#14976: integration with non symbolic bounds broken
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Reporter: burcin | Owner:
Type: defect | Status: new
Priority: critical | Milestone: sage-5.12
Component: symbolics | Resolution:
Keywords: integration | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Dependencies:
Stopgaps: |
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Comment (by nbruin):
Looking at the returned error, I do not get the impression this has
anything to do with maxima or with checking whether something is real-
valued. The error we're getting is that attributes like `variables` and
`derivative` end up being looked up on sage integer objects rather than on
SR elements. This must happen somewhere during the picking apart of the
expression:
{{{
sage: g
integrate(f(a), a, 0, a^2)
sage: [type(o) for o in g.operands()]
[sage.symbolic.expression.Expression,
sage.symbolic.expression.Expression,
sage.symbolic.expression.Expression,
sage.symbolic.expression.Expression]
sage: g.operands()[2].diff(a)
0
}}}
as you see, all quantities involved are symbolic expressions and this
"symbolic constant 0" has no problem being differentiated.
{{{
sage: g.derivative(a)
AttributeError
sage: %debug
ipdb> up
> /usr/local/sage/5.7/local/lib/python2.7/site-
packages/sage/symbolic/integration/integral.py(224)_tderivative_()
223 return ans + f.subs(x==b)*b.diff(diff_param) \
--> 224 - f.subs(x==a)*a.diff(diff_param)
225
ipdb> p [(c,type(c)) for c in [f,x,a,b,diff_param]]
[(f(a), <type 'sage.symbolic.expression.Expression'>), (a, <type
'sage.symbolic.expression.Expression'>), (0, <type
'sage.rings.integer.Integer'>), (a^2, <type
'sage.symbolic.expression.Expression'>), (a, <type
'sage.symbolic.expression.Expression'>)]
}}}
I suspect that this lower bound `a=0` (here a is the local variable in
`_tderivative`) is coming from the lower integration bound involved in the
definition of `g`, and apparently this bound got stripped out of SR a
little prematurely for this purpose. Probably replacing the code above
with
{{{
return ans + f.subs(x==b)*SR(b).diff(diff_param) \
- f.subs(x==a)*SR(a).diff(diff_param)
}}}
would solve the problem. However it might be worthwhile to look why `a`
got stripped out of SR in the first place and whether that should simply
be prevented at the spot (so that `_tderivative` gets called with symbolic
`a,b` regardless of whether they happen to be integer constants)
--
Ticket URL: <http://trac.sagemath.org/ticket/14976#comment:2>
Sage <http://www.sagemath.org>
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