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)
or may be a new method
(2) ex.is_trivially_zero()
So that users/developers can make their choice depending on their need.
Cheers,
Golam
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