On Mar 12, 2009, at 11:23 AM, Carl Witty wrote: > On Thu, Mar 12, 2009 at 12:57 AM, Florent Hivert > <florent.hiv...@univ-rouen.fr> wrote: >> >> 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: > ... >> 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 ? > > +1 for having < refer to mathematical orderings (so it raises an > exception where no standard mathematical ordering is defined), and for > having a separate sysorder comparison for the somewhat-rare cases when > you really want to sort.
I could actually go for this as well. Python provides richcmp (used for < and friends) and cmp, and I think the later could be the "sysorder" (which would hopefully be less arbitrary than a memory address, specifically respect the mathematical notions of equality at least) and the former the mathematical order. On the other hand, I would rather GF(5)(1) == pi return False than raise an error. I would also still advocate using coercions, so GF(5)(1) == 1 returns True (though the argument that RealField(20)(pi) == RealField(50)(pi) returns False is a good one.) > I've think I've voted the other way in previous discussions of this > topic. I changed my mind because: > > 1) I've seen a lot more mathematicians be confused/annoyed by having > defined orderings between mathematically-unordered objects since then > > 2) I used to think that Python more-or-less required that all objects > be ordered. I don't remember where I got that idea, but it's wrong; > somebody pointed out that Python-native complex numbers are unordered. > > The standard low-level Python data structures are the list and the > dictionary; neither depends on orderings. (Dictionaries are hash > tables, so they use hashes and equality.) I don't know of any > contexts where Python implicitly depends on orderings. > > This has been discussed before; for example, see > http://groups.google.com/group/sage-devel/browse_thread/thread/ > fa1c998160d41f62/bc550ad42bc08cc0?lnk=gst#bc550ad42bc08cc0 > > My suggestion in that thread of using "cmp" for sysorder is possible, > but I doubt if it's a good idea... it makes it easy to make > implementation mistakes, because by default cmp() and < use the same > code. This could be changed, and probably would be a good thing (though a lot of work--I don't know how much depends on the current semantics). The cmp code isn't the prettiest right now. But I think this is a distinct topic than whether or not to use coercions in comparison. - Robert --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
