source 2007 Bernstein--Lange
compute XX = X1^2
compute XXXX = XX^2
compute YY = Y1^2
compute ZZ = Z1^2
compute ZZZZ = ZZ^2
compute M = XX+ZZ
compute XZ = (X1+Z1)^2-M
compute XZXZ = XZ^2
compute X3 = (Y1+XZ)^2-YY-XZXZ
compute Y3 = (ZZZZ+XXXX)(4 YY+2 a XZXZ)+XZXZ^2
compute Z3 = 2 (ZZZZ-XXXX)