Research

Multiplicative independence of algebraic numbers and expressions


Reference:

Richardson, D., 2001. Multiplicative independence of algebraic numbers and expressions. Journal of Pure and Applied Algebra, 164 (1-2), pp. 231-245.

Related documents:

This repository does not currently have the full-text of this item.
You may be able to access a copy if URLs are provided below.

Official URL:

http://dx.doi.org/10.1016/S0022-4049(00)00156-0

Abstract

A list of complex numbers is multiplicatively independent if no integral-exponent power product of them is equal to 1, unless all exponents are zero. A method of deciding multiplicative independence is given, for complex numbers in a finitely generated field, with given proper set of generators. This is based on computing an upper bound on absolute value for possible minimal non-zero integral exponents. As a consequence of this, a solution which does not use numerical approximation, depending on the Schanuel conjecture, can be given for the problem of deciding equality between two numbers given as closed-form. expressions using exp, log, radicals, and field operations. It is argued, however, that an efficient solution of this problem is likely to use numerical approximation, together with an upper bound, depending on the syntax of the expressions for the numbers, for the amount of precision needed to distinguish the numbers if they are not the same. A conjecture is stated (the uniformity conjecture) which attempts to provide such an upper bound.

Details

Item Type Articles
CreatorsRichardson, D.
DOI10.1016/S0022-4049(00)00156-0
DepartmentsFaculty of Science > Computer Science
RefereedYes
StatusPublished
ID Code5607
Additional InformationID number: ISI:000171099100015

Export

Actions (login required)

View Item