On Jan 16, 2008 12:34 PM, John Cremona <[EMAIL PROTECTED]> wrote:
> William is right that with Python there is no need to have variable
> numbers of return variables (for Python functions, I don't mean
> Magma). In situations like is_isomorphic() we can always return a
> tuple of 2 values, either (true, i) with i an isomorphism or (false,
> None). So the calling program can unpack the tuple into 2 values and
> only look at the second if the first is true. However that breaks
> code which looks correct if written simply as
> if E2.is_isomorphic(E2):
> do something
Hmm. I think it should be that
E1.is_isomorphic(E2)
always returns one boolean. 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. As long as there are examples
and documentation this is easy to use and very easy to read.
Justin says:
> Trying to unwind code that relies
> on this will be a headache, and we should be considering
> maintainability as we go. It's always tough to start tackling a
> large code base long after the original developers have moved on, and
> this kind of trickery won't help a bit.
In any case, we have to make it possible to use things in Magma from
Sage that people want to use. Just not doing so isn't an option.
> Still on this specific subthread, I think there must be many
> situations where as well as David's comment that computing one iso is
> not much more work than checking if one exists, one can compute *all*
> isos in not much more time than computing one. In that case I would
> want to implement E1.isomorphisms_to(E2) [note the "s"!] which
> returns a possibly empty list of all iso's from E1 to E2. Then
> E1.is_isomorphic_to(E2) can be *literally* synonymous with
> E1.isomorphisms_to(E2) thanks to Pythons convention that a list is
> "true" if and only if not empty (you can see that I have been reading
> up on Python!). And then E1.isomorphism_to(E2) can return
> E1.isomorphisms_to(E2)[0] with suitable error-catching if the list was
> empty. And finally, E1.isomorphisms_to(E1) would return the set of
> automorphisms of E1.
I don't think I like that. Shouldn't a function named
is_something(...) return True
or False by default? Taking this further, what would you do with n.is_prime()
for n an integer? Or with something like x.is_zero_divisor()?
> All the above is certainly good for the case of ellitpic curves which
> have finite automorphsm groups (and almost always of size 2) so the
> above lists are mainly of length 0 or 2. But maybe elsewhere too?
>
> John
>
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