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Semi-Regular Sequences over F2

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Año de publicación Ca. 2015
Idioma Inglés

Descripción: Abstract: The concept of semi-regular sequences was introduced in order to assess the complexity of Gröumlbner basis algorithms such as F4 for the solution of polynomial equations. Despite the experimental evidence that semi-regular sequences are common, it was unknown whether there existed semi-regular sequences for all n, except in extremely trivial situations. In the present work, I prove some results on the existence and non-existence of semi-regular sequences. It was observed by J. Schlather and T. Hodges that if an element of degree d in Β(n)-variables is semi-regular, then we must have n≤3d. In this thesis, I establish precisely when the elementary symmetric polynomial of degree d is semi-regular. In particular, when d=2t and n=3d, the elementary symmetric polynomial of degree d is semi-regular establishing that the bound given by J. Schlather and T. Hodges is sharp for infinitely many n. For the general case of existence of semi-regular sequences Bardet, Faug&egravere and Salvy conjecture that the proportion π(n, m, d1, . . . , dm) of semiregular sequences over F2 in the set Ε(n, m, d1, . . . , dm) of algebraic systems of mequations of degrees d1, . . . , dm in n-variables tends to 1 as n tends to infinity. In this work, I show that for a fixed choice of (m, d1, . . . , dm), we have that limn→∞ π(n, m, d1, .. . , dm ) — 0 showing that the conjecture is false in this case.
Citación recomendada (normas APA)
: Sergio Daladier Molina Aristizábal, "Semi-Regular Sequences over F2", Colombia:-, 2015. Consultado en línea en la Biblioteca Digital de Bogotá (https://www.bibliotecadigitaldebogota.gov.co/resources/3711543/), el día 2025-05-25.

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Fuente Biblioteca Virtual Banco de la República
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Año de publicación Ca. 2015
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Cobertura Colombia

Semi-Regular Sequences over F2

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