The authors examine technology's current and future influence on trading and the structure
of markets. Order processing speeds and new algorithmic tools have driven market volumes …

We present algorithms to compute the Smith Normal Form of matrices over two families of
local rings. The algorithms use the black-box model which is suitable for sparse and structured …

We present an algorithm for factoring a polynomial, f , in one variable with rational coefficients.
Our algorithm is a variant of the Belabas [Belabas] version of the van Hoeij [van Hoeij] …

For a prime $p$ and a matrix $A \in \mathbb{Z}^{n \times n}$, write $A$ as $A = p (A \,\mathrm{quo}\,
p) + (A \,\mathrm{rem}\, p)$ where the remainder and quotient operations are …

… David Saunders, and Andy Novocin. Chapter 3 is based on collaboration with Mark Giesbrecht,
and B. … Chapter 6 is based on collaboration with Mark Giesbrecht, and Andy Novocin. …

… At that time Andy Novocin began implementing the new algorithm Mark van Hoeij and he
had developed [4] for factorization of polynomials over the integers. Of course this meant that …

We revisit a divide-and-conquer algorithm, originally described by Brent and Kung for
composition of power series, showing that it can be applied practically to composition of …

… The latter is achieved with an algorithm implemented by Andy Novocin and the author [7]. …
The Z[x] module has a first implementation of the new factorisation algorithm of Novocin and …

We investigate two practical divide-and-conquer style algorithms for univariate polynomial
arithmetic. First we revisit an algorithm originally described by Brent and Kung for composition …

Interpolation is the process of learning an unknown polynomial f from some set of its evaluations.
We consider the interpolation of a sparse polynomial, ie, where f is comprised of a small…