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Description
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
Upstream: Reported upstream. Developers acknowledge bug.
CC: @kcrisman @rwst @sagetrac-jakobkroeker
Component: symbolics
Issue created by migration from https://trac.sagemath.org/ticket/9555