On 03/12/2009 04:34 AM, Robert Bradshaw wrote: > Wow, this thread has generated a lot of discussion! :)
I am sorry for having started this. :-) > 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. Really? sage: parent(1) Integer Ring sage: parent(a) Number Field in a with defining polynomial x^2 + 1 Are you saying that I can compare an integer with an element of K without coercion. Where can I find the code for this? > Coercion is what allows on to > write 1 < 3/2 < 2. On the other hand, Why is 'a' so different from 3/2? > 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 Aha... that means Sage just consideres K as an ordered set, but the order is not necessarily compatible with operations K. Of course K is not an ordered field. By the way... there is a bug already mentioned earlier in this thread. sage: a>one True So > is not even an order on the *set* K, because a is not the same as one. > --for example if one wants to sort a list (for > printing or searching) or use elements in sets or as keys in > dictionaries OK. > or simply throw an error on an illegal value like 0. That has to do with a zero-test not ordering. Ralf --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
