imageset of first interval of singularities included

fixes sympy/sympy#10113 // edited by skirpichev Signed-off-by: Sergey B Kirpichev <skirpichev@gmail.com>
skirpichev · Jul 16, 2016 · 12db386 · 12db386
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diff --git a/sympy/sets/sets.py b/sympy/sets/sets.py
@@ -978,8 +978,8 @@ def _eval_imageset(self, f):
         else:
             return imageset(f, Interval(self.start, sing[0],
                                         self.left_open, True)) + \
-                Union(*[imageset(f, Interval(sing[i], sing[i + 1]), True, True)
-                        for i in range(1, len(sing) - 1)]) + \
+                Union(*[imageset(f, Interval(sing[i], sing[i + 1], True, True))
+                        for i in range(0, len(sing) - 1)]) + \
                 imageset(f, Interval(sing[-1], self.end, True, self.right_open))
 
     @property

diff --git a/sympy/sets/tests/test_sets.py b/sympy/sets/tests/test_sets.py
@@ -862,3 +862,13 @@ def test_issue_9637():
                              Interval(2, 3, left_open=True)), a, evaluate=False))
     assert Complement(a, S.Reals) == Complement(a, S.Reals, evaluate=False)
     assert Complement(a, Interval(1, 3)) == Complement(a, Interval(1, 3), evaluate=False)
+
+
+def test_issue_10113():
+    f = x**2/(x**2 - 4)
+    assert imageset(x, f, S.Reals) == Union(Interval(-oo, 0, True),
+                                            Interval(1, oo, True, True))
+    assert imageset(x, f, Interval(-2, 2)) == Interval(-oo, 0, True)
+    assert imageset(x, f, Interval(-2, 3)) == Union(Interval(-oo, 0, True),
+                                                    Interval(Rational(9, 5),
+                                                             oo, False, True))