On 8 October 2013 20:21, Marco Streng <marco.str...@gmail.com> wrote: > > > > 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.
I agree, and anyone who knows enough to ever type "pushout" will certainly not be happy. On the otherhand, will anyone be happy if for coprime m and n, every comparison Mod(a,m)==Mod(b,n) is True since the only place they can be compared is the trivial ring? John > > >> >> >> 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. -- 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.
