reviewer comments

Author: yyyyx4

src/sage/schemes/elliptic_curves/ell_point.py

@@ -560,39 +560,59 @@ def has_order(self, n):
             sage: P._order
             7
 
+        It also works with a :class:`~sage.structure.factorization.Factorization` object::
+
+            sage: E = EllipticCurve(GF(419), [1,0])
+            sage: P = E(-33, 8)
+            sage: P.has_order(factor(21))
+            True
+            sage: P._order
+            21
+
         This method can be much faster than computing the order and comparing::
 
+            sage: # not tested -- timings are different each time
             sage: p = 4 * prod(primes(3,377)) * 587 - 1
             sage: E = EllipticCurve(GF(p), [1,0])
-            sage: %timeit P = E.random_point(); P.set_order(multiple=p+1)   # not tested
+            sage: %timeit P = E.random_point(); P.set_order(multiple=p+1)
             72.4 ms ± 773 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)
-            sage: %timeit P = E.random_point(); P.has_order(p+1)            # not tested
+            sage: %timeit P = E.random_point(); P.has_order(p+1)
             32.8 ms ± 3.12 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)
             sage: fac = factor(p+1)
-            sage: %timeit P = E.random_point(); P.has_order(fac)            # not tested
+            sage: %timeit P = E.random_point(); P.has_order(fac)
             30.6 ms ± 3.48 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)
 
-        The order is cached once it has been confirmed once::
+        The order is cached once it has been confirmed once, and the cache is
+        shared with :meth:`order`::
 
+            sage: # not tested -- timings are different each time
             sage: P, = E.gens()
             sage: delattr(P, '_order')
-            sage: %time P.has_order(p+1)  # not tested
-            CPU times: user 62.1 ms, sys: 6.27 ms, total: 68.3 ms
-            Wall time: 68.8 ms
+            sage: %time P.has_order(p+1)
+            CPU times: user 83.6 ms, sys: 30 µs, total: 83.6 ms
+            Wall time: 83.8 ms
             True
-            sage: %time P.has_order(p+1)  # not tested
-            CPU times: user 5 µs, sys: 0 ns, total: 5 µs
-            Wall time: 5.48 µs
+            sage: %time P.has_order(p+1)
+            CPU times: user 31 µs, sys: 2 µs, total: 33 µs
+            Wall time: 37.9 µs
             True
+            sage: %time P.order()
+            CPU times: user 11 µs, sys: 0 ns, total: 11 µs
+            Wall time: 16 µs
+            5326738796327623094747867617954605554069371494832722337612446642054009560026576537626892113026381253624626941643949444792662881241621373288942880288065660
             sage: delattr(P, '_order')
-            sage: %time P.has_order(fac)  # not tested
-            CPU times: user 69.7 ms, sys: 14 µs, total: 69.8 ms
-            Wall time: 70.3 ms
+            sage: %time P.has_order(fac)
+            CPU times: user 68.6 ms, sys: 17 µs, total: 68.7 ms
+            Wall time: 68.7 ms
             True
-            sage: %time P.has_order(fac)  # not tested
-            CPU times: user 15 µs, sys: 0 ns, total: 15 µs
-            Wall time: 17.4 µs
+            sage: %time P.has_order(fac)
+            CPU times: user 92 µs, sys: 0 ns, total: 92 µs
+            Wall time: 97.5 µs
             True
+            sage: %time P.order()
+            CPU times: user 10 µs, sys: 1e+03 ns, total: 11 µs
+            Wall time: 14.5 µs
+            5326738796327623094747867617954605554069371494832722337612446642054009560026576537626892113026381253624626941643949444792662881241621373288942880288065660
         """
         if hasattr(self, '_order'):                 # already known
             if not isinstance(n, Integer):