2021 to present

Qiao-Long Huang and Michael Monagan.
Preprint: A New Sparse Polynomial GCD by Separating Terms
Submitted January 2024 to ISSAC '24, Raleigh, North Carolina, July 16&nash;19, 2024.

Mahsa Ansari and Michael Monagan.
Preprint: A Modular Algorithm to Compute the Resultant of Multivariate Polynomials over Algebraic Number Fields Presented with Multiple Extensions
Submitted May 2024 to CASC '24, Rennes, France, September 2–6, 2024.

Mahsa Ansari and Michael Monagan.
Preprint: Computing GCDs of Multivariate Polynomials over Algebraic Number Fields Presented with Multiple Extensions
Submitted May 2023 to CASC '23, Havana, Cuba, August 28 to September 1, 2023.

Ayoola Jinadu and Michael Monagan.
Preprint: Solving Parametric Linear Systems using Sparse Rational Function Interpolation
Submitted May 2023 to CASC '23, Havana, Cuba, August 28 to September 1, 2023.

Tian Chen and Michael Monagan.
Preprint: A New Black Box Factorization Algorithm: the Non-monic Case
Submitted February 2023 to ISSAC '23, Tromso, Norway, July 24–27, 2023.

Michael Monagan.
How to program with formulas in Maple.
Maple Transactions 3(1), Article 15169, 2023.

Ayoola Jinadu and Michael Monagan.
Preprint: An Interpolation Algorithm for computing Dixon Resultants.
Submitted May 2022 to CASC '22, Gebze, Turkey, August 22–26, 2022.

Michael Monagan and Garrett Paluck.
Preprint: Linear Hensel lifting for Zp[x,y] for n factors with cubic cost.
Submitted February 2022 to ISSAC '22, Lille, France, July 4–7, 2022.

Michael Monagan.
Preprint: Speeding up polynomial GCD, a crucial operation in Maple.
Submitted November 2021 to Maple Transactions.

Tian Chen and Michael Monagan.
Preprint: Factoring Multivariate Polynomials Represented by Black Boxes: A Maple + C Implementation.
Submitted October 2021 to the post conference proceedings of CASC '21.

2011 to 2020

Tian Chen and Michael Monagan.
Preprint: The Complexity and Parallel Implementation of two Sparse Multivariate Hensel Lifting Algorithms for Polynomial Factorization.
Submitted May 2020 to Computer Algebraic in Scientific Computing.

Pierre Fortin, Ambroise Fleury, François Lemaire, and Michael Monagan.
Preprint: High performance SIMD modular arithmetic for polynomial evaluation.
Submitted April 2020 to Concurrency and Computation: Practice and Experience.

Joris van der Hoeven and Michael Monagan.
Preprint: An implementation of the tangent Graeffe root finding algorithm.
Accepted April 2020 for the International Congress on Mathematical Software 2020.

Jiaxiong Hu and Michael Monagan
Preprint: A fast parallel sparse polynomial GCD algorithm.
Accepted December 2019 for the Journal of Symbolic Computation.

Michael Monagan and Baris Tuncer
Preprint: Polynomial Factorization in Maple 2019
Accepted August 2019 for the 2019 Maple Conference, Waterloo, Ontario, October 2019.

Michael Monagan.
Preprint: Linear Hensel Lifting in Z[x] and Zp[x,y] with Cubic Cost.
Accepted April 2019 for ISSAC 2019, Beijing, July 2019.

Deepak Kapur, Dong Lu, Michael Monagan, Yao Sun, and Dingkang Wang.
An Efficient Algorithm for Computing Parametric Multivariate Polynomial GCD
Accepted July 4, 2019 for the Journal of Symbolic Computation.


Deepak Kapur, Dong Lu, Michael Monagan, Yao Sun, and Dingkang Wang.
Preprint: An Efficient Algorithm for Computing Parametric Multivariate Polynomial GCD
Accepted April 8, 2018 for ISSAC 2018, Beijing, China, July 2019.

Michael Monagan and Baris Tuncer
Preprint: Factoring multivariate polynomials with many factors and huge coefficients.
Accepted June 2018 for CASC 2018, Lille, France, September 2019.
The preprint fixes two errors in Algorithm 2 WMDS in the CASC proceedings version.

Michael Monagan and Baris Tuncer
Preprint: Sparse multivariate polynomial factorization: a high-performance design and implementation.
Accepted for ICMS 2018, Notre Dame, South Bend, Indiana, July 2018.

Michael Monagan and Baris Tuncer
Preprint: The complexity of sparse Hensel lifting and sparse polynomial factorization.
Accepted February 2019 for the Journal of Symbolic Computation. Published Version

John Kluesner and Michael Monagan
Preprint: Resolving zero divisors using Hensel lifting.
Accepted for SYNASC 2017, Timisoara, Romania, September 2017.

Michael Monagan and Roman Pearce
Preprint: An Algorithm For Splitting Polynomial Systems Based On F4
Accepted for PASCO 2017, Kaiserslautern, Germany, July 2017.

Michael Monagan and Alan Wong
Preprint: Fast Parallel Multi-point Evaluation of Sparse Polynomials
Accepted for PASCO 2017, Kaiserslautern, Germany, July 2017.

Michael Monagan and Baris Tuncer
Preprint: Using Sparse Interpolation in Hensel Lifting.
Accepted for CASC 2016, Bucharest, Romania, September 2016.

Marshall Law and Michael Monagan
Preprint: Computing Characteristic Polynomials of Matrices of Structured Polynomials.
Accepted for CASC 2016, Bucharest, Romania, September 2016.

