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.
Cheers,
Golam
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