On Tue, Oct 8, 2013 at 1:08 PM, Peter Bruin <pjbr...@gmail.com> wrote: > Hello, > > >> > 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. > > > I agree too; I don't know why "pushout" raises an error if m, n are coprime > instead of returning the zero ring (just to make Mod(1, m) == Mod(1, n) > evaluate to False?), but it is inconsistent and hopefully unnecessary. The > code gives no good reason, just the following comment: > > # quotient by gcd would result in the trivial ring/group/... > # Rather than create the zero ring, we claim they can't be > merged > >> 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? > > > It is already a bit dubious to require that two ring elements be equal if > there is _some_ common non-zero ring that both of them can be coerced into; > I don't see why Mod(a,m) == Mod(b,n) should be True just because a and b > happen to be equal mod gcd(m,n) when that gcd is smaller than both m and n. > > I don't know if Sage uses exactly the same rules to find a common parent for > comparison as it does for arithmetic operations, but it certainly looks like > that is the case. I could imagine stricter rules for finding such a parent > for comparison. An algorithm that at least makes my list of examples work > is the following: > > 1) to evaluate "a == b": if A (resp. B) is the parent of a (resp. b) and P > is the push-out of A and B (tensor product in the case of rings), then "a == > b" yields True if and only if the images of a, b in P are equal *and* at > least one of A, B maps injectively to P
I may be misunderstanding where you're going with this, but are you proposing that sage: Mod(1,5) == 1 False # your proposal? -- since ZZ-->GF(5) is not injective This would be inconsistent with what is done in several other math software packages: PARI: ? Mod(2,5) == 2 %1 = 1 Magma: > GF(5)!2 eq 2; true Consistency with the choices of other systems for basic things like this has some relevance... -- William Stein Professor of Mathematics University of Washington http://wstein.org -- 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.
