The following seems like odd behavior to me.
Dave
I. No problem:
sage: integral(log(x)/x^(1.002),x)
500*(-log(x)/x^(1/500) - 500/x^(1/500))
sage: s(10)-s(1)
500*(-log(10)/10^(1/500) - 500/10^(1/500)) + 250000
sage: n(_)
2.64282437870861
II. Problem:
sage: integral(log(x)/x^(1.002),x,1,10)
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
/home/davidp/<ipython console> in <module>()
/usr/local/sage-3.4-Fedora_release_9-i686-Linux/local/lib/python2.5/
site-packages/sage/misc/functional.pyc in integral(x, *args, **kwds)
435 """
436 if hasattr(x, 'integral'):
--> 437 return x.integral(*args, **kwds)
438 else:
439 from sage.calculus.calculus import SR
/usr/local/sage-3.4-Fedora_release_9-i686-Linux/local/lib/python2.5/
site-packages/sage/calculus/calculus.pyc in integral(self, v, a, b)
3068 else:
3069 try:
-> 3070 return self.parent()(self._maxima_().integrate
(v, a, b))
3071 except TypeError, error:
3072 s = str(error)
/usr/local/sage-3.4-Fedora_release_9-i686-Linux/local/lib/python2.5/
site-packages/sage/interfaces/maxima.pyc in integral(self, var, min,
max)
1994 if max is None:
1995 raise ValueError, "neither or both of min/max
must be specified."
-> 1996 return I(var, min, max)
1997
1998 integrate = integral
/usr/local/sage-3.4-Fedora_release_9-i686-Linux/local/lib/python2.5/
site-packages/sage/interfaces/expect.pyc in __call__(self, *args,
**kwds)
1332
1333 def __call__(self, *args, **kwds):
-> 1334 return self._obj.parent().function_call(self._name,
[self._obj] + list(args), kwds)
1335
1336 def help(self):
/usr/local/sage-3.4-Fedora_release_9-i686-Linux/local/lib/python2.5/
site-packages/sage/interfaces/expect.pyc in function_call(self,
function, args, kwds)
1252 self._check_valid_function_name(function)
1253 return self.new("%s(%s)"%(function, ",".join([s.name()
for s in args]+
-> 1254 ['%s=%s'%
(key,value.name()) for key, value in kwds.items()])))
1255
1256 def call(self, function_name, *args, **kwds):
/usr/local/sage-3.4-Fedora_release_9-i686-Linux/local/lib/python2.5/
site-packages/sage/interfaces/expect.pyc in new(self, code)
1065
1066 def new(self, code):
-> 1067 return self(code)
1068
1069
###################################################################
/usr/local/sage-3.4-Fedora_release_9-i686-Linux/local/lib/python2.5/
site-packages/sage/interfaces/expect.pyc in __call__(self, x, name)
1000 return x
1001 if isinstance(x, basestring):
-> 1002 return cls(self, x, name=name)
1003 try:
1004 return self._coerce_from_special_method(x)
/usr/local/sage-3.4-Fedora_release_9-i686-Linux/local/lib/python2.5/
site-packages/sage/interfaces/expect.pyc in __init__(self, parent,
value, is_name, name)
1375 except (TypeError, KeyboardInterrupt,
RuntimeError, ValueError), x:
1376 self._session_number = -1
-> 1377 raise TypeError, x
1378 self._session_number = parent._session_number
1379
TypeError: Computation failed since Maxima requested additional
constraints (try the command 'assume(>0)' before integral or limit
evaluation, for example):
an integer?
III. Problem:
sage: numerical_integral(log(x)/x^(1.002),x,1,10)
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
/home/davidp/<ipython console> in <module>()
/usr/local/sage-3.4-Fedora_release_9-i686-Linux/local/lib/python2.5/
site-packages/sage/gsl/integration.so in
sage.gsl.integration.numerical_integral (sage/gsl/integration.c:2008)
()
TypeError: invalid integration algorithm
Dave
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