Comment #2 on issue 3552 by asmeu...@gmail.com: Expression with square root
doesn't simplify well
http://code.google.com/p/sympy/issues/detail?id=3552
Actually, there's an even simpler version:
In [12]: minpoly(value)
Out[12]:
4 3 2
x - 4⋅x - 5⋅x + 18⋅x - 11
In [13]: solve(minpoly(value))
Out[13]:
⎡ _______________ _________________
_________________ _______________ ⎤
⎢ ╱ ___ ╱ ___ ╱
___ ╱ ___ ⎥
⎢ ╲╱ 22 + 10⋅╲╱ 5 ╲╱ - 10⋅╲╱ 5 + 22 ╲╱ - 10⋅╲╱ 5 +
22 ╲╱ 22 + 10⋅╲╱ 5 ⎥
⎢1 + ──────────────────, 1 - ────────────────────, 1 +
────────────────────, - ────────────────── + 1⎥
⎣ 2 2
2 2 ⎦
In [14]: [N(i) for i in solve(minpoly(value))]
Out[14]: [4.33019067678556, 1.0 - 0.300283106000778⋅ⅈ, 1.0 +
0.300283106000778⋅ⅈ, -2.33019067678556]
In [15]: N(value)
Out[15]: 4.33019067678556
In [16]: print solve(minpoly(value))[0]
1 + sqrt(22 + 10*sqrt(5))/2
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