#17553: substitute_function() can leave limits unevaluated
-----------------------------+------------------------
Reporter: wonder | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.4
Component: symbolics | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
-----------------------------+------------------------
Comment (by wonder):
Unfortunately that workaround doesn't work when exponentials are involved.
The `repr` stage causes the constant `e` to be replaced by an unbound
variable `e`:
{{{
sage: l = limit( function('f')(x), x=0.1 )
sage: ls = l.substitute_function( function('f'), (1 - exp(x)).function(x)
)
sage: ls
limit(-e^x + 1, x, 0.1)
sage: mls = maxima(repr(ls))
sage: mls
1-e^0.1
sage: N(mls)
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
<ipython-input-22-518484fcab94> in <module>()
----> 1 N(mls)
/usr/local/sage/local/lib/python2.7/site-packages/sage/misc/functional.pyc
in numerical_approx(x, prec, digits, algorithm)
1466 except (TypeError, ValueError):
1467 pass
-> 1468 return sage.rings.complex_field.ComplexField(prec)(x)
1469
1470 n = numerical_approx
/usr/local/sage/local/lib/python2.7/site-
packages/sage/rings/complex_field.pyc in __call__(self, x, im)
349 if im is not None:
350 x = x, im
--> 351 return Parent.__call__(self, x)
352
353 def _element_constructor_(self, x):
/usr/local/sage/local/lib/python2.7/site-packages/sage/structure/parent.so
in sage.structure.parent.Parent.__call__
(build/cythonized/sage/structure/parent.c:9666)()
/usr/local/sage/local/lib/python2.7/site-
packages/sage/structure/coerce_maps.so in
sage.structure.coerce_maps.DefaultConvertMap_unique._call_
(build/cythonized/sage/structure/coerce_maps.c:4263)()
/usr/local/sage/local/lib/python2.7/site-
packages/sage/structure/coerce_maps.so in
sage.structure.coerce_maps.DefaultConvertMap_unique._call_
(build/cythonized/sage/structure/coerce_maps.c:4170)()
/usr/local/sage/local/lib/python2.7/site-
packages/sage/rings/complex_field.pyc in _element_constructor_(self, x)
388 pass
389 try:
--> 390 return x._complex_mpfr_field_( self )
391 except AttributeError:
392 pass
/usr/local/sage/local/lib/python2.7/site-
packages/sage/interfaces/maxima_abstract.pyc in _complex_mpfr_field_(self,
C)
1287
8.0751148893563733350506651837615871941533119425962889089783e-62 +
1.4142135623730950488016887242096980785696718753769480731767*I
1288 """
-> 1289 return C(self._sage_())
1290
1291 def _mpfr_(self, R):
/usr/local/sage/local/lib/python2.7/site-
packages/sage/rings/complex_field.pyc in __call__(self, x, im)
349 if im is not None:
350 x = x, im
--> 351 return Parent.__call__(self, x)
352
353 def _element_constructor_(self, x):
/usr/local/sage/local/lib/python2.7/site-packages/sage/structure/parent.so
in sage.structure.parent.Parent.__call__
(build/cythonized/sage/structure/parent.c:9666)()
/usr/local/sage/local/lib/python2.7/site-
packages/sage/structure/coerce_maps.so in
sage.structure.coerce_maps.DefaultConvertMap_unique._call_
(build/cythonized/sage/structure/coerce_maps.c:4263)()
/usr/local/sage/local/lib/python2.7/site-
packages/sage/structure/coerce_maps.so in
sage.structure.coerce_maps.DefaultConvertMap_unique._call_
(build/cythonized/sage/structure/coerce_maps.c:4170)()
/usr/local/sage/local/lib/python2.7/site-
packages/sage/rings/complex_field.pyc in _element_constructor_(self, x)
388 pass
389 try:
--> 390 return x._complex_mpfr_field_( self )
391 except AttributeError:
392 pass
/usr/local/sage/local/lib/python2.7/site-
packages/sage/symbolic/expression.so in
sage.symbolic.expression.Expression._complex_mpfr_field_
(build/cythonized/sage/symbolic/expression.cpp:8185)()
/usr/local/sage/local/lib/python2.7/site-
packages/sage/symbolic/expression.so in
sage.symbolic.expression.Expression._eval_self
(build/cythonized/sage/symbolic/expression.cpp:7521)()
TypeError: Cannot evaluate symbolic expression to a numeric value.
sage: maxima(ls)
'limit(1-%e^_SAGE_VAR_x,_SAGE_VAR_x,0.1)
sage: maxima(SR(mls))
1-_SAGE_VAR__e^0.1
}}}
Here's what I'm trying out to work around this:
{{{
sage: srls = SR(maxima(repr(ls)))
sage: srls
-_e^0.1 + 1
sage: srls.subs( { SR.symbol('_e'): e } )
-e^0.1 + 1
sage: N(srls.subs( { SR.symbol('_e'): e } ))
-0.105170918075648
}}}
I've tried poking around the maxima_lib module for a more straightforward
way to ask Maxima to evaluate the limit without the data loss involved in
the `repr` step, but so far I haven't found my way. Advice would be
welcome. Thanks for this wonderfully useful package and for all the bug
fixes!
--
Ticket URL: <http://trac.sagemath.org/ticket/17553#comment:1>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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