Jiaxiong Hu and Michael Monagan
Preprint: A fast parallel sparse polynomial GCD algorithm.
Accepted for ISSAC 2016, Waterloo, Ontario, July 2016.
Correction: Corrects an error in the linear algebra in Section 1.4

Michael Monagan and Baris Tuncer
Preprint: Some results on counting roots of polynomials and Sylvester's resultant.
Accepted for FPSAC 2016, Vancouver, British Columbia, July, 2015.

Matthew Gibson and Michael Monagan
Preprint: Optimizing and Parallelizing the Modular GCD Algorithm
Accepted for PASCO 2015, Bath, England, July, 2015.

Marshall Law and Michael Monagan
Preprint: A parallel implementation for polynomial multiplication modulo a prime.
Accepted for PASCO 2015, Bath, England, July, 2015.

Michael Monagan and Roman Pearce
Preprint: A Compact Parallel Implementation of F4
Accepted for PASCO 2015, Bath, England, July, 2015.

Michael Monagan and Roman Pearce
Preprint: The design of Maple's sum-of-products and POLY data structures for representing mathematical objects.
Communications of Computer Algebra 48(4): 166‐186, December 2014.

Michael Monagan and Roman Pearce
Preprint: POLY: A new polynomial data structure for Maple 17.
To appear in the Proceedings of ASCM 2012, Springer Verlag, 2014. Conference held October 26-28, 2012, Beijing, China.

Michael Monagan and Roman Pearce.
Preprint: Sparse Polynomial Powers Using Heaps.
Accepted for CASC 2012, Maribor, Slovenia, September 2012.

Michael Monagan and Roman Pearce
Preprint: POLY: A new polynomial data structure for Maple 17.
Accepted for the ISSAC 2012 software demo session, ISSAC '12, Grenoble, France, July, 2012.

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

2001 to 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.

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.

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.

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.

J. Carette, Wenqin Zhou, D.J. Jeffrey, and M.B. Monagan.
Linear Algebra using Maple's LargeExpressions Package
Maple 2006 Conference Proceedings, pp. 14–25, MapleSoft, ISBN 1-897310-13-7, 2006.

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. van Hoeij, M. Monagan.
A Modular GCD Algorithm over Number Fields Presented with Multiple Field Extensions.
Unpublished manuscript giving details of Maple and Magma implementations of our modular GCD algorithm for L[x,y,z,...] and treatment of the case when L is not a field. November 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.

J. Farr, M. Khatarinejad, S. Khodadad, and M. Monagan.
A Graph Theory Package for Maple.
Proceedings of the 2005 Maple Conference MapleSoft, pp. 260–271, 2005.

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.

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.

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

2000 and earlier

Michael B. Monagan and Allan D. Wittkopf
On the Design and Implementation of Brown’s Algorithm over the Integers and Number Fields
ISSAC 2000, ACM Press, (2000), 225–233.

Erich Kaltofen and Michael Monagan
On the Genericity of the Modular Polynomial GCD Algorithm. Proceedings of ISSAC '99, 59–66, ACM Press, 1999.

Dominique Villard and Michael Monagan
ADrien: An Implementation of Automatic Differentiation in Maple. Proceedings of ISSAC '99, 221–228, ACM Press, 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.

Roger Margot and Michael Monagan.
Preprint: Computing Univatiate GCDs over Number Fields.
Proceedings of SODA '98, ACM-SIAM, 42–49, 1998.

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.

R. M. Corless, D. J. Jeffrey, M. B. Monagan and Pratibha. Two Perturbation Calculations in Fluid Mechanics using Large-expression Management. J. Symbolic Computation 4(4) 427–443, 1997.

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.

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

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.

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

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.

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.

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.

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
Preprint: Using Leslie matrices as an application of eigenvalues and eigenvectors in a first course in Linear Algebra.
Accepted August 2019 for the 2019 Maple Conference, Waterloo, Ontario, October 2019.
Talk Slides

Michael Monagan
Preprint: Internet Page Ranking Algorithms.
Appeared in The Maple Reporter, Maplesoft, Issue 3, March 2014.


Michael Monagan
Preprint: The Mortgage Payment Problem: Approximating a Discrete Process with a Differential Equation.
Appeared in The Maple Reporter, issue 2, February 2014.

Michael Monagan
Preprint: The House Warming Model
Appeared in The Maple Reporter, Maplesoft, Issue 1, January 2014.

Michael Monagan
Preprint: Groebner Bases: What are they and what are they useful for?
Appeared in The Maple Reporter, Maplesoft, Issue 10, October 2014.

Michael Monagan
Preprint: Measuring River Flow
Appeared in The Maple Reporter, Maplesoft, Issue 12, January 2013.

Michael Monagan.
Preprint: Teaching commutative algebra and algebraic geometry using computer algebra systems.
Appeared in Research Journal of Mathematics and Technology (RJMT) 2(1), 32–41, April 2013 (print version)
and in Electronic Journal of Mathematics and Technology (eJMT) 7(1), 52–61, February 2013 (electronic version).

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.

Aaron Bradord, Michael Monagan and Colin Percival.
Integer Factorization and Computing Discrete Logarithms in Maple.
Maple 2006 Conference Proceedings, pp. 2–13, MapleSoft, ISBN 1-897310-13-7, 2006.

Simon Lo, Michael Monagan, Roman Pearce
Generic Linear Algebra and Quotient Rings in Maple
Maple 2006 Conference Proceedings, pp. 179–188, 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.

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

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.