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05/12/2023
Dimension results for extremal-generic polynomial systems over complete toric varieties
We study polynomial systems with prescribed monomial supports in the Cox...
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03/14/2022
Computing a Group Action from the Class Field Theory of Imaginary Hyperelliptic Function Fields
We explore algorithmic aspects of a simply transitive commutative group ...
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07/06/2020
Refined Analysis of the Asymptotic Complexity of the Number Field Sieve
The classical heuristic complexity of the Number Field Sieve (NFS) is th...
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11/20/2018
A Fast Randomized Geometric Algorithm for Computing Riemann-Roch Spaces
We propose a probabilistic Las Vegas variant of Brill-Noether's algorith...
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06/15/2018
Counting points on genus-3 hyperelliptic curves with explicit real multiplication
We propose a Las Vegas probabilistic algorithm to compute the zeta funct...
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10/10/2017
Improved Complexity Bounds for Counting Points on Hyperelliptic Curves
We present a probabilistic Las Vegas algorithm for computing the local z...
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05/19/2016
Computing Small Certificates of Inconsistency of Quadratic Fewnomial Systems
Bézout 's theorem states that dense generic systems of n multivariate qu...
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05/09/2016
Critical Point Computations on Smooth Varieties: Degree and Complexity bounds
Let V ⊂ C n be an equidimensional algebraic set and g be an n-variate po...
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10/19/2015