Golam Mortuza Hossain wrote:
> Hi,
>
>
> On Thu, Aug 20, 2009 at 1:28 PM, William Stein<wst...@gmail.com> wrote:
>> On Thu, Aug 20, 2009 at 4:11 AM, Golam Mortuza
>> Hossain<gmhoss...@gmail.com> wrote:
>>> Hi,
>>>
>>> It takes too long to check whether x is in a list in new symbolics
>>>
>>> ---------
>>> sage: var('x,x1,x2,x3,x4')
>>> (x, x1, x2, x3, x4)
>>> sage: f = function('f')
>>> sage: mylist = [x1,x2,x3,x4,f(x1),f(x2),f(x3),f(x4)]
>>>
>>> sage: timeit('x in mylist')
>>> 5 loops, best of 3: 461 ms per loop
>>> --------
>>>
>>> If your program needs to check it couple of more times
>>> ----------
>>> sage: timeit('x in mylist')
>>> 5 loops, best of 3: 1.26 s per loop
>>> sage: timeit('x in mylist')
>>> 5 loops, best of 3: 3.4 s per loop
>>> ----------
>>>
>>> For a comparison
>>> ---------
>>> sage: timeit('x1 in mylist')
>>> 625 loops, best of 3: 473 ns per loop
>>> ---------
>>>
>>> Reason for this huge discrepancy stems from the fact that
>>> except for last example, in all previous cases maxima is called
>>> to check the equality.
>>>
>>> Thus it seems, new symbolics depends on maxima for basic
>>> operations even now.
>>>
>>> I don't know the rationale behind this design given pynac has
>>> a method to compare two symbolic expression (ex1.is_equal(ex2)).
>>>
>>> In any case, this design ensures writing a program in new symbolics
>>> where some basic tests like "if x in list" needs to done, is no better than
>>> old symbolics.
>>>
>> That's not for any list, but it is for the one you constructed.
>
>
> That why I wrote "symbolics" in the title :-). BTW, I encountered
> this while doing my own work using sage. So I consider this as
> a serious drawback.
>
>
>> I
>> think to get the new symbolics out at some point we finally gave in
>> and made the compare method fall back to Maxima (in case several
>> pynac-based methods failed) so that massive amounts of user code and
>> doctests wouldn't break. Fixing this is obviously something that
>> needs to be done. Hopefully you will do it! :-)
>
> I guess, a policy decision is involved here as to whether use mathematical
> identities by default or as an option during comparison. To clarify:
>
> ex = sin(x)^2 + cos(x)^2 - 1
>
> In pynac, for above expression "ex.is_zero()" test will result False by
> default
> where as current maxima based comparison will return True.
>
> Personally, I feel we should have a flag something like
>
> (1) ex.is_zero(use_identity=False)
>
perhaps ex.is_zero(simplify=False) ?
> or may be a new method
>
> (2) ex.is_trivially_zero()
+1
Jason
--
Jason Grout
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