More tests

Author: user202729

src/sage/schemes/elliptic_curves/period_lattice.py

@@ -1727,6 +1727,56 @@ def elliptic_logarithm(self, P, prec=None, reduce=True):
             1.17058357737548897849026170185581196033579563441850967539191867385734983296504066660506637438866628981886518901958717288150400849746892393771983141354 - 1.13513899565966043682474529757126359416758251309237866586896869548539516543734207347695898664875799307727928332953834601460994992792519799260968053875*I
             sage: L.elliptic_logarithm(P, prec=1000)
             1.17058357737548897849026170185581196033579563441850967539191867385734983296504066660506637438866628981886518901958717288150400849746892393771983141354014895386251320571643977497740116710952913769943240797618468987304985625823413440999754037939123032233879499904283600304184828809773650066658885672885 - 1.13513899565966043682474529757126359416758251309237866586896869548539516543734207347695898664875799307727928332953834601460994992792519799260968053875387282656993476491590607092182964878750169490985439873220720963653658829712494879003124071110818175013453207439440032582917366703476398880865439217473*I
+
+        Elliptic curve over ``QQbar``::
+
+            sage: E = EllipticCurve(QQbar, [sqrt(2), I])
+            sage: L = E.period_lattice()
+            sage: P = E.lift_x(3)
+            sage: L.elliptic_logarithm(P)
+            -1.97657221097437 - 1.05021415535949*I
+            sage: L.elliptic_exponential(_)
+            (3.00000000000000 + 9.20856947066460e-16*I : -5.59022723358798 - 0.0894418024719718*I : 1.00000000000000)
+            sage: L.elliptic_logarithm(P, prec=100)
+            -3.4730631218714889933426781799 + 0.44627675553762761312098773197*I
+            sage: L.elliptic_exponential(_)
+            (3.0000000000000000000000000000 - 1.4773628579202938936348512161e-30*I : -5.5902272335879800026836302686 - 0.089441802471969391005702381090*I : 1.0000000000000000000000000000)
+
+        Real approximate field, negative discriminant. Note that the output precision uses the precision of the base field::
+
+            sage: E = EllipticCurve(RealField(100), [1, 6])
+            sage: L = E.period_lattice()
+            sage: L.real_flag
+            -1
+            sage: P = E(3, 6)
+            sage: L.elliptic_logarithm(P)
+            2.4593388737550379526023682666
+            sage: L.elliptic_exponential(_)
+            (3.0000000000000000000000000000 : 5.9999999999999999999999999999 : 1.0000000000000000000000000000)
+
+        Real approximate field, positive discriminant::
+
+            sage: E = EllipticCurve(RealField(100), [-4, 3])
+            sage: L = E.period_lattice()
+            sage: L.real_flag
+            1
+            sage: P = E.lift_x(4)
+            sage: L.elliptic_logarithm(P)
+            0.51188849089267627141925354967
+            sage: L.elliptic_exponential(_)
+            (4.0000000000000000000000000000 : -7.1414284285428499979993998114 : 1.0000000000000000000000000000)
+
+        Complex approximate field::
+
+            sage: E = EllipticCurve(ComplexField(100), [I, 3*I+4])
+            sage: L = E.period_lattice()
+            sage: L.real_flag
+            0
+            sage: P = E.lift_x(4)
+            sage: L.elliptic_logarithm(P)
+            -1.1447032790074574712147458157 - 0.72429843602171875396186134806*I
+            sage: L.elliptic_exponential(_)
+            (4.0000000000000000000000000000 + 1.2025589033682610849950210280e-30*I : -8.2570982991257407680322611854 - 0.42387771989714340809597881586*I : 1.0000000000000000000000000000)
         """
         if P.curve() is not self.E:
             raise ValueError("Point is on the wrong curve")