+1 On Nov 22, 9:00 am, Robert Bradshaw <rober...@math.washington.edu> wrote: > On Mon, Nov 21, 2011 at 11:36 PM, William Stein <wst...@gmail.com> wrote: > > On Mon, Nov 21, 2011 at 4:50 PM, David Roe <r...@math.harvard.edu> wrote: > >> The coercion graph in Sage is supposed to be transitive. This > >> assumption is explicit in the documentation of sage.structure.coerce > >> for example. But we have the following: > > >> sage: R = Zmod(6) > >> sage: S = Zmod(3) > >> sage: T = GF(3) > >> sage: T.has_coerce_map_from(S) > >> True > >> sage: S.has_coerce_map_from(R) > >> True > >> sage: T.has_coerce_map_from(R) > >> False > > > I think that should return True, since there is a canonical map from > > Z/6Z to GF(3). > > >> Any opinions on which of these results should change? I'm thinking > >> about such coercions between finite rings in the context of residue > >> fields and quotients of p-adic rings, so you can also ask yourself if > >> you want a coercion from Zmod(250) to Zp(5).quotient(5^3). > > > I want such a coercion, since again there is a canonical map Z/250Z > > --> Z/5^3Z \isom Z_5 / 5^3 Z_5. > > +1. My thoughts exactly. > > - Robert
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