Status: Valid
Owner: ----
Labels: Type-Defect Priority-Medium Simplify
New issue 3552 by ronan.l...@gmail.com: Expression with square root doesn't
simplify well
http://code.google.com/p/sympy/issues/detail?id=3552
Consider the following expression:
In [39]: y = 1/(x-1) + 1/(x+1) + x + 1
In [40]: value = y.subs(x, sqrt(2 + sqrt(5))); str(value)
Out[40]: 1/(1 + sqrt(2 + sqrt(5))) + 1/(-1 + sqrt(2 + sqrt(5))) + 1 +
sqrt(2 + sqrt(5))
Simplify() doesn't do much on it, even though it can be simplified, with
some work.
In [41]: str(simplify(value))
Out[41]: 1/(1 + sqrt(2 + sqrt(5))) - 1/(-sqrt(2 + sqrt(5)) + 1) + 1 +
sqrt(2 + sqrt(5))
In [42]: value.together().expand().together().simplify().simplify()
Out[42]:
___________ ______________
╱ ___ ╱ ___
╲╱ 2 + ╲╱ 5 ╲╱ 10 + 5⋅╲╱ 5
1 + ────────────── + ─────────────────
2 2
NB: sqrt(2 + sqrt(5)) is the location of a local minimum of the function,
so this isn't an artificial case.
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