30 citations · 70 across the 24 of their papers we have counts for
27 papers · 1 filter
Computing Smith Forms Modulo of Sparse Matrices Faster Than Matrix Multiplication
Mark Giesbrecht
Let be a prime and the ring of integers modulo . Any is unimodularly equivalent to its Smith form \[ S=diag\bigl(\underbr…
On Factoring Quantum-Plane Skew Polynomials over
Mark Giesbrecht
We study algorithms for factorization in the quantum plane of (dilation) skew polynomials over a function field of a cyclotomic field: \[ \mathsf{R}=\mathsf{K}(t)[x;σ], \qquad \mat…
Fast Deterministic Normal Bases and Circulant Polynomial Determinants
Mark Giesbrecht, Armin Jamshidpey, Éric Schost
Let describe an algebraic extension of a finite field , where is a prime power and is monic and irreducible…
Refined bit complexity for the computation of at least one point per connected component of a smooth complete intersection real algebraic set
Jesse Elliott, Mark Giesbrecht, Edern Gillot +2
We refine the bit complexity analysis of an algorithm for the computation of at least one point per connected component of a smooth real algebraic set, yielding exponential speedup…
Subquadratic-Time Algorithms for Normal Bases
Mark Giesbrecht, Armin Jamshidpey, Éric Schost
For any finite Galois field extension , with Galois group , there exists an element whose orbit $G…
Efficient q-Integer Linear Decomposition of Multivariate Polynomials
Mark Giesbrecht, Hui Huang, George Labahn +1
We present two new algorithms for the computation of the q-integer linear decomposition of a multivariate polynomial. Such a decomposition is essential for the treatment of q-hyper…