From 6973ae918c96b64d248eaa96d8318027f16746c8 Mon Sep 17 00:00:00 2001 From: Sebastian Spindler Date: Thu, 9 May 2024 01:12:15 +0200 Subject: [PATCH] Moved old tests to examples Amend: Fixed typo --- src/sage/schemes/elliptic_curves/ell_point.py | 22 +++++++++++++++++++ 1 file changed, 22 insertions(+) diff --git a/src/sage/schemes/elliptic_curves/ell_point.py b/src/sage/schemes/elliptic_curves/ell_point.py index 84a4b051793..99e3e8c81fa 100644 --- a/src/sage/schemes/elliptic_curves/ell_point.py +++ b/src/sage/schemes/elliptic_curves/ell_point.py @@ -1818,6 +1818,17 @@ def weil_pairing(self, Q, n, algorithm=None): sage: z.multiplicative_order() 360 + Another larger example:: + + sage: F = GF(65537^2, modulus=[3,-1,1], name='a') + sage: F.inject_variables() + Defining a + sage: E = EllipticCurve(F, [0,1]) + sage: P = E(22, 28891) + sage: Q = E(-93, 2728*a + 64173) + sage: P.weil_pairing(Q, 7282, algorithm='sage') + 53278*a + 36700 + An example over a number field:: sage: # needs sage.rings.number_field @@ -2051,6 +2062,17 @@ def tate_pairing(self, Q, n, k, q=None): sage: Px.weil_pairing(Qx, 41)^e == num/den True + An example over a large base field:: + + sage: F = GF(65537^2, modulus=[3,46810,1], name='z2') + sage: F.inject_variables() + Defining z2 + sage: E = EllipticCurve(F, [0,1]) + sage: P = E(22, 28891) + sage: Q = E(-93, 40438*z2 + 31573) + sage: P.tate_pairing(Q, 7282, 2) + 34585*z2 + 4063 + TESTS: The point ``P (self)`` must have ``n`` torsion::