Browsing Mathematics (Faculty of) by Supervisor "Schost, Eric"
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Algorithms for Linearly Recurrent Sequences of Truncated Polynomials
(University of Waterloo, 20210817)Linear recurrent sequences are those whose elements are defined as linear combinations of preceding elements, and finding recurrence relations is a fundamental problem in computer algebra. In this paper, we focus on sequences ... 
Analysis of Randomized Algorithms in Real Algebraic Geometry
(University of Waterloo, 20200902)Consider the problem of computing at least one point in each connected component of a smooth real algebraic set. This is a basic and important operation in real and semialgebraic geometry: it gives an upper bound on the ... 
Fast Algorithms for Finding the Characteristic Polynomial of a Rank2 Drinfeld Module
(University of Waterloo, 20180921)This thesis introduces a new Monte Carlo randomized algorithm for computing the characteristic polynomial of a rank2 Drinfeld module. We also introduce a deterministic algorithm that uses some ideas seen in Schoof's ... 
Homotopy algorithms for solving structured determinantal systems
(University of Waterloo, 20201217)Multivariate polynomial systems arising in numerous applications have special structures. In particular, determinantal structures and invariant systems appear in a wide range of applications such as in polynomial optimization ...