Add regression test

Closes sympy/sympy#12345

diofant/solvers/tests/test_polysys.py

@@ -138,3 +138,18 @@ def test_solve_sympyissue_6785_RR():
     assert roots[0][y].epsilon_eq(-499.474999374969, 1e12)
     assert roots[1][x] == 0
     assert roots[1][y].epsilon_eq(500.474999374969, 1e12)
+
+
+def test_sympyissue_12345():
+    eqs = (x**2 - y - sqrt(2), x**2 + x*y - y**2)
+    r0, r1, r2, r3 = Poly(y**4 - 3*y**3 + y**2*(-3*sqrt(2) + 1) +
+                          2*sqrt(2)*y + 2, y).all_roots()
+    sol = [{x: sqrt(2)*r0**3/2 - 3*sqrt(2)*r0**2/2 - 2*r0 + sqrt(2)*r0/2 + 1,
+            y: r0},
+           {x: sqrt(2)*r1**3/2 - 3*sqrt(2)*r1**2/2 - 2*r1 + sqrt(2)*r1/2 + 1,
+            y: r1},
+           {x: sqrt(2)*r2**3/2 - 3*sqrt(2)*r2**2/2 - 2*r2 + sqrt(2)*r2/2 + 1,
+            y: r2},
+           {x: sqrt(2)*r3**3/2 - 3*sqrt(2)*r3**2/2 - 2*r3 + sqrt(2)*r3/2 + 1,
+            y: r3}]
+    assert solve_poly_system(eqs, x, y) == sol

docs/release/notes-0.9.rst

@@ -125,8 +125,9 @@ Issues closed
 * :sympyissue:`11911` typo in docs of printing
 * :sympyissue:`10489` Mathematical Symbol does not seem to serialize correctly LaTeX printer
 * :sympyissue:`10336` nsimplify problems with `oo` and `inf`
+* :sympyissue:`12345` nonlinsolve (solve_biquadratic) gives no solution with radical
 
-.. last pr: #390
+.. last pr: #448
 
 See also full `list of closed issues
 <https://github.com/diofant/diofant/issues?q=is%3Aissue+milestone%3A0.9.0+is%3Aclosed>`_