Results 61 to 70 of about 2,550,362 (221)
Dual Numbers and Operational Umbral Methods
Axioms, 2019 Dual numbers and their higher-order version are important tools for numerical computations, and in particular for finite difference calculus. Based on the relevant algebraic rules and matrix realizations of dual numbers, we present a novel point of view,
Nicolas Behr +3 more
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Splitting full matrix algebras over algebraic number fields
Journal of Algebra, 2012 Let K be an algebraic number field of degree d and discriminant D over Q. Let A be an associative algebra over K given by structure constants such that A is isomorphic to the algebra M_n(K) of n by n matrices over K for some positive integer n. Suppose that d, n and D are bounded.
Ivanyos, Gábor +2 more
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Counting Perron Numbers by Absolute Value [PDF]
, 2015 We count various classes of algebraic integers of fixed degree by their largest absolute value. The classes of integers considered include all algebraic integers, Perron numbers, totally real integers, and totally complex integers.
Calegari, Frank, Huang, Zili
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IEEE Access, 2019 As a part of the field of cryptography, rotation symmetric Boolean functions have rich cryptographic significance. In this paper, based on the knowledge of integer compositions, we present a new construction of odd-variable rotation symmetric Boolean ...
Yindong Chen +3 more
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Schanuel's Conjecture and Algebraic Roots of Exponential Polynomials [PDF]
, 2009 In this paper we prove that assuming Schanuel's conjecture, an exponential polynomial in one variable over the algebraic numbers has only finitely many algebraic solutions.
Shkop, Ahuva C.
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On two notions of complexity of algebraic numbers
, 2007 we derive new, improved lower bounds for the block complexity of an irrational algebraic number and for the number of digit changes in the b-ary expansion of an irrational algebraic number.
Bugeaud, Yann, Evertse, Jan-Hendrik
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Colour by Numbers: Solving Algebraic Equations Without Algebra
Spreadsheets in Education, 2005 A series of Excel models is described. They allow solution of f(x) = 0 by examining change of sign of function values. The function is graphed and change of sign easily detected by a change of colour. Prominent Excel features used are Names, Chart Wizard
Stephen J. Sugden
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Most General Algebraic Specifications for an Abstract Datatype of Rational Numbers
Scientific Annals of Computer Science, 2020 The notion of a most general algebraic specification of an arithmetical datatype of characteristic zero is introduced. Three examples of such specifications are given. A preference is formulated for a specification by means of infinitely many equations
Jan A. Bergstra
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Perturbation Methods for Acoustic Systems with Interval Parameters
Archives of Acoustics, 2008 The aim of the paper is to present a new algebraic system with strictly defined new interval numbers and specifically defined addition and multiplication operations.
Jerzy SKRZYPCZYK
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On algebraic approximations of certain algebraic numbers
Journal of Number Theory, 2003 The main result of the present paper consists of an effective improvement on Liouville's bound for the approximations by rational numbers to algebraic numbers of a special type. Namely, the author considers \(n\)-th roots of imaginary quadratic irrationals.
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