## Publications and Preprints

#### 2011 to present

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: 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.

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.

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.

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 **Z***n*

*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.

Submitted May 2019 to 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

Submitted August 2012 to eJMT (electronic Journal of Mathematics and Technology).

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.