adjust random tests for generators of elliptic curves

Author: chriswuthrich

src/sage/schemes/elliptic_curves/ell_rational_field.py

@@ -2319,6 +2319,22 @@ def gens(self, proof=None, **kwds):
             sage: E1.gens(algorithm="pari")   #random
             [(-400 : 8000 : 1), (0 : -8000 : 1)]
 
+        TESTS::
+
+            sage: E = EllipticCurve('389a')
+            sage: len(E.gens())
+            2
+            sage: E.saturation(E.gens())[1]
+            1
+            sage: len(E.gens(algorithm="pari"))
+            2
+            sage: E.saturation(E.gens(algorithm="pari"))[1]
+            1
+            sage: E = EllipticCurve([-3/8,-2/3])
+            sage: P = E.lift_x(10/9)
+            sage: set(E.gens()) <= set([P,-P])
+            True
+
         """
         if proof is None:
             from sage.structure.proof.proof import get_flag
@@ -2370,23 +2386,29 @@ def _compute_gens(self, proof,
             sage: proved
             True
 
-        TESTS::
-
             sage: E = EllipticCurve([-127^2,0])
-            sage: E.gens(use_database=False, algorithm="pari")
-            Traceback (most recent call last):
-            ...
-            RuntimeError: generators could not be determined. So far we found []. Hint: increase pari_effort.
-            sage: E.gens(use_database=False, algorithm="pari",pari_effort=4)
+            sage: E.gens(use_database=False, algorithm="pari",pari_effort=4)   # random
             [(611429153205013185025/9492121848205441 : 15118836457596902442737698070880/924793900700594415341761 : 1)]
 
+        TESTS::
+
+            sage: P = E.lift_x(611429153205013185025/9492121848205441)
+            sage: set(E.gens(use_database=False, algorithm="pari",pari_effort=4)) <= set([P+T for T
+            ....:  in E.torsion_points()] + [-P+T for T in E.torsion_points()])
+            True
+
             sage: E = EllipticCurve([-157^2,0])
             sage: E.gens(use_database=False, algorithm="pari")
             Traceback (most recent call last):
             ...
             RuntimeError: generators could not be determined. So far we found []. Hint: increase pari_effort.
-            sage: E.gens(use_database=False, algorithm="pari",pari_effort=10) # long time
+            sage: ge = E.gens(use_database=False, algorithm="pari",pari_effort=10)
+            sage: ge   #random
             [(-166136231668185267540804/2825630694251145858025 : 167661624456834335404812111469782006/150201095200135518108761470235125 : 1)]
+            sage: P = E.lift_x(-166136231668185267540804/2825630694251145858025)
+            sage: set(E.gens(use_database=False, algorithm="pari",pari_effort=4)) <= set([P+T for T
+            ....:  in E.torsion_points()] + [-P+T for T in E.torsion_points()])
+            True
 
         """
         # If the optional extended database is installed and an
@@ -2532,6 +2554,11 @@ def gens_certain(self):
 
         TESTS::
 
+            sage: E = EllipticCurve('37a1')
+            sage: P = E([0,-1])
+            sage: set(E.gens()) <= set([P,-P])
+            True
+
             sage: E = EllipticCurve([2, 4, 6, 8, 10])
             sage: E.gens_certain()
             Traceback (most recent call last):