Comment #5 on issue 3887 by smi...@gmail.com: sympy 0.7.2 hangs when trying
to solve a simple algebraic equation
http://code.google.com/p/sympy/issues/detail?id=3887
after Floats are replaced with Rationals, a failure occurs when trying to
convert the expression to a Poly:
e
-exp(54240381056521*alpha/250000000000) + 100
Poly(e)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "sympy\polys\polytools.py", line 95, in __new__
return cls._from_expr(rep, opt)
File "sympy\polys\polytools.py", line 206, in _from_expr
return cls._from_dict(rep, opt)
File "sympy\polys\polytools.py", line 155, in _from_dict
return cls.new(DMP.from_dict(rep, level, domain), *gens)
File "sympy\polys\polyclasses.py", line 255, in from_dict
return cls(dmp_from_dict(rep, lev, dom), dom, lev)
File "sympy\polys\densebasic.py", line 1021, in dmp_from_dict
return dup_from_dict(f, K)
File "sympy\polys\densebasic.py", line 971, in dup_from_dict
for k in xrange(n, -1, -1):
OverflowError: Python int too large to convert to C long
Aaron points out that it tries to make a 54240381056521 degree polynomial,
which won't work with the dense representation (it needs a list of
54240381056521 terms).
This can be seen in the solutions to the following:
Poly(exp(2*x)+3)
Poly(exp(x)**2 + 3, exp(x), domain='ZZ')
The generator is exp(x) and the expression is quadratic in that. So two
solutions are obtained:
solve(exp(2*x)-3)
[log(3)/2 + I*pi, log(3)/2]
and 3 solutions are obtained if the numerator is 3:
solve(exp(3*x)-3)
[log(3**(1/3)), log(-3**(1/3)/2 - 3**(5/6)*I/2), log(-3**(1/3)/2 +
3**(5/6)*I/2)
]
And unless rational=False, something with a Float will be recast in
Rational, so this, for example, also gives 3 roots:
solve(exp(.3*x)-3)
[3.66204096222703, 3.66204096222703 - 20.943951023932*I, 3.66204096222703 +
20.9
43951023932*I]
If you don't want that, you can use the rational=False flag
solve(exp(.3*x)-3,rational=False)
[3.33333333333333*log(3)]
q=14.7296138519
solve(exp(-alpha * q**2) - 0.01, alpha, rational=False)
[0.0212257459123917]
This, then, is the expected behavior at present, because Floats are recast.
There is a flag to avoid this, so I would suggest marking this as WontFix.
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