Sage's "in" is not a mathematical "\in", Sage's "RR" is not the field of > real numbers. Peter is arguing to make them behave more like they are. > Others are arguing not to change these things for various reasons. (And I > will not get myself tangled up in that, since I don't know enough about > floating point standards, nor do I know the reasons behind Sage's > definition of "in".) > > As a user of Sage who is also trying to convert others to Sage, I would advocate making the "in" keyword behave like "\in" and having RR and other fields behave like their mathematical counterparts. As a matter of programming, this can possibly be achieved by having the programer-friendly implementation of RR etc be the primary implementations and then writing user-friendly wrappers to these that behave intuitively. This could be something like Peter is advocating with exceptions = True.
My reading of this thread is that the problem extends beyond the infinity ring, and that comparisons in general may not behave in an intuitive mathematical way. For example: sage: GF(2)(1) == 1 True sage: GF(2)(3) == 1 True I see why these work on an implementation level, but this is strange: sage: A = matrix(GF(2), 2, [2,0,0,1]) sage: B = matrix(2, [2,0,0,1]) sage: A == B True sage: A.rank() 1 sage: B.rank() 2 So we have a non-invertible matrix equal to an invertible matrix. I think for most users, if two objects evaluate as equal, they should behave the same under operations like * and +. This example breaks that assumption. Also strange: sage: C = matrix(GF(2), 2, [1, 0, 0, 1]) sage: C in GL(2,RR) True I think we'd benefit generally from thinking about use cases involving novice Sage users and modifying the coercion framework (or whichever component is involved here) to deal with these use cases. -Greg -- 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.
