Kernel: SageMath (stable)
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(1.4626517459071817, 1.6238696453143372e-14)
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---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-13-62abbe355e45> in <module>()
----> 1 vf.trapezoid(Integer(4))
/ext/sage/sage-8.3_1804/local/lib/python2.7/site-packages/sage/symbolic/expression.pyx in sage.symbolic.expression._eval_on_operands.new_f (build/cythonized/sage/symbolic/expression.cpp:73036)()
12682 new_args = list(ex._unpack_operands())
12683 new_args.extend(args)
> 12684 return f(ex, *new_args, **kwds)
12685 return new_f
12686
/ext/sage/sage-8.3_1804/local/lib/python2.7/site-packages/sage/functions/piecewise.pyc in trapezoid(self, parameters, variable, N)
1013 x0 = a+i*h
1014 x1 = a+(i+1)*h
-> 1015 rsum += func(x0, x1)
1016 return piecewise(rsum)
1017
/ext/sage/sage-8.3_1804/local/lib/python2.7/site-packages/sage/functions/piecewise.pyc in func(x0, x1)
1001 """
1002 def func(x0, x1):
-> 1003 f0, f1 = self(x0), self(x1)
1004 return [[(x0,x1), f0 + (f1-f0) * (x1-x0)**(-1)
1005 * (self.default_variable()-x0)]]
/ext/sage/sage-8.3_1804/local/lib/python2.7/site-packages/sage/symbolic/expression.pyx in sage.symbolic.expression._eval_on_operands.new_f (build/cythonized/sage/symbolic/expression.cpp:73036)()
12682 new_args = list(ex._unpack_operands())
12683 new_args.extend(args)
> 12684 return f(ex, *new_args, **kwds)
12685 return new_f
12686
/ext/sage/sage-8.3_1804/local/lib/python2.7/site-packages/sage/functions/piecewise.pyc in __call__(self, parameters, variable, value, **kwds)
452 if value is not None:
453 substitution[variable] = value
--> 454 return self.subs(substitution)
455
456 def _fast_float_(self, *args):
/ext/sage/sage-8.3_1804/local/lib/python2.7/site-packages/sage/symbolic/expression.pyx in sage.symbolic.expression.Expression.substitute (build/cythonized/sage/symbolic/expression.cpp:32803)()
5297 sig_on()
5298 try:
-> 5299 res = self._gobj.subs_map(smap, 0)
5300 finally:
5301 sig_off()
/ext/sage/sage-8.3_1804/local/lib/python2.7/site-packages/sage/functions/piecewise.pyc in _subs_(self, subs_map, options, parameters, x)
233 if domain.contains(point):
234 return subs_map.apply_to(func, 0)
--> 235 raise ValueError('point {} is not in the domain'.format(point))
236
237 @staticmethod
ValueError: point 0 is not in the domain
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Object `trapezoid` not found.
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Signature: vf.trapezoid(*args, **kwds)
Docstring:
Return the piecewise line function defined by the trapezoid rule
for numerical integration based on a subdivision of each domain
interval into N subintervals.
EXAMPLES:
sage: f = piecewise([[[0,1], x^2], [RealSet.open_closed(1,2), 5-x^2]])
sage: f.trapezoid(2)
piecewise(x|-->1/2*x on (0, 1/2), x|-->3/2*x - 1/2 on (1/2, 1), x|-->7/2*x - 5/2 on (1, 3/2), x|-->-7/2*x + 8 on (3/2, 2); x)
sage: f = piecewise([[[-1,1], 1-x^2]])
sage: f.trapezoid(4).integral(definite=True)
5/4
sage: f = piecewise([[[-1,1], 1/2+x-x^3]]) ## example 3
sage: f.trapezoid(6).integral(definite=True)
1
Init docstring: x.__init__(...) initializes x; see help(type(x)) for signature
File: ~/Sage Intros/sage/symbolic/expression.pyx
Type: instancemethod
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Object `vf.riemann_sum_integral_approximation` not found.
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---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
/ext/sage/sage-8.3_1804/local/lib/python2.7/site-packages/IPython/core/oinspect.pyc in psearch(self, pattern, ns_table, ns_search, ignore_case, show_all)
1006 namespaces_seen.add(id(ns))
1007 tmp_res = list_namespace(ns, type_pattern, filter,
-> 1008 ignore_case=ignore_case, show_all=show_all)
1009 search_result.update(tmp_res)
1010
/ext/sage/sage-8.3_1804/local/lib/python2.7/site-packages/IPython/utils/wildcard.pyc in list_namespace(namespace, type_pattern, filter, ignore_case, show_all)
105 results = {}
106 for name, obj in iteritems(filtered):
--> 107 ns = list_namespace(dict_dir(obj), type_pattern,
108 ".".join(pattern_list[1:]),
109 ignore_case=ignore_case, show_all=show_all)
/ext/sage/sage-8.3_1804/local/lib/python2.7/site-packages/IPython/utils/wildcard.pyc in dict_dir(obj)
69 # thing. In particular, Traits use this pattern
70 try:
---> 71 ns[key] = getattr(obj, key)
72 except AttributeError:
73 pass
TypeError: descriptor '__weakref__' for 'EvaluationMethods' objects doesn't apply to 'Expression_with_dynamic_methods' object