\\ \\ wf.gp \\ dd(x,y,a1,a2,a3,a4,a6)=(2*y+a1*x+a3) \\ ll(x,y,a1,a2,a3,a4,a6)=(2*x^3+2*a2*x+a4-a1*y)/(2*y+a1*x+a3) \\ ll(x,y)=lla(x,y)/dd(x,y) lla(x,y,a1,a2,a3,a4,a6)=(3*x^2+2*a2*x+a4-a1*y); \\ nn(x,y,a1,a2,a3,a4,a6)=(-x^3+a4*x+2*a6-a3*y)/(2*y+a1*x+a3) \\ nn(x,y)=nna(x,y)/dd(x,y) nna(x,y,a1,a2,a3,a4,a6)=(-x^3+a4*x+2*a6-a3*y); y2red(p,x,y,a1,a2,a3,a4,a6)=polcoeff(p,2,'y)*(x^3+a2*x^2+a4*x+a6-a1*x*y-a3*y)+polcoeff(p,1,'y)*y+polcoeff(p,0,'y); y3red(p,x,y,a1,a2,a3,a4,a6)=polcoeff(p,3,'y)*((x^3+a2*x^2+a4*x+a6)*y-(a1*x+a3)*(x^3+a2*x^2+a4*x+a6-a1*x*y-a3*y))+polcoeff(p,2,'y)*(x^3+a2*x^2+a4*x+a6-a1*x*y-a3*y)+polcoeff(p,1,'y)*y+polcoeff(p,0,'y); y4red(p,x,y,a1,a2,a3,a4,a6)=polcoeff(p,4,'y)*((x^3+a2*x^2+a4*x+a6)^2-2*(x^3+a2*x^2+a4*x+a6)*(a1*x+a3)*y+(a1*x+a3)^2*(x^3+a2*x^2+a4*x+a6-a1*x*y-a3*y))+polcoeff(p,3,'y)*((x^3+a2*x^2+a4*x+a6)*y-(a1*x+a3)*(x^3+a2*x^2+a4*x+a6-a1*x*y-a3*y))+polcoeff(p,2,'y)*(x^3+a2*x^2+a4*x+a6-a1*x*y-a3*y)+polcoeff(p,1,'y)*y+polcoeff(p,0,'y); \\ xx2(x,y,a1,a2,a3,a4,a6)=ll(x,y,a1,a2,a3,a4,a6)^2+a1*ll(x,y,a1,a2,a3,a4,a6)-a2-2*x xx2a(x,y,a1,a2,a3,a4,a6)=y2red((lla(x,y,a1,a2,a3,a4,a6)^2+a1*lla(x,y,a1,a2,a3,a4,a6)*dd(x,y,a1,a2,a3,a4,a6)-(a2+2*x)*dd(x,y,a1,a2,a3,a4,a6)^2),x,y,a1,a2,a3,a4,a6); yy2a(x,y,a1,a2,a3,a4,a6)=y3red(-(lla(x,y,a1,a2,a3,a4,a6)+a1*dd(x,y,a1,a2,a3,a4,a6))*xx2a(x,y,a1,a2,a3,a4,a6)-nna(x,y,a1,a2,a3,a4,a6)*dd(x,y,a1,a2,a3,a4,a6)^2-a3*dd(x,y,a1,a2,a3,a4,a6)^3,x,y,a1,a2,a4,a4,a6); llla(x,y,a1,a2,a3,a4,a6)=y3red(yy2a(x,y,a1,a2,a3,a4,a6)-y*dd(x,y,a1,a2,a3,a4,a6)^3,x,y,a1,a2,a3,a4,a6); dd2(x,y,a1,a2,a3,a4,a6)=y2red((xx2a(x,y,a1,a2,a3,a4,a6)-x*dd(x,y,a1,a2,a3,a4,a6)^2),x,y,a1,a2,a3,a4,a6); nnna(x,y,a1,a2,a3,a4,a6)=y3red((y*dd(x,y,a1,a2,a3,a4,a6)*xx2a(x,y,a1,a2,a3,a4,a6)-yy2a(x,y,a1,a2,a3,a4,a6)*x),x,y,a1,a2,a3,a4,a6); xx3a(x,y,a1,a2,a3,a4,a6)=y4red((llla(x,y,a1,a2,a3,a4,a6)^2+a1*llla(x,y,a1,a2,a3,a4,a6)*dd(x,y,a1,a2,a3,a4,a6)*dd2(x,y,a1,a2,a3,a4,a6)-(a2+x)*dd(x,y,a1,a2,a3,a4,a6)^2*dd2(x,y,a1,a2,a3,a4,a6)^2-xx2a(x,y,a1,a2,a3,a4,a6)*dd2(x,y,a1,a2,a3,a4,a6)^2),x,y,a1,a2,a3,a4,a6);