#9555: Series expansions at singularities don't work
---------------------------------+------------------------------------------
Reporter: fredrik.johansson | Owner: burcin
Type: defect | Status: new
Priority: major | Milestone:
Component: symbolics | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
---------------------------------+------------------------------------------
Calling the series() method on a symbolic expression at a singularity
(algebraic, logarithmic, essential) returns nonsense, inconsistent
results, or raises an exception:
Examples:
{{{
sage: sqrt(x).series(x,0)
Order(1)
sage: sqrt(x).series(x,1)
Order(x)
sage: sqrt(x).series(x,2)
---------------------------------------------------------------------------
RuntimeError Traceback (most recent call
last)
/home/fredrik/sage/<ipython console> in <module>()
/home/fredrik/sage/local/lib/python2.6/site-
packages/sage/symbolic/expression.so in
sage.symbolic.expression.Expression.series
(sage/symbolic/expression.cpp:12811)()
RuntimeError: power::eval(): division by zero
}}}
{{{
sage: (log(x) + x).series(x,0)
Order(1)
sage: (log(x) + x).series(x,1)
(log(x)) + Order(x)
sage: (log(x) + x).series(x,2)
(log(x)) + 1*x
}}}
{{{
sage: exp(1/x).series(x,0)
Order(1)
sage: exp(1/x).series(x,1)
---------------------------------------------------------------------------
RuntimeError Traceback (most recent call
last)
/home/fredrik/sage/<ipython console> in <module>()
/home/fredrik/sage/local/lib/python2.6/site-
packages/sage/symbolic/expression.so in
sage.symbolic.expression.Expression.series
(sage/symbolic/expression.cpp:12811)()
RuntimeError: power::eval(): division by zero
sage: exp(1/x).series(x,2)
---------------------------------------------------------------------------
RuntimeError Traceback (most recent call
last)
/home/fredrik/sage/<ipython console> in <module>()
/home/fredrik/sage/local/lib/python2.6/site-
packages/sage/symbolic/expression.so in
sage.symbolic.expression.Expression.series
(sage/symbolic/expression.cpp:12811)()
RuntimeError: power::eval(): division by zero
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9555>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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