Dear Robert,
> The issue here is that comparison is useful outside of the purely
> mathematical context--for example if one wants to sort a list (for
> printing or searching) or use elements in sets or as keys in
> dictionaries or simply throw an error on an illegal value like 0.
Sure. But if python allows for it, I'd rather not to mix mathematics and
implementation detail. Is there a way to have a different order. In MuPAD we
had a function sysorder. Let me quote the doc:
1 - A unique internal order exists for almost all objects that are created
in a MuPAD session. sysorder compares two objects according to this in-
ternal order.
!! The exceptions are domains. (Note: ie: class in python language)
2 - One should not try and use the internal order to sort objects accord-
ing to specific criteria. E.g., its does not necessarily reflect the
natural ordering of numbers or strings. Further, the internal order
may differ between different MuPAD versions.
I like point 1) but implementing it relies on some feature of the memory
management (unique rep + systematic computation of some hash value).
As you can guess 2) was more a pain than anything else...
Nevertheless I retain the idea of two orders one which is mathematically sound
and the other one which is use for internal. Of course I'd rather keeping the
usual < <= notation for the mathematical one. My dream is that the internal
one is just an extension of the mathematical one when the later has no
meaning, but this is too mush asking. Ideed, the mathematical sound < can be
very time consuming to compute. Whereas for most data structure applications
you require that it is fast to compute. Is there any low level python
data structures using search trees on something equivalent ?
> Operations like these would be much more of a pain if most objects in
> Sage threw errors on comparison.
I agrees for sysorder. Not for <...
Cheers,
Florent
--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to sage-devel@googlegroups.com
To unsubscribe from this group, send email to
sage-devel-unsubscr...@googlegroups.com
For more options, visit this group at http://groups.google.com/group/sage-devel
URLs: http://www.sagemath.org
-~----------~----~----~----~------~----~------~--~---
