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'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. Carl --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
