Algebraic independence of real numbers with low density of nonzero digits (survey)We study transcendence and algebraic independence of the value f(z;w(n))=∑n=1∞zw(n), where z is an algebraic number with 0<|z|<1 and w(n) (n=1,2,…) is a strictly increasing sequence of non...
Most number types represent some subset of the real numbers. From those types we expect functionality to compute the sign, absolute value or double approximations. In particular we can expect an order on such a type that reflects the order along the real axis. All these properties are gathered...
\quad • integrally\ closed ( or normal ): Every element of the fraction field of A that is the root of a monic polynomial in A[x] lies in A. \quad • maximal: There are no intermediate rings strictly between A and its fraction field. Various combinations of these properties can...
of properties analogous to those of integral rational numbers; however, the unique factorization theorem has no place in the theory of algebraic integers. To preserve unique factorization, Kummer introduced his so-called ideal numbers. The second trend is the theory of approximation of algebraic ...
This is an elementary introductory book into real algebraic and semi- algebraic sets. Chapter 1 starts with properties of real polynomials of one variable. Chapter 2 is a leisurely introduction to semi-algebraic sets. It contains the Tarski-Seidenberg theorem, the ojasiewicz inequality and the tria...
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PropertiesAll algebraic numbers are computable and so they are definable.The set of algebraic numbers is countable. Put simply, the list of whole numbers is "countable", and you can arrange the algebraic numbers in a 1-to-1 manner with whole numbers, so they are also countable....
An interval is a set of real numbers defined below [62]: (25.12)[a,b]={x|a≤x≤b}. If floating point arithmetic is used to evaluate these interval numbers there is no guarantee that the roundings of the bounds are performed conservatively.1 Rounded interval arithmetic (RIA) [1],[55...
An algebraic expression is a combination of letters called ___ and real numbers called ___ Algebraic Expressions The method of translating real-life problems into mathematical language is known as writing expressions. When compared with other expressions, equations, and inequalities...
2) real algebraic number 实代数数 1. In this paper,according to resultants,Descartes sign rules,real roots isolating and properties of real continuous functions,a new algorithm for determining the sign ofreal algebraic numbers was introduced. ...