Issue 1169: unify symbols and var
http://code.google.com/p/sympy/issues/detail?id=1169
Comment #9 by Vinzent.Steinberg:
These strange issues appear with the patch:
>>> from sympy import *
>>> [sympify(arg) for arg in (sin(x), ('x',0,1))]
[sin(x), (x, 0, 1)]
>>> integrate(*_)
sin(1)
>>> integrate(sin(x), (x, 0, 1))
1 - cos(1)
Don't have a clue what's causing this.
>>> def NS(e, n=15, **options):
... return str(sympify(e).evalf(n, **options))
...
>>> NS(pi - 4*Integral('sqrt(1-x**2)', (x, 0, 1)), 15, maxprec=30,
chop=True)
'-.0e-16'
In fact, this is numerically zero (for 15 accurate decimal digits). Don't
know why it
doesn't work anymore.
>>> var('x y z w')
(x, y, z, w)
>>> e = (x-y)*(z-y) + sin((x-y)*(z-y))
>>> substs, reduced = cse([e],
optimizations=[(cse_opts.sub_pre,cse_opts.sub_post)])
>>> substs
[(x0, z - y), (x1, x - y), (x2, x0*x1)]
# according to test:[(x0, z-y), (x1, x-y), (x2, x0*x1)]
>>> import itertools
>>> x0,x1,x2 = list(itertools.islice(cse_main.numbered_symbols(), 0, 3))
>>> substs == [(x0, z-y), (x1, x-y), (x2, x0*x1)]
True
No clue why this comparison fails in the tests.
>>> n, k = symbols('nk', integer=True)
>>> C0, C1, C2 = symbols('C0', 'C1', 'C2')
>>> rsolve_poly([-1, 1], n, n) == C0 + (n**2 - n)/2
False
>>> rsolve_poly([-1, 1], n, n)
C0 - n/2 + 1/2*n**2
>>> C0 + (n**2 - n)/2
C0 - n/2 + 1/2*n**2
The new result is like before, but the comparison fails for some reason.
>>> solution = rsolve_ratio([-2*n**3+n**2+2*n-1, 2*n**3+n**2-6*n,
... -2*n**3-11*n**2-18*n-9, 2*n**3+13*n**2+22*n+8], 0, n)
>>> solution
(3*C1 - 2*C1*n)/(2 - 2*n**2)
>>> solution in [ (-3*C1 + 2*C1*n)/(-2 + 2*n**2),
... ( 3*C1 - 2*C1*n)/( 2 - 2*n**2) ]
False
Same here.
>>> rsolve_hyper([n**2-2, -2*n-1, 1], 0, n)
C0*RisingFactorial(2**(1/2), n) + C1*RisingFactorial(-2**(1/2), n)
>>> _ in [C0*rf(sqrt(2), n) + C1*rf(-sqrt(2), n),
... C1*rf(sqrt(2), n) + C0*rf(-sqrt(2), n)]
False
Again.
It seems that sometimes x != x due to the patch. Any idea why?
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