[GAP Forum] Real field

[Mathieu Dutour]

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