Coordinates do not define a point on Elliptic Curve over complex field? [closed]
I have an elliptic curve defined over $\mathbb{C}$ by the equation $y^2 = x^3 + i$ and a point $P = (0, \frac{1+I}{\sqrt{2}})$ on this curve, however when I translate it into code I get an error.
First of all, let's define the elliptic curve:
E = EllipticCurve(CC, [0, I])
print(E)
Obtaining:
Elliptic Curve defined by y^2 = x^3 + 1.00000000000000*I over Complex Field with 53 bits of precision
So, up to now everything looks fine, but then if I insert:
P = E([0, (1 + I)/math.sqrt(2)])
Here is what I obtain:
KeyError Traceback (most recent call last)
/usr/lib/python3/dist-packages/sage/structure/category_object.pyx in sage.structure.category_object.CategoryObject.getattr_from_category (build/cythonized/sage/structure/category_object.c:6958)()
837 try:
--> 838 return self.__cached_methods[name]
839 except KeyError:
KeyError: 'point_homset'
During handling of the above exception, another exception occurred:
AttributeError Traceback (most recent call last)
/usr/lib/python3/dist-packages/sage/schemes/projective/projective_subscheme.py in point(self, v, check)
117 try:
--> 118 return self._point(self.point_homset(), v, check=check)
119 except AttributeError: # legacy code without point_homset
/usr/lib/python3/dist-packages/sage/schemes/elliptic_curves/ell_point.py in __init__(self, curve, v, check)
259 """
--> 260 point_homset = curve.point_homset()
261 if is_SchemeMorphism(v) or isinstance(v, EllipticCurvePoint_field):
/usr/lib/python3/dist-packages/sage/structure/category_object.pyx in sage.structure.category_object.CategoryObject.__getattr__ (build/cythonized/sage/structure/category_object.c:6880)()
831 """
--> 832 return self.getattr_from_category(name)
833
/usr/lib/python3/dist-packages/sage/structure/category_object.pyx in sage.structure.category_object.CategoryObject.getattr_from_category (build/cythonized/sage/structure/category_object.c:7043)()
846
--> 847 attr = getattr_from_other_class(self, cls, name)
848 self.__cached_methods[name] = attr
/usr/lib/python3/dist-packages/sage/cpython/getattr.pyx in sage.cpython.getattr.getattr_from_other_class (build/cythonized/sage/cpython/getattr.c:2547)()
388 dummy_error_message.name = name
--> 389 raise AttributeError(dummy_error_message)
390 cdef PyObject* attr = instance_getattr(cls, name)
AttributeError: 'ComplexField_class_with_category' object has no attribute '__custom_name'
During handling of the above exception, another exception occurred:
TypeError Traceback (most recent call last)
<ipython-input-1-06cb782d02c0> in <module>
1 E = EllipticCurve(CC,[Integer(0),I])
2 print(E)
----> 3 P = E([Integer(0), (Integer(1)+I)/math.sqrt(Integer(2))])
4 print(P)
/usr/lib/python3/dist-packages/sage/schemes/elliptic_curves/ell_generic.py in __call__(self, *args, **kwds)
547 args = tuple(args[0])
548
--> 549 return plane_curve.ProjectivePlaneCurve.__call__(self, *args, **kwds)
550
551 def _reduce_point(self, R, p):
/usr/lib/python3/dist-packages/sage/schemes/generic/scheme.py in __call__(self, *args)
264 return S
265 args = S
--> 266 return self.point(args)
267
268 @cached_method
/usr/lib/python3/dist-packages/sage/schemes/projective/projective_subscheme.py in point(self, v, check)
118 return self._point(self.point_homset(), v, check=check)
119 except AttributeError: # legacy code without point_homset
--> 120 return self._point(self, v, check=check)
121
122 return self.point_homset()(v, check=check)
/usr/lib/python3/dist-packages/sage/schemes/elliptic_curves/ell_point.py in __init__(self, curve, v, check)
300 test = y**2 + (a1*x+a3)*y - (((x+a2)*x+a4)*x+a6)
301 if not test == 0:
--> 302 raise TypeError("Coordinates %s do not define a point on %s" % (list(v), curve))
303
304 SchemeMorphism_point_abelian_variety_field.__init__(self, point_homset, v, check=False)
TypeError: Coordinates [0.000000000000000, 0.707106781186547 + 0.707106781186547*I, 1.00000000000000] do not define a point on Elliptic Curve defined by y^2 = x^3 + 1.00000000000000*I over Complex Field with 53 bits of precision