Comment #5 on issue 2656 by asmeurer: Solve exp(x*log(x) - 1, x)
http://code.google.com/p/sympy/issues/detail?id=2656
Maple gives a solution in terms of some RootOf's of non-polynomials:
solve(2.0*sqrt(2)*x**2*exp(-0.03125*(log(x) - 1.5)**2)/sqrt(pi) -
0.0625*sqrt(2)*erf(-log(x) + 1.5) - 0.5, x);
2
67 2 1/2 1/2
exp(RootOf(32 exp(-1/32 _Z +
-- _Z - 9/128) - 4 RootOf(exp(_Z) - 2, index = 1) pi + pi erf(_Z -
3/2)))
32
Which basically means that it tries to iteratively solve the equation, and
whenever it gets to an expression it can't invert, it uses a RootOf. You
can close it if you want, or leave it open to some day get something like
that.
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