Algebraic Algorithms and Computer Algebra Systems

2011

Michael Monagan.
Preprint: A new edge selection heuristic for computing the Tutte polynomial of an undirected graph.
Submitted December 2011 to FPSAC '12 , Nagoya, Japan, July 2012.

Michael Monagan.
Preprint: Sparse Polynomial Powers Using Heaps.
Submitted April 2012 to CASC 2012 , Maribor, Solvenia, September 2012.

Michael Monagan and Roman Pearce.
Preprint: Sparse Polynomial Pseudo Division Using a Heap
J. Symb. Cmpt., 46(7) pp. 807–822, 2011.

Andrew Arnold and Michael Monagan.
Preprint: Calculating cyclotomic polynomials of very large height.
Math. Comp. 80(276) pp. 2359–2379, October, 2011.

2010

Mahdi Javadi and Michael Monagan.
Preprint: Parallel Sparse Polynomial Interpolation over Finite Fields
Submitted November 2010 to the Journal of Symbolic Computation.

Michael Monagan and Roman Pearce.
Preprint: Polynomial Multiplication and Division in Maple 14
Communications in Computer Algebra, 44:4 (2010) 205–209.

Andrew Arnold and Michael Monagan.
A high-performance algorithm for calculating cyclotomic polynomials.
Proceedings of PASCO 2010, ACM Press, 112-120, 2010.

Michael Monagan and Roman Pearce.
Parallel Sparse Polynomial Division using Heaps.
Proceedings of PASCO 2010, ACM Press, 105-111, 2010.

Mahdi Javadi and Michael Monagan.
Parallel Sparse Polynomial Interpolation over Finite Fields.
Proceedings of PASCO 2010, ACM Press, 160-168, 2010.

Liang Chen and Michael Monagan.
Preprint: Algorithms for Solving Linear Systems over Cyclotomic Fields.
J. Symb. Cmpt., 45(9) pp. 902-917, 2010.

2009

Mahdi Javadi and Michael Monagan.
In-place Arithmetic for Univariate Polynomials over an Algebraic Number Field
Proceedings of the Joint Conference of ASCM 2009 and MACIS 2009. COE Lecture Notes 22, Kyushu University, pp. 330-341, 2009.

Paul Vrbik and Michael Monagan.
Lazy and Forgetful Polynomial Arithmetic and Applications.
Computer Algebra in Scientific Computing (CASC '09) 226–239, Springer Verlag LNCS 5743, 2009.

Mahdi Javadi and Michael Monagan.
On Factorization of Multivariate Polynomials over Algebraic Number and Function Fields.
Proceedings of ISSAC '09, 199–206, ACM Press, 2009.

Michael Monagan and Roman Pearce.
Parallel Sparse Polynomial Multiplication Using Heaps.
Proceedings of ISSAC '09, 263–269, ACM Press, 2009.

2007

Michael Monagan and Roman Pearce.
Polynomial Division using Dynamic Arrays, Heaps, and Packed Exponent Vectors.
Computer Algebra in Scientific Computing (CASC '07) Springer Verlag LNCS 4770, (2007) 295–315.

Mahdi Javadi and Michael Monagan.
A Sparse Modular GCD Algorithm for Polynomial GCD Computation over Algebraic Function Fields.
Proceedings of ISSAC '07, ACM Press, (2007) 187–194.

Simon Lo, Michael Monagan and Allan Wittkopf.
Preprint: Strongly Connected Graph Components and Computing Characteristic Polynomials of Integer Matrices in Maple
Accepted March 2007 for Communications in Computer Algebra.

2006

Michael Monagan and Roman Pearce.
Rational Simplification Modulo a Polynomial Ideal.
Proceedings of ISSAC '06, ACM Press, (2006), 239–245.

Sara Khodadad and Michael Monagan.
Fast Rational Function Reconstruction.
Proceedings of ISSAC '06, ACM Press, (2006), 184–190.

2005

J. de Kleine, M. B. Monagan, A. D. Wittkopf.
Algorithms for the Non-monic case of the Sparse Modular GCD Algorithm.
Proceedings of ISSAC '05, ACM Press, (2005), 124–131.

Michael Monagan.
Probabilistic Algorithms for Resultants.
Proceedings of ISSAC '05, ACM Press, (2005), 245–252.

Simon Lo, Michael Monagan, Allan Wittkopf.
A Modular Algorithm for Computing the Characteristic Polynomial of an Integer Matrix in Maple.
Proceedings of the 2005 Maple Conference, MapleSoft, (2005), 369–376.

2004

Michael Monagan.
Maximal Quotient Rational Reconstruction: An Almost Optimal Algorithm for Rational Reconstruction.
Proceedings of ISSAC '04, ACM Press (2004) 243–249.

