name short Weierstrass curves
parameter a
parameter b
coordinate x
coordinate y
satisfying y^2 = x^3 + a x + b
addition x = (y2-y1)^2/(x2-x1)^2-x1-x2
addition y = (2 x1+x2) (y2-y1)/(x2-x1)-(y2-y1)^3/(x2-x1)^3-y1
doubling x = (3 x1^2+a)^2/(2 y1)^2-x1-x1
doubling y = (2 x1+x1) (3 x1^2+a)/(2 y1)-(3 x1^2+a)^3/(2 y1)^3-y1
negation x = x1
negation y = -y1
toweierstrass weierx = x
toweierstrass weiery = y
a0 = 1
a1 = 0
a2 = 0
a3 = 0
a4 = a
a6 = b
fromweierstrass x = weierx
fromweierstrass y = weiery