Source code for sympy.calculus.singularities
from sympy.solvers import solve
from sympy.simplify import simplify
[docs]def singularities(expr, sym):
"""
Finds singularities for a function.
Currently supported functions are:
- univariate real rational functions
Examples
========
>>> from sympy.calculus.singularities import singularities
>>> from sympy import Symbol
>>> x = Symbol('x', real=True)
>>> singularities(x**2 + x + 1, x)
()
>>> singularities(1/(x + 1), x)
(-1,)
References
==========
.. [1] http://en.wikipedia.org/wiki/Mathematical_singularity
"""
if not expr.is_rational_function(sym):
raise NotImplementedError("Algorithms finding singularities for"
" non rational functions are not yet"
" implemented")
else:
return tuple(sorted(solve(simplify(1/expr), sym)))