Comment #6 on issue 1724 by asmeurer: conjugate doesn't work for rational
powers
http://code.google.com/p/sympy/issues/detail?id=1724
I don't think we should return a numeric solution when we are looking for a
symbolic one. If the symbolic one can't be found, I think we should
raise. If
that is not enough for the user, then he can then resort to numeric methods.
If you look at the source, we are evaluating the conjugate of a power as
conjugate(x**y) == conjugate(x)**y. But I think this only holds when y is
an integer
(which is why it is screwing up on these rational powers that don't have I
explicitly in them).
I don't know if this is the best way or even if it would work in general,
but it seems that maybe this could be a method to solve issue 216 and hence
this one
using the fact that roots returns nicer expressions:
In [14]: a = S("(-29/54 + 93**(1/2)/18)**(1/3)")
In [15]: a.evalf()
Out[15]: 0.0542694215230746 + 0.0939973953753372⋅ⅈ
In [16]: a
Out[16]:
⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽
╱ ⎽⎽⎽⎽
╱ 29 ╲╱ 93
3 ╱ - ── + ──────
╲╱ 54 18
In [17]: roots(x**3 - a**3, x).keys()
Out[17]:
⎡ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽
⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎤
⎢ ╱ ⎽⎽⎽⎽ ╱ ⎽⎽⎽⎽
╱ ⎽⎽⎽⎽ ╱ ⎽⎽⎽⎽ ⎥
⎢ ╱ 29 ╲╱ 93 ⎽⎽⎽ ╱ 29 ╲╱ 93 ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽
╱ 29 ╲╱ 93 ⎽⎽⎽ ╱ 29 ╲╱ 93 ⎥
⎢3 ╱ ── - ────── ⅈ⋅╲╱ 3 ⋅3 ╱ ── - ────── ╱ ⎽⎽⎽⎽ 3
╱ ── - ────── ⅈ⋅╲╱ 3 ⋅3 ╱ ── - ────── ⎥
⎢╲╱ 54 18 ╲╱ 54 18 ╱ 29 ╲╱ 93
╲╱ 54 18 ╲╱ 54 18 ⎥
⎢────────────────── - ──────────────────────────, -3 ╱ ── - ────── ,
────────────────── + ──────────────────────────⎥
⎣ 2 2 ╲╱ 54
18 2 2 ⎦
In [18]: map(N, roots(x**3 - a**3, x).keys())
Out[18]: [0.0542694215230746 - 0.0939973953753372⋅ⅈ, -0.108538843046149,
0.0542694215230746 + 0.0939973953753372⋅ⅈ]
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