[GAP Forum] Real field

[David Joyner]

Frank Luebeck has written some utilities for doing just this type of thing:

http://www.math.rwth-aachen.de/~Frank.Luebeck/gap/FUtil/index.html

Perhaps they will help.

++++++++++++++++++++++++++++++++++++++++++++++++

On 8/7/07, Mathieu Dutour <Mathieu.Dutour at ens.fr> wrote:
> Thank you for this reference I will look at it.
>
> But the main problem is not there. I have my existing
> software for polyhedral computations of polytope defined over
> the rational numbers. I want to work with 600-cell, 120-cell
> whose vertices are defined over Q(Sqrt(5)) preferably without
> having to modify the code.
>
> The question is on the structure of GAP itself. Is it possible
> to redefine the ">" test so that it is the natural order
> of the real field, which is used, when comparing two elements
> of Q(Sqrt(5)) ?
>
>   Mathieu
>
> On Tue, Aug 07, 2007 at 12:19:20PM +0300, pasechni at ima.umn.edu wrote:
> >> One can implement in GAP exact algorithms for real algebraic numbers, as described e.g. in the recent monograph Algorithms in Real Algebraic Geometry by Basu, Pollack, and Roy (there is also an online version of it on the net).
> >> But this is quite a bit of work.
> >> HTH,
> >> Dima
> >>
> >> -original message-
> >> Subject: [GAP Forum] Real field
> >> From: "Mathieu Dutour" <Mathieu.Dutour at ens.fr>
> >> Date: 06/08/2007 13:37
> >>
> >> Dear all,
> >>
> >> I would like to work with numbers of the form (1+Sqrt(5))/2
> >> in order to work with 600-cell, 120-cell and such kind of
> >> polytopes.
> >>
> >> Currently such numbers are coded in GAP with cyclotomic
> >> extensions, which means that we have no comparison and functions
> >> like (1+Sqrt(5))/2 > 30  does not return what I would like.
> >>
> >> Is there a way to code a real field like Q(Sqrt(5)) in GAP
> >> so as to have reliable comparison operator?
> >>
> >> --
> >> Mathieu Dutour Sikiric               Researcher in Mathematics
> >> Telephone:.(+385)1 4571 237  and Computer Science
> >> Cell Phone: (+385)9 19 36 30 80      Laboratory of satellite oceanography
> >> E-mail: Mathieu.Dutour at ens.fr        Rudjer Boskovic Institute
> >> http://www.liga.ens.fr/~dutour       Zagreb Croatia
> >> skype name: mathieudutour
> >>
> >> _______________________________________________
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>
> --
> Mathieu Dutour Sikiric          Researcher in Mathematics
> Telephone:.(+385)1 4571 237     and Computer Science
> Cell Phone: (+385)9 19 36 30 80 Laboratory of satellite oceanography
> E-mail: Mathieu.Dutour at ens.fr   Rudjer Boskovic Institute
> http://www.liga.ens.fr/~dutour  Zagreb Croatia
> skype name: mathieudutour
>
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