On Mon, May 3, 2021 at 9:46 AM Ilia <ilia.smi...@orange.fr> wrote:
>
> Thanks for the quick fix! I still have a question about the proposed patch:
>
> Suppose we have two algebraic numbers x and y whose minimal polynomials are
> distinct, but whose values are very close together, e.g. x =
> AA(1+2*2^(-1000))^(1/2); y = AA(1+3*2^(-1000))^(1/3). This guarantees that x
> and y are distinct, but does not tell the sign of x-y yet. With the proposed
> patch, sign(x-y) will try to exactify x-y, which will be very long. Is there
> any reason not simply add _more_precision() to both until the intervals
> separate (as I suggested above)?
How does one know where to stop? Or you'd want to let it run out of memory?
practically speaking, these computations should be done with a much
more efficient RBF:
sage: x = AA(1+2*2^(-1000))^(1/2); y = AA(1+3*2^(-1000))^(1/3)
sage: R=RealBallField(10000)
sage: R(y)>R(x)
False
sage: R(y)<R(x)
True
note that if precision is insufficient, both tests will return False
sage: R=RealBallField(1000)
sage: R(y)>R(x)
False
sage: R(y)<R(x)
False
>
> Best
> --
> Ilia
>
> On Monday, May 3, 2021 at 5:28:46 AM UTC+2 Travis Scrimshaw wrote:
>>
>> Hi Ilia,
>> It would be possible to improve the QQbar element sign() method to check
>> the case when they have the same minimum polynomials. See
>> https://trac.sagemath.org/ticket/31767 for a proposal.
>>
>> Best,
>> Travis
>>
>>
>> On Thursday, April 29, 2021 at 9:43:49 PM UTC+10 Ilia wrote:
>>>
>>>
>>> Hello everyone,
>>>
>>> (This is my first post on sage-devel. I hope I will not break any unwritten
>>> rules, please be forgiving if I do!)
>>>
>>> When I run the following code:
>>>
>>> x1 = AA(2^(1/100))
>>> x2 = AA(2^(1/100))
>>> x1 == x2
>>>
>>> Sage quickly and correctly replies "True". Also,
>>>
>>> 1/(x1-x2)
>>>
>>> quickly raises a ZeroDivisionError. So far, so good. But now try running
>>>
>>> sign(x1-x2)
>>>
>>> Sage does not seem to terminate in any reasonable time.
>>>
>>> After looking at the code, it turns out that both the _richcmp_ method
>>> called by "x1 == x2", and the __bool__() method (which checks nonzeroness)
>>> called by "1/(x1-x2)", include a check that makes them realize that x1 and
>>> x2 are equal, hence obtain the result. For __bool__(), this is quite clever
>>> as it involves extracting the _left and _right parts from an ANBinaryExpr
>>> representing a sum or difference.
>>>
>>> But inexplicably, the sign() method does not include a similar check, and
>>> (as traceback shows) tries instead to exactify x1-x2 which takes forever.
>>> Wouldn't it be an improvement if it did? In fact, I think it would make
>>> sense for the sign() method to call __bool__() first. This way, if it
>>> returns False (as in this case), we have the result immediately; and if it
>>> returns True, we can simply repeatedly add _more_precision() until we can
>>> resolve the number from zero (with the guarantee that this will eventually
>>> terminate). Do you see any reason not to do this?
>>>
>>> Also, I wonder why exactification even takes so long in this case.
>>> Traceback shows that Sage tries to take a union of the two fields, which it
>>> defers to PARI, which then stalls. But even admitting that Sage fails to
>>> immediately see equality of the elements themselves, presumably it should
>>> at least detect equality of the fields they generate; and it should not
>>> take long to unify a field (even a complicated one) with itself, should it?
>>>
>>> My configuration: SageMath version 9.1, running on Ubuntu 18.04.3 LTS
>>> (64-bit).
>>>
>>> Best
>>> --
>>> Ilia
>>>
> --
> You received this message because you are subscribed to the Google Groups
> "sage-devel" group.
> To unsubscribe from this group and stop receiving emails from it, send an
> email to sage-devel+unsubscr...@googlegroups.com.
> To view this discussion on the web visit
> https://groups.google.com/d/msgid/sage-devel/95976c4e-67e9-4011-a188-962c66fa75efn%40googlegroups.com.
--
You received this message because you are subscribed to the Google Groups
"sage-devel" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to sage-devel+unsubscr...@googlegroups.com.
To view this discussion on the web visit
https://groups.google.com/d/msgid/sage-devel/CAAWYfq0%3D282odMHpgPkkr390D%3DJyK_YuPqs089FvqJgtr5_ppA%40mail.gmail.com.
