
Development of a package of "generic" Maple routines for linear algebra
that permit the calling routine to compute over any field, Euclidean domain,
integral domain or ring. The applications which motivated the development are
matrices (of polynomials) over finite fields.
M. Monagan
Implementation of a new rational number reconstruction method which reduces the number of primes needed in a
modular algorithm. Incorporated this algorithm into a modular GCD algorithm for polynomials over number fields.
M. Monagan, E. ChebTerrab
A numerical differentiation routine for computing single, multiple and partial derivatives to arbitrary precision. This
enables us to compute numerical values of derivatives of special functions for which there is no closed form.
R. Pearce, J. Farr, M. Monagan
A Groebner basis implementation which automatically employs the FGLM algorithm (for the zero dimensional
case) and the Groebner walk algorithm (for the general case) to speed up Groebner basis computations, in particular
lex Groebner bases.
R. Pearce, M. Monagan
A package of Maple routines for computing with polynomial ideals. The package contains routines for computing
the prime(ary) decomposition of an ideal, radical of an ideal, and computations in quotient rings.
A. Wittkopf, M. Monagan
A new modular GCD algorithm for multivariate polynomials over the integers which uses a modified sparse
interpolation which generalizes Zippel's algorithm to the nonmonic case. Implemented in Maple.

