name Jacobi intersections parameter a coordinate s coordinate c coordinate d satisfying s^2+c^2=1 satisfying a s^2+d^2=1 addition s = (c2 s1 d2+d1 s2 c1)/(c2^2+(d1 s2)^2) addition c = (c2 c1-d1 s2 s1 d2)/(c2^2+(d1 s2)^2) addition d = (d1 d2-a s1 c1 s2 c2)/(c2^2+(d1 s2)^2) doubling s = (c1 s1 d1+d1 s1 c1)/(c1^2+(d1 s1)^2) doubling c = (c1 c1-d1 s1 s1 d1)/(c1^2+(d1 s1)^2) doubling d = (d1 d1-a s1 c1 s1 c1)/(c1^2+(d1 s1)^2) negation s = -s1 negation c = c1 negation d = d1 neutral s = 0 neutral c = 1 neutral d = 1 toweierstrass x = (d-1)(1-a)/(c a-d+1-a) toweierstrass y = s(1-a)a/(c a-d+1-a) a0 = 1 a1 = 0 a3 = 0 a2 = 2-a a4 = 1-a a6 = 0 fromweierstrass s = -2 y/(((y/x)^2+a)x) fromweierstrass c = 1-2/((y/x)^2+a)-2 (1-a)/(((y/x)^2+a)x) fromweierstrass d = 1-2 a/((y/x)^2+a)