Re: Irrational numbers

From: Marcel Martin (mm_at_ellipsa.no.spam.net)
Date: 11/03/03 

Date: Mon, 03 Nov 2003 23:21:37 +0100

Mok-Kong Shen a écrit :
>
> Marcel Martin wrote:
> >
> > Though I do not quite understand where you want to go, I suppose that
> > the relation C. Percival was talking of is a polynomial of degree 4.
> > If so, it is not difficult to obtain, multiply
> >
> > x - (a sqrt(p) + b sqrt(q) + c)
> > by x - (a sqrt(p) - b sqrt(q) + c)
> >
> > this eleminates "sqrt(q)". Then you multiply the obtained polynomial
> > by its 'conjugate' on sqrt(p). And you get a degree-4 polynomial of
> > which the coefficients belong to the same set than a, b and c.
>
> Suppose that relation is '(polynomial of x) = 0'.

Yes. But even if it was P(x) = u, setting Q(x) = P(x) - u would
give a '(polynomial of x) = 0'.

> Substituting, one would get a non-linear equation
> in the five unknowns. How does one solve that?

I don't know. Maybe using lattices (but I am the last one who
can help you on that).
In my previous post, I just wanted to show you that the relation
pointed out by C. Percival (assuming this is what he meant) exists
and is not complicated from a theoretical point of view.

mm

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