Trac #34723: elliptic_curves/hom_velusqrt.py: random test failure

Sage 9.7 on x86_64:
{{{
sage -t --long --random-seed=190440690778015682984135421278300846991
/nix/store/jv3l7isa1hf4bjvf40lmrflzmyd696kz-sage-
src-9.7/src/sage/schemes/elliptic_curves/hom_velusqrt.py
**********************************************************************
File "/nix/store/jv3l7isa1hf4bjvf40lmrflzmyd696kz-sage-
src-9.7/src/sage/schemes/elliptic_curves/hom_velusqrt.py", line 1089, in
sage.schemes.elliptic_curves.hom_velusqrt.EllipticCurveHom_velusqrt._eva
l
Failed example:
    E, K = _random_example_for_testing()
Exception raised:
    Traceback (most recent call last):
      File "/nix/store/g4h4aagj23nf3br90zn0545s8aqgbvxd-
python3-3.10.8-env/lib/python3.10/site-packages/sage/doctest/forker.py",
line 695, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/nix/store/g4h4aagj23nf3br90zn0545s8aqgbvxd-
python3-3.10.8-env/lib/python3.10/site-packages/sage/doctest/forker.py",
line 1101, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.schemes.elliptic_curves.hom_velusqrt.EllipticC
urveHom_velusqrt._eval[16]>", line 1, in <module>
        E, K = _random_example_for_testing()
      File "/nix/store/g4h4aagj23nf3br90zn0545s8aqgbvxd-
python3-3.10.8-env/lib/python3.10/site-
packages/sage/schemes/elliptic_curves/hom_velusqrt.py", line 1225, in
_random_example_for_testing
        assert K.order() == deg
    AssertionError
}}}

URL: https://trac.sagemath.org/34723
Reported by: gh-collares
Ticket author(s): Lorenz Panny
Reviewer(s): Frédéric Chapoton

Author: Release Manager

src/sage/schemes/elliptic_curves/hom_velusqrt.py

@@ -1389,7 +1389,7 @@ def _random_example_for_testing():
         sage: 5 <= K.order()
         True
     """
-    from sage.all import prime_range, choice, randrange, GF, gcd
+    from sage.all import prime_range, choice, randrange, GF, lcm, Mod
     while True:
         p = choice(prime_range(2, 100))
         e = randrange(1,5)
@@ -1411,9 +1411,10 @@ def _random_example_for_testing():
             deg = choice(ds)
             break
     G = A.torsion_subgroup(deg)
+    os = G.generator_orders()
     while True:
-        v = [randrange(deg) for _ in range(G.ngens())]
-        if gcd([deg] + v) == 1:
+        v = [randrange(o) for o in os]
+        if lcm(Mod(c,o).additive_order() for c,o in zip(v,os)) == deg:
             break
     K = G(v).element()
     assert K.order() == deg