src/sage/rings/function_field/function_field_test.py: new pytests

Move the existing TestSuite() runs for function fields to
pytest. These are long/slow tests that are not instructive as examples
in the documentation. As a side effect, we fix some "slow doctest"
warnings present in the CI.

Author: orlitzky

src/sage/rings/function_field/function_field_test.py

@@ -0,0 +1,58 @@
+import pytest
+
+# sage.misc.sage_unittest.TestSuite imports are local to avoid
+# pytest warnings.
+from sage.rings.finite_rings.finite_field_constructor import FiniteField
+from sage.rings.function_field.constructor import FunctionField
+from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
+from sage.rings.rational_field import QQ
+
+class TestFunctionField:
+    r"""
+    Run the long/slow TestSuite() methods on some function fields
+    that are constructed in the documentation. These used to be run in
+    a ``TESTS::`` block, but they are more appropriate here.
+    """
+    def test_function_field_S_M_N_testsuite(self):
+        from sage.misc.sage_unittest import TestSuite
+
+        K = FunctionField(FiniteField(5**2,'a'), 'x')
+        x = K.gen()
+        R = PolynomialRing(K, 'y')
+        y = R.gen()
+        L = K.extension(y**3 - (x**3 + 2*x*y + 1/x))
+        S = PolynomialRing(L, 't')
+        t = S.gen()
+        M = L.extension(t**2 - x*y)
+        N = FunctionField(K, 'u')
+        TestSuite(S).run(verbose=True, raise_on_failure=True, max_runs=8)
+        TestSuite(M).run(verbose=True, raise_on_failure=True, max_runs=1)
+        TestSuite(N).run(verbose=True, raise_on_failure=True, max_runs=1)
+
+    # The test suites for K,L,O were inadvertently made to be over
+    # QQbar in commit 5f162a448cb708fed40bebc1345fd656f918aed3. We use
+    # the old, faster definitions over QQ.
+    def test_function_field_K_L_O_testsuite(self):
+        from sage.misc.sage_unittest import TestSuite
+
+        K = FunctionField(QQ, 'x');
+        x = K.gen()
+        Y = PolynomialRing(K, 'Y').gen()
+        L = K.extension(Y**2 + Y + x + 1/x, 'y')
+        O = L.maximal_order()
+        TestSuite(K).run(verbose=True, raise_on_failure=True, max_runs=16)
+        TestSuite(L).run(verbose=True, raise_on_failure=True, max_runs=2)
+        TestSuite(O).run(verbose=True, raise_on_failure=True)
+
+    def test_function_field_R_testsuite(self):
+        from sage.misc.sage_unittest import TestSuite
+
+        F = FunctionField(QQ, 'x')
+        R = PolynomialRing(F, 'Y')
+        TestSuite(R).run(verbose=True, raise_on_failure=True)
+
+    def test_function_field_J_testsuite(self):
+        from sage.misc.sage_unittest import TestSuite
+
+        J = FunctionField(FiniteField(5), 'x')
+        TestSuite(J).run(verbose=True, raise_on_failure=True)