There is no way in python to detect how many arguments a function
result will be assigned to, and I'm not a fan of magma's way of doing
it. WIth variable length tuples one has to check the length of a
tuple before unpacking it.
There is a function E1.isomorphism_to(E2) that actually computes the
isomorphism. I think is_isomorphism should just return True or False
(is_* has that convention). Then one can do such things as
if E.is_isomporhic(F):
...
Perhaps an optional argument "compute" which computes and then caches
or returns the actual isomorphism.
- Robert
On Jan 16, 2008, at 6:03 AM, John Cremona wrote:
> What a coincidence -- the patch I am working on *will* (have the
> capability to) return both a boolean and an isomorphism for
> is_isomorphic() on elliptic curves. I was wondering how to do that
> and assumed that it would be a tuple. Rather than make the tuple's
> length (1 or 2) depend on the input I would always return a tuple of
> length 2 but the second item would be None iff the first has false.
> Isn't that a reasonable way of doing it?
>
> I don't like requiring the trapping of errors, though I realise that
> it is very Pythonesque to do so. But if we allow the input line
> sage: phi = E1.isomorphism(E2)
>
> then we *must* raise an error when the things are not isomorphic,
> just as
> sage: QQ(2).nth_root(2)
> raises as ValueError (though sqrt(2) does not as it creates a
> symbolic sqrt(2)).
>
> This is going beyond the original thread, I know.
>
> On 16/01/2008, David Kohel <[EMAIL PROTECTED]> wrote:
>>
>> There was a thread on multiple return values coming from Magma,
>> since renamed to "Integer points on conics"
>>
>> William pointed out that one can access the multiple return values
>> using nvals:
>>
>> x = magma.XGCD(15, 10)
>> x,y,z = magma.XGCD(15, 10, nvals = 3)
>>
>> The first returns an integer, while the second returns a tuple.
>>
>> Q1: Is this an acceptable general construction for Python and/or
>> SAGE,
>> namely to return a different type depending on the values passed into
>> it? Is it acceptable when it is controlled by nvals in exactly this
>> way?
>>
>> As William pointed out, very different algorithms can be called
>> depending on the
>> number of arguments requested in Magma. The following is an example:
>>
>> sage: E = magma.EllipticCurve([1,3])
>> sage: magma.IsIsomorphic(E,E)
>> true
>> sage: bool, phi = magma.IsIsomorphic(E,E,nvals=2)
>> sage: phi
>> Elliptic curve isomorphism from: Elliptic Curve defined by y^2 =
>> x^3 +
>> x + 3 over Rational Field to Elliptic Curve defined by y^2 = x^3 +
>> x +
>> 3 over Rational Field
>> Taking (x : y : 1) to (x : y : 1)
>>
>> Currently in SAGE we have:
>>
>> sage: E = EllipticCurve([1,3])
>> sage: E.is_isomorphic(E)
>> True
>>
>> Q2: Would the following be acceptable way of implementing equivalent
>> functionality in SAGE?:
>>
>> sage: bool, phi = E.is_isomorphic(E, nvals=2)
>>
>> Note that often (in many concexts) it more expensive to return an
>> isomorphism, but only slightly more so compared with recomputing the
>> isomorphism test. If the answer to my question is "no, it not
>> acceptable SAGE/Python syntax", then how should we implement this
>> functionality? One possibility is:
>>
>> sage: phi = E1.isomorphism(E2)
>>
>> and to trap an error if is_isomorphic returns false. Is this a
>> better?
>>
>>>
>>
>
>
> --
> John Cremona
>
>
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