A Verified Implementation of Algebraic Numbers in Isabelle/HOL
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DOI: 10.1007/s10817-018-09504-w
Abstract: We formalize algebraic numbers in Isabelle/HOL. Our development serves as a verified implementation of algebraic operations on real and complex numbers. We moreover provide algorithms that can identify all the real or complex roots of… read more here.
Keywords: implementation algebraic; algebraic numbers; verified implementation; numbers isabelle ... See more keywords
Simplex-Module Algorithm for Expansion of Algebraic Numbers in Multidimensional Continued Fractions
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DOI: 10.1007/s10958-017-3506-1
Abstract: The simplex-module algorithm for expansion of algebraic numbers α = (α1, . . . , αd) in multidimensional continued fractions is suggested. The method is based on minimal rational simplices s, where α ∈ s,… read more here.
Keywords: algebraic numbers; simplex module; algorithm expansion; module algorithm ... See more keywords
A dynamical construction of small totally p-adic algebraic numbers
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DOI: 10.1016/j.jnt.2019.01.021
Abstract: We give a dynamical construction of an infinite sequence of distinct totally $p$-adic algebraic numbers whose Weil heights tend to the limit $\frac{\log p}{p-1}$, thus giving a new proof of a result of Bombieri-Zannier. The… read more here.
Keywords: totally adic; construction small; dynamical construction; algebraic numbers ... See more keywords
On the Degree of Product of Two Algebraic Numbers
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DOI: 10.3390/math11092131
Abstract: A triplet (a,b,c) of positive integers is said to be product-feasible if there exist algebraic numbers α, β and γ of degrees (over Q) a, b and c, respectively, such that αβγ=1. This work extends… read more here.
Keywords: degree product; product; algebraic numbers; product feasible ... See more keywords