solvers: workaround real_roots() sorting for simple roots

Closes sympy/sympy#20902

diofant/solvers/inequalities.py

@@ -206,6 +206,7 @@ def solve_poly_inequality(poly, rel):
             raise NotImplementedError(f"Couldn't determine truth value of {t}")
 
     reals, intervals = poly.real_roots(multiple=False), []
+    reals = sorted(reals, key=lambda r: r[0])
 
     if rel == '==':
         for root, _ in reals:

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

@@ -35,3 +35,4 @@ 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