Hi Marco, - making the "in" keyword treat infinity as a special case. >> > > Either Sage's RR has an infinity element or it does not. And in this case > the coercion framework correctly recognizes this and gives the output > accordingly. >
I think it is more subtle than that. The current RR does have _an_ infinity element, and this should of course map to Infinity in the InfinityRing under the canonical coercion map. What is not so clear to me is why the +infinity element of RR should compare _equal_ to Infinity (i.e. whether the fact that RR(oo) == oo yields True, as William noted, is a good thing). Actually, I'm starting to think that once you allow RR(oo) as a valid construction, you should indeed let the coercion framework evaluate RR(oo) == oo to True, *but* that the user should be able to construct a variant of RR that forbids RR(oo). I'm thinking of something like the following: sage: R = RealField(prec=53, exceptions=True) sage: R(oo) TypeError: unable to coerce +Infinity (<class 'sage.rings.infinity.PlusInfinity'>) to a real number sage: RR(oo) +infinity sage: oo in R False sage: oo in RR True sage: R(NaN) TypeError: unable to coerce <class 'sage.symbolic.constants.NotANumber'> to a real number sage: RR(NaN) NaN sage: 1/R(0.) ZeroDivisionError sage: 1/RR(0.) +infinity If you are to introduce special cases, then some things are much worse: > > sage: Zmod(5)(3) in ZZ > True > Hmm. This would almost be an argument for more restrictive equality and containment testing. I just discovered this: sage: Mod(2,6)==Mod(4,8) True On the other hand, the following extremely similar example gives the opposite (and in my opinion more correct) result: sage: Mod(1,3)==Mod(2,4) False Unfortunately it is hard to think of a simple rule that gives the desired behaviour in all of the following cases: sage: Mod(1, 3) == ZZ(1) True # current behaviour; certainly OK sage: Mod(1, 3) == QQ(1) False # current behaviour; probably OK, but True wouldn't be completely wrong sage: Mod(1, 3) == Mod(1, 4) False # current behaviour; certainly OK sage: Mod(1,3) == Mod(1, 6) True # current behaviour; probably OK, but False wouldn't be completely wrong sage: Mod(2, 6)==Mod(4, 8) False # currently yields True sage: 2/1 in ZZ True sage: Mod(3, 5) in ZZ False # currently yields True sage: Mod(1,3) in Zmod(6) False # currently yields True sage: Mod(2,4) in Zmod(6) False # currently yields True Peter -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
