[GAP Forum] Real field

[Alexander Hulpke]

Dear Mathieu, Dear Forum,

> 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)) ?

In the current form alas no. The `<' comparison for cyclotomics is  
handled in the kernel before it ever gets to the \< operation in the  
library. Thus, short of rewriting the kernel you are stuck with the  
code as-is. (The reason the comparison between cyclotomics does not  
respect the real numbers is that this actually  rather delicate to do  
if you want to do it in full generality.)
You could get around this by creating new ``wrapper'' objects that  
simply embed a cyclotomic but this will substantially increase memory  
use and decrease arithmetic performance.

What I would do is (as annoying as it looks) to use your own function  
for the comparison and replace < and > (i.e. <> and not <) with it.
(As your field is just Q(sqrt(5)) it is easy to get rational part and  
ER(5)-part and use squaring to reduce to a rational comparison.)

What this unfortunately cannot resolve is if you are using other  
peoples code (or library code) which should use the new ordering.

Sorry to not being able to offer a better solution.

     Alexander