#14976: integration with non symbolic bounds broken
--------------------------+-------------------------------
    Reporter:  burcin     |            Owner:
        Type:  defect     |           Status:  new
    Priority:  critical   |        Milestone:  sage-5.12
   Component:  symbolics  |         Keywords:  integration
   Merged in:             |          Authors:
   Reviewers:             |  Report Upstream:  N/A
 Work issues:             |           Branch:
Dependencies:             |         Stopgaps:
--------------------------+-------------------------------
 [https://groups.google.com/d/topic/sage-support/o0rwQId7ELU/discussion
 Reported on sage-support by Victor Miller]:

 {{{
 sage: var('a'); function('f',a)
 sage: g = f(a).integrate(a,0,a^2)
 sage: g
 integrate(f(a),0,a^2)

 sage: g.derivative(a)

 Error in lines 1-1
 Traceback (most recent call last):
   File "/mnt/home/lQoU8m2s/.sagemathcloud/sage_server.py", line 498, in
 execute
     exec compile(block+'\n', '', 'single') in namespace, locals
   File "", line 1, in <module>
   File "expression.pyx", line 3006, in
 sage.symbolic.expression.Expression.derivative
 (sage/symbolic/expression.cpp:15855)
   File "derivative.pyx", line 216, in
 sage.misc.derivative.multi_derivative (sage/misc/derivative.c:2715)
   File "expression.pyx", line 3078, in
 sage.symbolic.expression.Expression._derivative
 (sage/symbolic/expression.cpp:16245)
   File "/usr/local/sage/sage-5.10.rc1/local/lib/python2.7/site-
 packages/sage/symbolic/integration/integral.py", line 224, in
 _tderivative_
     - f.subs(x==a)*a.diff(diff_param)
   File "element.pyx", line 344, in
 sage.structure.element.Element.__getattr__ (sage/structure/element.c:3871)
   File "misc.pyx", line 257, in
 sage.structure.misc.getattr_from_other_class (sage/structure/misc.c:1696)
 AttributeError: 'sage.rings.integer.Integer' object has no attribute
 'diff'

 sage: g1 = f(a).integrate(a)
 sage: g1(0)
 Error in lines 1-1
 Traceback (most recent call last):
   File "/mnt/home/lQoU8m2s/.sagemathcloud/sage_server.py", line 498, in
 execute
     exec compile(block+'\n', '', 'single') in namespace, locals
   File "", line 1, in <module>
   File "expression.pyx", line 3973, in
 sage.symbolic.expression.Expression.__call__
 (sage/symbolic/expression.cpp:19900)
   File "ring.pyx", line 685, in
 sage.symbolic.ring.SymbolicRing._call_element_
 (sage/symbolic/ring.cpp:7672)
   File "expression.pyx", line 3824, in
 sage.symbolic.expression.Expression.substitute
 (sage/symbolic/expression.cpp:19177)
   File "/usr/local/sage/sage-5.10.rc1/local/lib/python2.7/site-
 packages/sage/symbolic/integration/integral.py", line 75, in _eval_
     if len(x.variables()) == 1:
   File "element.pyx", line 344, in
 sage.structure.element.Element.__getattr__ (sage/structure/element.c:3871)
   File "misc.pyx", line 257, in
 sage.structure.misc.getattr_from_other_class (sage/structure/misc.c:1696)
 AttributeError: 'sage.rings.integer.Integer' object has no attribute
 'variables'
 }}}

--
Ticket URL: <http://trac.sagemath.org/ticket/14976>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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