30 citations · 70 across the 24 of their papers we have counts for
6 papers · 1 filter
Faster Sparse Multivariate Polynomial Interpolation of Straight-Line Programs
Andrew Arnold, Mark Giesbrecht, Daniel S. Roche
Given a straight-line program whose output is a polynomial function of the inputs, we present a new algorithm to compute a concise representation of that unknown function. Our algo…
Computing GCRDs of Approximate Differential Polynomials
Mark Giesbrecht, Joseph Haraldson
Differential (Ore) type polynomials with approximate polynomial coefficients are introduced. These provide a useful representation of approximate differential operators with a stro…
Factoring Differential Operators in n Variables
Mark Giesbrecht, Albert Heinle, Viktor Levandovskyy
In this paper, we present a new algorithm and an experimental implementation for factoring elements in the polynomial n'th Weyl algebra, the polynomial n'th shift algebra, and ZZ^n…
Ranks of Quotients, Remainders and -Adic Digits of Matrices
Mustafa Elsheikh, Andy Novocin, Mark Giesbrecht
For a prime and a matrix , write as where the remainder and quotient operations are a…
Sparse interpolation over finite fields via low-order roots of unity
Andrew Arnold, Mark Giesbrecht, Daniel S. Roche
We present a new Monte Carlo algorithm for the interpolation of a straight-line program as a sparse polynomial over an arbitrary finite field of size . We assume a priori bo…
Relating -adic eigenvalues and the local Smith normal form
Mustafa Elsheikh, Mark Giesbrecht
Conditions are established under which the -adic valuations of the invariant factors (diagonal entries of the Smith form) of an integer matrix are equal to the -adic valuatio…