606.sagews

var('x')
p1 = plot((x**3 - 2)**0.5, (x, 2**(1.0/3), 20))
p2 = plot(-(x**3 - 2)**0.5, (x, 2**(1.0/3), 20))
p3 = point([0,10], pointsize=20, rgbcolor=(1,0,0))
line1 = line([(0,10), (5,5)], rgbcolor=(0,1,0))
(p1 + p2).show(figsize=[5,5], xmin=-4, xmax=6, ymin=-15, ymax=15)

E = EllipticCurve([0,0,0,0,-2])
print E
P = E([3,5])
Q = P
print P + Q

Elliptic Curve defined by y^2 = x^3 - 2 over Rational Field (129/100 : -383/1000 : 1)

print ((383/(10**3)) - 5) / ((129/(10**2)) - 3)

27/10

print 5 - 27/10 * 3

-31/10

print (27/10)^2 - 0 - 3 - 129/10^2

3

print -(27/10)^3 + (3 + 129/100)*(27/10) + 31/10

-5