I am a PhD student in the Symbolic Computation Group [web] in David R. Cheriton School of Computer Science [web], Faculty of Mathematics [web] at the University of Waterloo [web]. My supervisor is Mark Giesbrecht [web].
I finished my master's degree [web] at the Department of Computing and Software [web] at McMaster University [web], Hamilton, Canada. My supervisors were Spencer Smith [web] and Jacques Carette [web]. I earned my bachelor's degree [web] from Al-Azhar University, Cairo, Egypt.
I work on algorithms to compute Smith normal form [wiki]
of (mostly sparse) matrices over local rings [wiki] such as the integers modulo
prime power and polynomials modulo power of an irreducible polynomial.
A theme of my work is trying to link the invariant factors and the
determinantal divisors to eigenvalues over p-adic [wiki] field extensions.
I am also interested in proving some properties about matrices
under the application of the remainder operator [wiki].
Click here [web] to see my publications on Google Scholar.
Fast Computation of Smith Normal Form of Sparse Matrices Over Local Rings [PDF]
Improved Computation of Random Nullspace Vectors: Sparse Matrices, Small Finite Fields [PDF]
Ranks of Quotients, Remainders, and p-Adic Digits of Matrices [PDF]
Computing Invariant Factors using p-adic Eigenvalues [PDF]
Ranks of Remainder Matrices [PDF]
Rank Reduction and Local Smith Form [PDF]
Click here [web] to go to my LinkedIn profile.
Click here [web] to get my contact information.
Created on September 28, 2010. Last edited on October 1st, 2015 using Emacs.