2014-06-12 19:10 UTC+02:00, Robert Bradshaw <rober...@math.washington.edu>:
> On Thu, Jun 12, 2014 at 8:41 AM, Nils Bruin <nbr...@sfu.ca> wrote:
>> On Thursday, June 12, 2014 12:48:37 AM UTC-7, Marc Mezzarobba wrote:
>>>
>>> Sure. But why not have
>>>
>>> sage: bool(sin(x)^2+cos(x)^2==1)
>>> True
>>>
>>> return False as well, and let the user test that
>>>
>>> (rhs-lhs).simplify_full() == 0
>>
>> That would probably be even desirable if you want to make SR more
>> generally
>> usable in sage (imagine, say a cached function with SR elements as
>> arguments. You would probably end up with a routine that gets *slower* as
>> its cache fills)
>
> Also, I think we're at least consistent here. Do you have any examples
> where
>
> sage: bool((lhs - rhs).simplify_full() == 0) != bool(lhs == rhs)
>
> The fact that equality of symbolic expressions is undecidable in
> general, and even more limited in implementation, is something that we
> just have to live with.

We have to live with them but not to let Sage answers False when it
actually does not know the answer...

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