[boost] Constructible numbers? (was: Re: Interest in an arbitrary precision library?)

From: Daryle Walker (darylew_at_[hidden])
Date: 2005-09-14 01:12:03

On 9/13/05 8:17 AM, "Guillaume Melquiond" <guillaume.melquiond_at_[hidden]>
wrote:

[SNIP]
> [1] Rational numbers are constructible. Irrational numbers are
> constructible. Pi, E, and other common mathematical constants are
> constructible. Numbers derived from them are constructible. Omega (the
> halting problem encoding) is not constructible.

I couldn't find this mathematical definition of "constructible;" is it known
by another term?  (The only definition I know of is for those ancient Greek
compass & [unmarked] straight-edge puzzles.  But all the associated numbers
for those are a subset of algebraic numbers.  By that definition, pi and e
are not constructible, since they're transcendental.)  I looked in the
Wikipedia, BTW.  But maybe you mistyped; rational and irrational numbers
cover _every_ real number, so you didn't have to specify pi, e, common
constants, or derived values.

-- 
Daryle Walker
Mac, Internet, and Video Game Junkie
darylew AT hotmail DOT com