Comment #12 on issue 1015 by [email protected]:
limit((1+x/(n+sin(n)))**n,n,oo) doesn't work
http://code.google.com/p/sympy/issues/detail?id=1015
I see IEEE 754 has been envoked as justification for 1**nan == 1. IEEE 754
is a floating-point standard. 1**nan seems reasonable for floats to me,
but does not seem robust enough for symbolic use. When we define 1**oo ==
nan, we get the correct behavior out of limit().
In [1]: Limit((1+x/(n+sin(n)))**n,n,oo)
Out[1]:
n
⎛ x ⎞
lim ⎜────────── + 1⎟
n->∞⎝n + sin(n) ⎠
In [2]: _.doit()
---------------------------------------------------------------------------
In [1]: Limit((1+x/(n+sin(n)))**n,n,oo)
Out[1]:
n
⎛ x ⎞
lim ⎜────────── + 1⎟
n->∞⎝n + sin(n) ⎠
In [2]: _.doit()
---------------------------------------------------------------------------
PoleError Traceback (most recent call last)
<ipython-input-2-882323f1bef6> in <module>()
----> 1 _.doit()
sympy/series/limits.pyc in doit(self, **hints)
162 z = z.doit(**hints)
163 z0 = z0.doit(**hints)
--> 164 return limit(e, z, z0, str(dir))
sympy/series/limits.pyc in limit(e, z, z0, dir)
89 raise PoleError()
90 except (PoleError, ValueError):
---> 91 r = heuristics(e, z, z0, dir)
92 #print("\t*h*",r)
93 return r
sympy/series/limits.pyc in heuristics(e, z, z0, dir)
96 def heuristics(e, z, z0, dir):
97 if abs(z0) is S.Infinity:
---> 98 return limit(e.subs(z, 1/z), z, S.Zero, "+" if z0 is
S.Infinity else "-")
99
100 rv = None
sympy/series/limits.pyc in limit(e, z, z0, dir)
89 raise PoleError()
90 except (PoleError, ValueError):
---> 91 r = heuristics(e, z, z0, dir)
92 #print("\t*h*",r)
93 return r
sympy/series/limits.pyc in heuristics(e, z, z0, dir)
120 if rv in bad:
121 msg = "Don't know how to calculate the limit(%s, %s, %s,
dir=%s), sorry."
--> 122 raise PoleError(msg % (e, z, z0, dir))
123
124 return rv
PoleError: Don't know how to calculate the limit((x/(sin(1/n) + 1/n) +
1)**(1/n), n, 0, dir=+), sorry.
-----------------------------------
The switch from 1**oo == 1 to 1**oo == nan results in only two test fails:
assert 1**nan == 1 # as per IEEE 754
and
assert S(1) ** S.Infinity == 1
If the IEEE 754 standard was actually useful, I'd expect more test failures.
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