Browsing Theses by Supervisor "Schost, Eric"
Now showing items 1-4 of 4
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Algorithms for Linearly Recurrent Sequences of Truncated Polynomials
(University of Waterloo, 2021-08-17)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, 2020-09-02)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 semi-algebraic geometry: it gives an upper bound on the ... -
Fast Algorithms for Finding the Characteristic Polynomial of a Rank-2 Drinfeld Module
(University of Waterloo, 2018-09-21)This thesis introduces a new Monte Carlo randomized algorithm for computing the characteristic polynomial of a rank-2 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, 2020-12-17)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 ...