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From: Florian Weimer <fw@deneb.enyo.de>
Newsgroups: comp.lang.ada
Subject: Re: Large numbers (or is Ada the choice for me?)
Date: 10 Mar 2001 12:37:38 +0100
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dvdeug@x8b4e53cd.dhcp.okstate.edu (David Starner) writes:

> >Maybe a bad example - my point is that there exists a possibility of
> >generating numbers which are going to have an infinite number of decimal
> >places and memory only goes so far. Hence, you're going to need some sort of
> >approximation.
> 
> No, not if you want to expand the complexity. Every irrational number you 
> would probably need you could express in terms of pi, e, sqrt, cube roots,
> sin, and rational numbers.

It's true that most linear algebra problems can be expressed in
algebraic field extensions of, say, Q(pi, e), but there are some whose
solutions cannot be represented even by nested roots (for example,
eigenvalue problems).