> #Surface plotting
> A:=(3+cos(v))*cos(u);B:=(3+cos(v))*sin(u);C:=sin(v);
> plot3d([A,B,C],u=0..2*Pi,v=0..2*Pi,scaling=constrained,style=PATCHCONTOUR,shading=Z,orientation=[0,65]);
> #surface integrals int_S F dot dA; F(x,y,f(x,y)).<-fx,-fy, 1> dxdy
> with(linalg);
> diverge(vector([x^2,y^2,z^2]),[x,y,z]);
> diverge(vector([P,Q,R]),[x,y,z]);
> curl(vector([x*y*z,x*y*z,x*y*z]),[x,y,z]);
> #2 F=<x,y,z> f(x,y)=1-x-y; 0<=x<=2,0<=y<=3
> f:=1-x-y;int(int(dotprod(vector([x,y,f]),vector([-diff(f,x),-diff(f,y),1])),x=0..2),y=0..3);dotprod(vector([x,y,f]),vector([-diff(f,x),-diff(f,y),1]));
> crossprod(vector([1,0,fx]),vector([0,1,fy]));
> plot3d([t^3,t^4,(3*t^12-4*t^10)*s],t=0..1,s=0..1);
> plot3d([cos(t),sin(t),(sin(t)*cos(t))*s],t=0..2*Pi,s=0..1);
>