On Thu, Jun 12, 2014 at 10:19 AM, Vincent Delecroix
<20100.delecr...@gmail.com> wrote:
> 2014-06-12 19:13 UTC+02:00, Robert Bradshaw <rober...@gmail.com>:
>> On Thu, Jun 12, 2014 at 12:50 AM, Marc Mezzarobba <m...@mezzarobba.net>
>> wrote:
>>
>>> But here is a similar example right from the Sage library (adapted from
>>> http://wiki.sagemath.org/EqualityCoercion):
>>>
>>> sage: FiniteEnumeratedSet(GF(3))
>>> {0, 1, 2}
>>> sage: add(FiniteEnumeratedSet([0,1,2]))
>>> 0
>>
>> Um, isn't that what you want? The sum of the elements of GF(p^e) for
>> any odd prime is zero, which is a handy property.
>
> In two fresh Sage consoles
> {{{
> sage: sum(FiniteEnumeratedSet([0,1,2]))
> 3
> }}}
> and
> {{{
> sage: FiniteEnumeratedSet(GF(3))
> sage: sum(FiniteEnumeratedSet([0,1,2]))
> 0
> }}}
>
> Because FiniteEnumeratedSet has a cache on the input!
Indeed -- no question that this is definitely a bug. Somebody open a
ticket (if they haven't already).
But I would rather blame the use of caching rather than equality
testing. We can certainly fix this bug without changing the
definition of "==".
>
>>>>> sage: {42, QQbar(42)}
>>>>> {42, 42}
>>>>> sage: {42, SR(42)}
>>>>> {42}
>>>>> sage: {2^100, SR(2^100)}
>>>>> {1267650600228229401496703205376, 1267650600228229401496703205376}
>>>>
>>>> Hash is not as good as it could/should be for large symbolic integers.
>>>> And for AA/QQbar.
>>>
>>> And do you honestly think this will ever be fixed for all sage objects?
>>
>> For the common ones at least. And sometimes elements should not define
>> hash, as normalizing them is expensive, if even possible.
>
> Are we allowed to through errors for them?
If you do not define hash for an object (or throw an error), then it
is not possible to use that object in many data structures, e.g., as
keys in dictionaries, in sets, etc. It is possible to use it in
lists. Whether or not this is OK, depends on what you're trying to
do.
If hash wasn't defined on any SR elements, then instead of
sage: {42, SR(42)}
set([42])
we would get an error, such as:
TypeError: unhashable type: ...
The drawback is that we would also get errors on this:
sage: {pi, e}
TypeError: unhashable type: ...
-- William
--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org
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