Ticket #3674: sage-trac3674b.patch

a/sage/schemes/elliptic_curves/ell_rational_field.py

@@ -3702 +3702 @@
-        else:
-            h_gs = max(1, log_g2)
-        return max(R(1),h_j, h_gs)
+
+    def antilogarithm(self, z, prec=53):
+        """The rational point (if any) associated to this complex number
+           (inverse of elliptic logarithm)
+
+           INPUT:
+               z -- a complex number representing an element of
+               CC/L where L is the period lattice of the elliptic
+               curve
+
+           OUTPUT: The rational point which is the image of z under
+               the Weierstrass parametrization, if it exists and can
+               be determined from z with default precision
+
+           ALGORITHM: This uses the function ellztopoint from the pari library
+
+           WARNING: At present (3.0.4) it is not possible to pass the
+           precision parameter to ellztopoint!
+           
+           EXAMPLES:
+           sage: E=EllipticCurve('5077a1')                 
+           sage: Pi=E.gens()                               
+           sage: Pi
+           [(-2 : 3 : 1), (-7/4 : 25/8 : 1), (1 : -1 : 1)]
+           sage: zi=[P.elliptic_logarithm(100) for P in Pi]
+           sage: Qi = [E.antilogarithm(z) for z in zi]     
+           sage: Pi == Qi
+           True
+
+        """
+        
+        E_pari = self.pari_curve(prec)
+        CC = ComplexField(prec)
+        try:
+            coords = E_pari.ellztopoint(z)
+            if len(coords) == 1:
+                return self(0)
+            return self([CC(xy).real().simplest_rational() for xy in coords])
+        except:
+            raise ValueError, "No rational point computable from z"
-
-    def integral_points(self, mw_base='auto', both_signs=False):
-        """