M. van Hoeij and M. B. Monagan.
Algorithms for Polynomial GCD Computation over Function Fields.
Proceedings of ISSAC '04, ACM Press, (2004), 243–249.

2002

M. van Hoeij, M. Monagan.
A Modular GCD Algorithm over Number Fields Presented with Multiple Field Extensions.
Proceedings of ISSAC '2002, ACM Press, (2002), 109–116.

2001

J. Mulholland, M.B. Monagan.
Algorithms for Trigonometric Polynomials.
Proceedings of ISSAC '01, ACM Press, (2001), 245–252.

1999

M.B. Monagan and M.A. Slawinski.
The Sensitivity of Traveltime Inversion for an Anisotropic Parameter in Seismology.
MapleTech, 5, No 2, (1999), 109–116, Birkhauser.

1997

L. Bernardin, M. Monagan.
Efficient Multivariate Factorization Over Finite Fields.
Proceedings of AAECC '97, Springer-Verlag LNCS 1255, (1997), 15–28.

G.M. Monagan and M.B. Monagan.
A Toolbox for Program Manipulation and Efficient Code Generation with an Application to a Problem in Computer Vision.
Proceedings of ISSAC '97, ACM Press, (1997), 257–266.

D. Wuertz, M. Monagan, and R. Peikert.
The History of Packing Circles in a Square.
Maple in Mathematics and the Sciences, MapleTech, Special Issue, (1994) 35–42, Birkhauser.

1994

Michael Monagan and Dominik Gruntz.
Introduction to Gauss.
SIGSAM Bulletin, 28 No 2. (1994) 3–19.

1993

Michael Monagan.
Gauss: a Parameterized Domain of Computation System with Support for Signature Functions. Proceedings of DISCO '93, Springer-Verlag LNCS, 722, (1993), 81–94.

1992

Michael Monagan.
In-place Arithmetic for Polynomials over Zn
Proceedings of DISCO '92, Springer-Verlag LNCS, 721, (1993), 22–34.

1990

T.C. Scott, R.A. Moore, G.J. Fee, M.B. Monagan, G. Labahn and K.O. Geddes.
Perturbative Solutions of Quantum Mechanical Problems by Symbolic Computation: A Review.
Int. J. of Modern Physics, (1990) 1 No. 1, pp. 53–76.

1988

A.J. Granville and M.B. Monagan.
The First Case of Fermat's Last Theorem is True for all Prime Exponents up to 714,591,416,091,389.
Transactions of the AMS, 66, No 3, (1988), 206–211.

1986

Gaston H. Gonnet, Michael B. Monagan
Solving Systems of Algebraic Equations, or the Interface between Software and Mathematics
Computers and Mathematics, Stanford University, 1986.
Computer Science Research Report CS-89-13, University of Waterloo.

1984

Bruce Char, Gregory Fee, Keith Geddes, Gaston Gonnet, Michael Monagan, Stephen Watt.
On the Design and Performance of the MAPLE System
Computer Science Research Report CS-84-13, University of Waterloo.
Proceedings of the 1984 Macsyma Users Conference, Schenectady, New York, 1984.

Teaching Mathematics using Computers

Michael Monagan and John Ogilvie.
Improving the Teaching of Mathematics to Students of Science and Engineering.
Albanian Journal of Mathematics 4(4) 223–230, 2010.

J. Ogilvie, M. Monagan.
Teaching Mathematics to Students of Chemistry using Symbolic Computation.
Journal of Chemical Education, 84(5), 889-896, May 2007.

M. Ebrahimi, M. Ghebleh, M. Javadi, M. Monagan, and A. Wittkopf.
A Graph Theory Package for Maple, Part II: Graph Coloring, Graph Drawing, Support Tools and Networks.
Maple 2006 Conference Proceedings, pp. 99–112, MapleSoft, ISBN 1-897310-13-7, 2006.

M. Ebrahimi, M. Monagan.
New Options to Visualize Systems of Differential Equations in Maple,
Proceedings of the 2005 Maple Conference, pp. 260–271, Maplesoft, 2005.

M. Monagan,
2D and 3D Graphical Routines for Teaching Linear Algebra,
Proceedings of the 2002 Maple Summer Workshop, Waterloo Maple Inc., 2002.

Carollyne Guidera and Michael Monagan,
"Introductory Differential Equations: New Tools Give New Understanding to Students." Maple in the Mathematical Sciences
MapleTech, Birkhauser, 4, No 1., 59–67, 1997.

M. Monagan,
Worksheets and Notebooks: Can We Teach Mathematical Algorithms with Them?
J. Symbolic Computation, 23 No 5., 535–550, 1997.