Status: New
Owner: ----
Labels: Type-Defect Priority-Medium
New issue 3248 by [email protected]: summation() function --- internal
error is provoked.
http://code.google.com/p/sympy/issues/detail?id=3248
sympy from git, as of 25.04.2012:
And here is one example that leads to an internal error:
In [50]: summation( (-1)**k * binomial(2*n,k)**2, (k,0,oo))
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
/home/kjetil/py/sympy/sympy/sympy/<ipython-input-50-ba135c6f6f06> in
<module>()
----> 1 summation( (-1)**k * binomial(2*n,k)**2, (k,0,oo))
/home/kjetil/py/sympy/sympy/sympy/sympy/concrete/summations.pyc in
summation(f, *symbols, **kwargs)
307
308 """
--> 309 return Sum(f, *symbols, **kwargs).doit(deep=False)
310
311 def telescopic_direct(L, R, n, limits):
/home/kjetil/py/sympy/sympy/sympy/sympy/concrete/summations.pyc in
doit(self, **hints)
139 a, b = b, a
140
--> 141 f = eval_sum(f, (i, a, b))
142 if f is None:
143 return self
/home/kjetil/py/sympy/sympy/sympy/sympy/concrete/summations.pyc in
eval_sum(f, limits)
389 # this can save time when b-a is big.
390 # We should try to transform to partial fractions
--> 391 value = eval_sum_symbolic(f.expand(), (i, a, b))
392 if value is not None:
393 return value
/home/kjetil/py/sympy/sympy/sympy/sympy/concrete/summations.pyc in
eval_sum_symbolic(f, limits)
475 return r
476
--> 477 return eval_sum_hyper(f, (i, a, b))
478
479 def _eval_sum_hyper(f, i, a):
/home/kjetil/py/sympy/sympy/sympy/sympy/concrete/summations.pyc in
eval_sum_hyper(f, (i, a, b))
558
559 # Now b == oo, a != -oo
--> 560 res = _eval_sum_hyper(f, i, a)
561 if res is not None:
562 return Piecewise(res, (Sum(f, (i, a, b)), True))
/home/kjetil/py/sympy/sympy/sympy/sympy/concrete/summations.pyc in
_eval_sum_hyper(f, i, a)
523 h = hyper(ap, bq, x)
524
--> 525 return f.subs(i, 0)*hyperexpand(h), h.convergence_statement
526
527 def eval_sum_hyper(f, (i, a, b)):
/home/kjetil/py/sympy/sympy/sympy/sympy/simplify/hyperexpand.pyc in
hyperexpand(f, allow_hyper, rewrite)
2445 if not r.has(nan, zoo, oo, -oo):
2446 return r
-> 2447 return f.replace(hyper, do_replace).replace(meijerg, do_meijer)
2448
2449 from sympy.polys.polytools import Poly
/home/kjetil/py/sympy/sympy/sympy/sympy/core/basic.pyc in replace(self,
query, value, map)
1315 return None
1316
-> 1317 result = rec_replace(self)
1318
1319 if result is None:
/home/kjetil/py/sympy/sympy/sympy/sympy/core/basic.pyc in rec_replace(expr)
1306
1307 if result:
-> 1308 value = _value(expr, result)
1309
1310 if map:
/home/kjetil/py/sympy/sympy/sympy/sympy/core/basic.pyc in <lambda>(expr,
result)
1263 _value = lambda expr, result: value(*expr.args)
1264 elif callable(value):
-> 1265 _value = lambda expr, result: value(*expr.args)
1266 else:
1267 raise TypeError("given a type, replace() expects
another type or a callable")
/home/kjetil/py/sympy/sympy/sympy/sympy/simplify/hyperexpand.pyc in
do_replace(ap, bq, z)
2434
2435 def do_replace(ap, bq, z):
-> 2436 r = _hyperexpand(IndexPair(ap, bq), z, rewrite=rewrite)
2437 if r is None:
2438 return hyper(ap, bq, z)
/home/kjetil/py/sympy/sympy/sympy/sympy/simplify/hyperexpand.pyc in
_hyperexpand(ip, z, ops0, z0, premult, prem, rewrite)
1996 if unpolarify(z) in [1, -1] and (len(nip.ap), len(nip.bq)) ==
(2, 1):
1997 f = build_hypergeometric_formula(nip)
-> 1998 r = carryout_plan(f, ops).replace(hyper,
hyperexpand_special)
1999 if not r.has(hyper):
2000 return r + p
/home/kjetil/py/sympy/sympy/sympy/sympy/core/basic.pyc in replace(self,
query, value, map)
1315 return None
1316
-> 1317 result = rec_replace(self)
1318
1319 if result is None:
/home/kjetil/py/sympy/sympy/sympy/sympy/core/basic.pyc in rec_replace(expr)
1306
1307 if result:
-> 1308 value = _value(expr, result)
1309
1310 if map:
/home/kjetil/py/sympy/sympy/sympy/sympy/core/basic.pyc in <lambda>(expr,
result)
1263 _value = lambda expr, result: value(*expr.args)
1264 elif callable(value):
-> 1265 _value = lambda expr, result: value(*expr.args)
1266 else:
1267 raise TypeError("given a type, replace() expects
another type or a callable")
/home/kjetil/py/sympy/sympy/sympy/sympy/simplify/hyperexpand.pyc in
hyperexpand_special(ap, bq, z)
1911 if b.is_integer and b < 0:
1912 return 2*cos(pi*b/2)*gamma(-b)*gamma(b - a + 1) \
-> 1913 /gamma(-b/2)/gamma(b/2 - a + 1)
1914 else:
1915 return gamma(b/2 + 1)*gamma(b - a + 1) \
NameError: global name 'pi' is not defined
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