### Page URL:

http://www.maths.warwickac.uk/~masfaw/preprint.htmlPlease refer to the original URL for this document as it may be more up-to-date than the version you have.

### Publications:

*Modular Equations and Eta Evaluations*- Aust. Math. Soc. Gazette**,**Vol. 31 No. 1, Mar 2004, pp. 43--47.- Evaluation of the Dedekind Eta Function, (with Robin Chapman), Canad. Math. Bull. Vol. 49 (1), 2006, pp. 21--35.
*Schlaefli Modular Equations for Generalized Weber Functions*Ramanujan Journal, 15, 2008, pp. 435-468.- A New Class of Modular Equation for Weber Functions International Journal of Number Theory, Vol. 3, No. 1, (2007), pp. 141-157.
- An Identity for the Eta Function Involving Two Independent Complex Variables, (with Bruce Berndt), Bulletin of the London Mathematical Society 2007 39(2), pp. 345-347.
- Algorithm M4RM: Efficient Multiplication of Dense Matrices over GF(2), (with Gregory Bard and Martin Albrecht), Transactions on Mathematical Software, vol 37, (1), Jan 2010. pp 9:1--9:14.
- A New Class of Theta Function Identities in Two Variables (with Robin Chapman and Pee Choon Toh), Journal of Combinatorics and Number Theory, (vol 2, issue 3), pp 201--208.
- Congruent number theta coefficients to 10^12 (with Gonzalo Tornaria and Mark Watkins), Guillaume Hanrot, Francois-Morain, Emmanuel Thome (Eds.): Algorithmic Number Theory, 9th International Symposium, ANTS-IX, Nancy, France, July 19-23, 2010. Proceedings. Lecture Notes in Computer Science 6197 Springer 2010. pp. 186-200.
- Fast Library for Number Theory: an introduction, Mathematical Software - ICMS 2010 Third International Congress on Mathematical Software, Kobe, Japan, September 13-17, 2010, Proceedings Series: Lecture Notes in Computer Science, Vol. 6327, pp 88--91.
- Practical polynomial factoring in polynomial time (with Andy Novocin and Mark van Hoeij), Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation, San Jose, CA, June 8--11, 2011.
- Practical divide-and-conquer algorithms for polynomial arithmetic (with Andy Novocin) Proceedings 13th International Workshop, CASC 2011, Kassel, Germany, September 2011, Lecture Notes in Computer Science, Vol. 6885, pp 200--214.
- A one line factoring algorithm (positive rev iew) Journal of the Australian Mathematical Societey, vol. 92, (1), 2012, pp 61--69.

### Preprints:

- Class invariants from a new kind of Weber-like modular equation
- On the complexity of polynomial factorisation (with Andy Novocin and Mark van Hoeij)
- A generalized theta identity in two $\mathcal{H}_g$ variables, (with Marco Streng)

### Software Projects:

- FLINT : Fast Library for Number Theory
- MPIR : Multiple Precision Integers and Rationals
- BSDNT : BSD licensed Multiple Precision Integer Library
- Cesium : A new programming language for mathematicians.

### Expositions:

- Computing local Artin symbols in MAGMA
- Obstructions to the Hasse Principle for Curves: Covers of Elliptic Curves
- Notes on the GL_2 Main Conjecture a la
Coates, Fukaya, Kato, Sujatha and Venjakob (2004)

- A Guide to Theta Functions and Weber's Modular Equations
- Complex multiplication and explicit class field theory

### PhD Thesis, Macquarie University:

### Other Notes:

**Comments and Corrections:** Please email them to me.

Last Updated: (Jan 24, 2013)