Publications related to Transcendental extension

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On compact representations of Voronoi cells of lattices

Matthias Schymura, Christoph Hunkenschröder

In a seminal work, Micciancio and Voulgaris (SIAM J Comput 42(3):1364-1391, 2013) described a deterministic single-exponential time algorithm for the closest vector problem (CVP) on lattices. It is based on the computation of the Voronoi cell of the given ...

SPRINGER HEIDELBERG2020

New Results in Integer and Lattice Programming

Christoph Hunkenschröder

An integer program (IP) is a problem of the form

\min \{f(x) : \, Ax = b, \ l \leq x \leq u, \ x \in \Z^n\}

, where

A \in \Z^{m \times n}

b \in \Z^m

l,u \in \Z^n

, and

f: \Z^n \rightarrow \Z

is a separable convex objective function. The problem o ...

EPFL2020

On compact representations of Voronoi cells of lattices

Matthias Schymura, Christoph Hunkenschröder

In a seminal work, Micciancio & Voulgaris (2010) described a deterministic single-exponential time algorithm for the Closest Vector Problem (CVP) on lattices. It is based on the computation of the Voronoi cell of the given lattice and thus may need exponen ...

SPRINGER INTERNATIONAL PUBLISHING AG2018

The Particle-In-Fourier (PIF) Approach Applied to Gyrokinetic Simulations

Laurent Villard, Stephan Brunner, Emmanuel Lanti, Noé Thomas Elie Ohana, Claudio Gheller, Aaron Lewis Scheinberg

A widespread method for gyrokinetic simulations relies on the discretization of distribution functions with numerical markers. The electromagnetic field is typically represented on a grid by finite differences or finite elements (Particle-In-Cell, PIC). Wh ...

2017

An efficient deterministic test for Kloosterman sum zeros

Robert Granger

We propose a simple deterministic test for deciding whether or not a non-zero element

a \in \mathbb{F}_{2^n}

\mathbb{F}_{3^n}

is a zero of the corresponding Kloosterman sum over these fields, and analyse its complexity. The test seems to have been o ...

American Mathematical Society2014

Diagonal Quartic Surfaces And Transcendental Elements Of The Brauer Group

Evis Ieronymou

We exhibit central simple algebras over the function field of a diagonal quartic surface over the complex numbers that represent the 2-torsion part of its Brauer group. We investigate whether the 2-primary part of the Brauer group of a diagonal quartic sur ...

Cambridge University Press2010

Gomory-chvatal cutting planes and the elementary closure of polyhedra

Friedrich Eisenbrand

The elementary closure P'; of a polyhedrom P is the intersection of P with all its Gomory-Chvátal cutting planes. P'; is a rational polyhedron provided that P is rational. The Chvátal-Gomory procedure is the iterative application of the elementary closure ...

Universität des Saarlandes2000

New Results in Integer and Lattice Programming

Christoph Hunkenschröder

An integer program (IP) is a problem of the form

\min \{f(x) : \, Ax = b, \ l \leq x \leq u, \ x \in \Z^n\}

, where

A \in \Z^{m \times n}

b \in \Z^m

l,u \in \Z^n

, and

f: \Z^n \rightarrow \Z

is a separable convex objective function. The problem o ...

EPFL2020

An efficient deterministic test for Kloosterman sum zeros

Robert Granger

We propose a simple deterministic test for deciding whether or not a non-zero element

a \in \mathbb{F}_{2^n}

\mathbb{F}_{3^n}

is a zero of the corresponding Kloosterman sum over these fields, and analyse its complexity. The test seems to have been o ...

American Mathematical Society2014

Transcendental extension

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On compact representations of Voronoi cells of lattices

New Results in Integer and Lattice Programming

On compact representations of Voronoi cells of lattices

The Particle-In-Fourier (PIF) Approach Applied to Gyrokinetic Simulations

Lower bounds for Pythagoras numbers of function fields

An efficient deterministic test for Kloosterman sum zeros

Sound Compilation of Reals

The Truncated Tracial Moment Problem

Diagonal Quartic Surfaces And Transcendental Elements Of The Brauer Group

Gomory-chvatal cutting planes and the elementary closure of polyhedra

On compact representations of Voronoi cells of lattices

New Results in Integer and Lattice Programming

Gomory-chvatal cutting planes and the elementary closure of polyhedra

An efficient deterministic test for Kloosterman sum zeros

Sound Compilation of Reals

The Truncated Tracial Moment Problem

Diagonal Quartic Surfaces And Transcendental Elements Of The Brauer Group

The Particle-In-Fourier (PIF) Approach Applied to Gyrokinetic Simulations

Lower bounds for Pythagoras numbers of function fields

On compact representations of Voronoi cells of lattices