Birational Transformation
How do I apply a birational transformation x --> 1/x, then clear the denominators. Is there a way I could do that in SAGE?
x, y = QQ['x,y'].gens()
C = Curve(x^2+y^2)
# the code I'm looking for here
x2+y2↦1/x2+y2↦1/x2+x2y2/x2↦1+x2y2