Wow, this thread has generated a lot of discussion! :) On Mar 11, 2009, at 12:29 PM, Ralf Hemmecke wrote:
> Some more oil for the fire... > > sage: K=NumberField(x^2+1, 'a'); K > Number Field in a with defining polynomial x^2 + 1 > sage: a = K.0 > sage: a > a > sage: a*a > -1 > sage: a<1 > False > sage: a>1 > True > sage: 1<a > False > sage: 1>a > True > sage: version() > 'Sage Version 3.3, Release Date: 2009-02-21' > > Do I do something wrong or is autocoercion doing something strange > here? > In fact, I would have expected an error telling me that I cannot > compare > an element of K with any other thing. This is nothing to do with coercion. Coercion is what allows on to write 1 < 3/2 < 2. On the other hand, sage: K=NumberField(x^2+1, 'a'); K Number Field in a with defining polynomial x^2 + 1 sage: a = K.0 sage: one = K(1) sage: a*a -1 sage: one < a False sage: one > a True sage: one != a True 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. Operations like these would be much more of a pain if most objects in Sage threw errors on comparison. At the very least it's useful to be able to say to things are not equal (e.g. pi and 2 mod 5). Also, though some Parents (like the Integers) have an obvious ordering, others (say a permutation group) have many possible reasonable choices of orderings, and so we are already making an arbitrary choice to use < and > on them anyways. - 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 -~----------~----~----~----~------~----~------~--~---
