On Jan 17, 2008, at 6:33 AM, David Kohel wrote: >> E1.is_isomorphic(E2) >> >> always returns one boolean. > > +1
I agree too. > >> If you want the map too, you have write >> something explicit, e.g., >> >> t, phi = E1.is_isomorphic(E2, with_map=True) >> >> where phi will be None they aren't isomorphic. > > This is my question: do we have functions which can return > different types depending on the arguments passed in? I think this is best avoided. > Whatever its design flaws, it has been the philosophy that > this should not be the case in Magma. The alternative is > to have a different function: > > E1.is_isomorphic_with_isomorphism(E2) # or is_isomorphic_with_map > > I would like to hear from someone on the "correct" Python style. > Note that this syntax should be followed throughout the SAGE > language, in groups, rings, etc., so we should have a convention. > > I would also propose the syntax: > > E1.isomorphism(E2) > > rather than E1.isomorphism_to(E2) as the direction should be clear. > The latter implies E1.isomorphism_from(E2) should also exist, but > I don't see an argument or context in which E1.isomorphism(E2) and > E2.isomorphism(E1) would not suffice. Seems sensible to me. > Thus we could have: > > E1.is_isomorphic(E2) > E1.is_isomorphic_with_isomorphism(E2) # or > E1.is_isomorphic_with_map(E2) > E1.isomorphism(E2) > > The middle one could be replaced with > E1.is_isomorphism(E2,with_isomorphism=True) > (of with_map) if this is judged acceptable SAGE/Python syntax. I > would propose we endeavor to have the same return type (or None) > independent of the arguments given. The middle two seem redundant (with the first and last)--especially if we're going to replicate this over all of Sage (though perhaps it could be done at a very high level, which I would be much more OK with). I would propose that E1.isomorphism(E2) raise an exception if E1 is not isomorphic to E2, but one could pass in a flag to make it return None rather than raise an error (if that suits your efficiency/ programing style better). If there is more than one isomorphism, I don't think all of them should be computed and returned unless they are explicitly asked for. > John mentioned calculation of all isomorphisms. I propose that the > set > of all isomorphisms be a SAGE object. Thus > > X = Iso(E1,E2) # does nothing > X.cardinality() # tests is_isomorphic and j-invariant = 0 or 12^3 > X.representative() # computes an isomorphism > X.list() # computes all isomorphisms > > The advantage of creating X is that it can cache the above data > for efficiency. > > Moreover is E1 = E2, we could do > > G = Aut(E1) # or Iso(E1,E1) > G.group() > G.group_with_isomorphism() > A = AbelianGroup(2) > A.is_isomorphic(G) > A.is_isomorphic_with_isomorphism(G) > A.isomorphism(G) > > Again, this should be a common syntax throughout SAGE. +1 - Robert --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
