[Ecm-commits] r2589 - trunk

cvs commits ecm-commits at lists.gforge.inria.fr
Sun Feb 8 15:48:13 CET 2015


Author: bouvierc
Date: 2015-02-08 15:48:13 +0100 (Sun, 08 Feb 2015)
New Revision: 2589

Modified:
   trunk/parametrizations.c
Log:
More comments on how the parametrization -param 2 is computed


Modified: trunk/parametrizations.c
===================================================================
--- trunk/parametrizations.c	2015-02-07 10:40:17 UTC (rev 2588)
+++ trunk/parametrizations.c	2015-02-08 14:48:13 UTC (rev 2589)
@@ -271,6 +271,11 @@
 
 /* Parametrization ECM_PARAM_BATCH_2 */
 /* 2 <= sigma */
+/* Compute (x:y:z) = sigma*(-3:3:1) on the elliptic curve y^2 = x^3 + 36
+  using Jacobian coordinates; formulae were found at
+      https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html
+  Then we let x3 = (3*x+y+6)/(2*(y-3)), A = -(3*x3^4+6*x3^2-1)/(4*x3^3) and
+  x0 = 2 */
 int 
 get_curve_from_param2 (mpz_t f, mpres_t A, mpres_t x0, mpz_t sigma, mpmod_t n)
 {



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