2014•Unpublished venueRequires access

Identifi cación del tipo primitivo de la celda de Voronoi en retículos euclidianos 4 dimensionales Identifi cation of the primitive type of the Voronoi cell in 4-dimensional euclidean lattice

Juan Miguel Velásquez Soto

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Abstract

We will show a mathematical algorithm in order to determine the Voronoi Type of a Euclidean lattice in dimension 4. It is an implementation of Charve's reduction theory of positive definite quadratic forms (see (3)). This algorithm helps us to recognize lattice Types in order to try to solve the general problem of finding the optimal lattice quantizer in dimension 4. Abstract We will show a mathematical algorithm in order to determine the Voronoi Type of a Euclidean lattice in dimension 4. It is an implementation of Charve's reduction theory of positive definite quadratic forms (see (3)). This algorithm helps us to recognize lattice Types in order to try to solve the general problem of finding the optimal lattice quantizer in dimension 4. Abstract We will show a mathematical algorithm in order to determine the Voronoi Type of a Euclidean lattice in dimension 4. It is an implementation of Charve's reduction theory of positive definite quadratic forms (see (3)). This algorithm helps us to recognize lattice Types in order to try to solve the general problem of finding the optimal lattice quantizer in dimension 4. Abstract We will show a mathematical algorithm in order to determine the Voronoi Type of a Euclidean lattice in dimension 4. It is an implementation of Charve's reduction theory of positive definite quadratic forms (see (3)). This algorithm helps us to recognize lattice Types in order to try to solve the general problem of finding the optimal lattice quantizer in dimension 4. Abstract We will show a mathematical algorithm in order to determine the Voronoi Type of a Euclidean lattice in dimension 4. It is an implementation of Charve's reduction theory of positive definite quadratic forms (see (3)). This algorithm helps us to recognize lattice Types in order to try to solve the general problem of finding the optimal lattice quantizer in dimension 4. Abstract We will show a mathematical algorithm in order to determine the Voronoi Type of a Euclidean lattice in dimension 4. It is an implementation of Charve's reduction theory of positive definite quadratic forms (see (3)). This algorithm helps us to recognize lattice Types in order to try to solve the general problem of finding the optimal lattice quantizer in dimension 4.

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What this paper is about

We will show a mathematical algorithm in order to determine the Voronoi Type of a Euclidean lattice in dimension 4. It is an implementation of Charve's reduction theory of positive definite quadratic forms (see (3)). This algorithm helps us to recognize lattice Types in order to try to solve the general problem of finding the optimal lattice quantizer in dimension 4. Abstract We will show a mathematical algorithm in order to determine the Voronoi Type of a Euclidean lattice in dimension 4. It is an implementation of Charve's reduction theory of positive definite quadratic forms (see (3)). This algorithm helps us to recognize lattice Types in order to try to solve the general problem of finding the optimal lattice quantizer in dimension 4. Abstract We will show a mathematical algorithm in order to determine the Voronoi Type of a Euclidean lattice in dimension 4. It is an implementation of Charve's reduction theory of positive definite quadratic forms (see (3)). This algorithm helps us to recognize lattice Types in order to try to solve the general problem of finding the optimal lattice quantizer in dimension 4. Abstract We will show a mathematical algorithm in order to determine the Voronoi Type of a Euclidean lattice in dimension 4. It is an implementation of Charve's reduction theory of positive definite quadratic forms (see (3)). This algorithm helps us to recognize lattice Types in order to try to solve the general problem of finding the optimal lattice quantizer in dimension 4. Abstract We will show a mathematical algorithm in order to determine the Voronoi Type of a Euclidean lattice in dimension 4. It is an implementation of Charve's reduction theory of positive definite quadratic forms (see (3)). This algorithm helps us to recognize lattice Types in order to try to solve the general problem of finding the optimal lattice quantizer in dimension 4. Abstract We will show a mathematical algorithm in order to determine the Voronoi Type of a Euclidean lattice in dimension 4. It is an implementation of Charve's reduction theory of positive definite quadratic forms (see (3)). This algorithm helps us to recognize lattice Types in order to try to solve the general problem of finding the optimal lattice quantizer in dimension 4.

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Available abstract

We will show a mathematical algorithm in order to determine the Voronoi Type of a Euclidean lattice in dimension 4. It is an implementation of Charve's reduction theory of positive definite quadratic forms (see (3)). This algorithm helps us to recognize lattice Types in order to try to solve the general problem of finding the optimal lattice quantizer in dimension 4. Abstract We will show a mathematical algorithm in order to determine the Voronoi Type of a Euclidean lattice in dimension 4. It is an implementation of Charve's reduction theory of positive definite quadratic forms (see (3)). This algorithm helps us to recognize lattice Types in order to try to solve the general problem of finding the optimal lattice quantizer in dimension 4. Abstract We will show a mathematical algorithm in order to determine the Voronoi Type of a Euclidean lattice in dimension 4. It is an implementation of Charve's reduction theory of positive definite quadratic forms (see (3)). This algorithm helps us to recognize lattice Types in order to try to solve the general problem of finding the optimal lattice quantizer in dimension 4. Abstract We will show a mathematical algorithm in order to determine the Voronoi Type of a Euclidean lattice in dimension 4. It is an implementation of Charve's reduction theory of positive definite quadratic forms (see (3)). This algorithm helps us to recognize lattice Types in order to try to solve the general problem of finding the optimal lattice quantizer in dimension 4. Abstract We will show a mathematical algorithm in order to determine the Voronoi Type of a Euclidean lattice in dimension 4. It is an implementation of Charve's reduction theory of positive definite quadratic forms (see (3)). This algorithm helps us to recognize lattice Types in order to try to solve the general problem of finding the optimal lattice quantizer in dimension 4. Abstract We will show a mathematical algorithm in order to determine the Voronoi Type of a Euclidean lattice in dimension 4. It is an implementation of Charve's reduction theory of positive definite quadratic forms (see (3)). This algorithm helps us to recognize lattice Types in order to try to solve the general problem of finding the optimal lattice quantizer in dimension 4.

Key concepts: Voronoi diagram, Lattice (music), Mathematics, Euclidean geometry, Euclidean distance, Dimension (graph theory), Combinatorics, Quadratic equation

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Identifi cación del tipo primitivo de la celda de Voronoi en retículos euclidianos 4 dimensionales Identifi cation of the primitive type of the Voronoi cell in 4-dimensional euclidean lattice — Research Paper | ScholarLens