In the latest version of sage (at least what cloud.sagemath.org is
running), there is a problem with substituting constants into the formal
integrals of formal functions. See the examples below.
Victor
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'
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