2013/10/8 Peter Bruin <pjbr...@gmail.com> > sage: Mod(2,6)==Mod(4,8) > True >
> sage: Mod(1,3)==Mod(2,4) > False > Wow, that's because the first two are compared in the common quotient Zmod(2) of Zmod(6) and Zmod(8), but a special case was made to disallow using the common quotient Zmod(1) of Zmod(3) and Zmod(4): sage: (Mod(2,6)-Mod(4,8)).parent() # This is a mathematically reasonable answer, and explains the "True" above. Ring of integers modulo 2 sage: sage.categories.pushout.pushout(Zmod(8), Zmod(6)) Ring of integers modulo 2 sage: (Mod(1,3)-Mod(2,4)).parent() # And here is the reason for the "False" above. TypeError: unsupported operand parent(s) for '-': 'Ring of integers modulo 3' and 'Ring of integers modulo 4' sage: sage.categories.pushout.pushout(Zmod(4), Zmod(3)) # And here is the reason for the TypeError above: CoercionException: Trivial quotient intersection. So it seems that sage.categories.pushout.pushout(Zmod(m), Zmod(n)) is Zmod(gcd(m,n)) unless m and n are coprime, in which case it raises an error. This looks like a rather inconsistent choice to me. > > 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. > -- 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.
