Comment #11 on issue 3699 by smi...@gmail.com: solve() should be able to
tell you when it knows it's found all the solutions
http://code.google.com/p/sympy/issues/detail?id=3699
One way something can be learned about the function is to check its series:
eq=(sinh(x)*sinh (sinh (x))+cosh (x)*cosh (sinh (x))-3)
eq.series(2)
sinh(x)*sinh(sinh(x)) + cosh(x)*cosh(sinh(x)) - 3
eq.series(3)
sinh(x)*sinh(sinh(x)) + cosh(x)*cosh(sinh(x)) - 3
eq.series()
-2 + 2*x**2 + x**4 + O(x**6)
solve(_.removeO())
[-I*sqrt(1 + sqrt(3)), I*sqrt(1 + sqrt(3)), -sqrt(-1 + sqrt(3)), sqrt(-1 +
sqrt(3))]
[w.n() for w in _]
[-1.65289165028107*I, 1.65289165028107*I, -0.855599677167352,
0.855599677167352]
sol=_
nsolve(eq, x, sol[-1])
mpf('0.83173851663805556')
nsolve(eq, x, sol[-2])
mpf('-0.83173851663805556')
Perhaps this will only work well if there is a root near 0.
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