> restart;#t is theta
> x:=u*cos(theta)-v*sin(theta);y:=u*sin(theta)+v*cos(theta);
> e1:=a*x^2+b*x*y+c*y^2;
> e2:=expand(e1);
> e3:=collect(e2,[u,v],distributed);
> c1:=op(e3)[3];
> c2:=coeff(e3,u);
> c3:=coeff(c2,v);
> c4:=expand(c3/(cos(theta)^2));
> f:=subs({cos(theta)=C,sin(theta)=S},c4);
> f2:=subs({S=0,C=1}, f);
> f2:=subs({S=1/sqrt(2),C=1/sqrt(2)}, f);
> simplify(subs(theta=0,c3));
> simplify(subs(theta=Pi/2,c3));
> solve(c3=0,theta);
> expand((a-c)^2);
> m:=array(1..2,1..2,[[a, b],[b,c]]);
> id:=array(1..2,1..2,[[1,0],[0,1]]);
> with(linalg);
> eigenvals(m);
> eigenvectors(m);
> restart;tay:=taylor(exp(x),x=0,3);poly:=convert(tay,'polynom');
> readlib(mtaylor);mtaylor(exp(x+y),[x=0,y=0],3);
> subs(x=x+y,poly);
>