Fix sorting in RootOf.real_roots()

diofant/polys/rootisolation.py

@@ -859,7 +859,7 @@ def as_tuple(self):
 
     def is_disjoint(self, other):
         """Return ``True`` if two isolation intervals are disjoint."""
-        return self.b <= other.a or other.b <= self.a
+        return self.b < other.a or other.b < self.a
 
     def refine(self):
         """Perform one step of real root refinement algorithm."""

diofant/solvers/inequalities.py

@@ -329,7 +329,6 @@ def solve_rational_inequalities(eqs):
 
             for interval in global_intervals:
                 if interval.contains(oo) is true and expr.limit(gen, oo, '-') is false:
-                    print(111)
                     interval -= FiniteSet(oo)
                 elif interval.contains(-oo) is true and expr.limit(gen, -oo) is false:
                     interval -= FiniteSet(-oo)

diofant/tests/polys/test_rootoftools.py

@@ -335,9 +335,10 @@ def test_RootOf_evalf_caching_bug():
 
 def test_RootOf_real_roots():
     assert (x**5 + x + 1).as_poly().real_roots() == [RootOf(x**3 - x**2 + 1, 0)]
-    assert (x**5 + x + 1).as_poly().real_roots(radicals=False) == [RootOf(
-        x**3 - x**2 + 1, 0)]
+    assert (x**5 + x + 1).as_poly().real_roots(radicals=False) == [RootOf(x**3 - x**2 + 1, 0)]
     assert (x**7 - 0.1*x + 1).as_poly(x).real_roots() == [RootOf(10*x**7 - x + 10, 0)]
+    assert ((x - 2)*(x - 1)*(x**2 - 2)).as_poly().real_roots() == [-sqrt(2), 1, sqrt(2), 2]
+    assert ((x + 1)**3*(3*x + 1)).as_poly().real_roots(multiple=False) == [(-1, 3), (Rational(-1, 3), 1)]
 
 
 def test_RootOf_all_roots():

diofant/tests/solvers/test_inequalities.py

@@ -403,3 +403,16 @@ def test_diofantissue_836():
 
 def test_sympyissue_20861():
     assert reduce_inequalities([3/x < 0, x >= 2, x >= 7], x) is false
+
+
+def test_sympyissue_20902():
+    eq = y/((1 + y)**2)
+
+    assert (reduce_inequalities(eq.subs({y: 3*x + 2}).diff(x) > 0) ==
+            (Integer(-1) < x) & (x < Rational(-1, 3)))
+    assert (reduce_inequalities(eq.subs({y: 3*x + 3}).diff(x) > 0) ==
+            (Rational(-4, 3) < x) & (x < Rational(-2, 3)))
+    assert (reduce_inequalities(eq.subs({y: 3*x + 4}).diff(x) > 0) ==
+            (Rational(-5, 3) < x) & (x < Integer(-1)))
+    assert (reduce_inequalities(eq.subs({y: 3*x + 2}).diff(x) > 0) ==
+            (Integer(-1) < x) & (x < Rational(-1, 3)))

docs/release/notes-0.13.rst

@@ -34,3 +34,5 @@ for complete list of issues and pull requests involved in this release.
 These Sympy issues also were addressed:
 
 * :sympyissue:`20861`: reduce_inequalities() gives impossible answer
+* :sympyissue:`20874`: Port the PRS algorithm to the sparse polynomial implementation
+* :sympyissue:`20902`: Incorrect inequality solving: False returned instead of answer