Using Maple to find Groebner Bases and Implicit Equations
First you have to fetch the Groebner Package in Maple
> | with(Groebner); |
Now you define your polynomials
Say we are given x(t)=t^2-2t and y(t)=(t^3+1)/(t-2)
> | f1:=t^2-2*t-x; f2:= t^3+1-y*(t-2); f3:= s*(t-2)-1; |
Now we can find our basis using the lex order s>t>x>y
> | gbasis([f1,f2,f3],plex(s,t,x,y)); |
Look at this ideal and take out the polynomial in only x and y.
We find that the implicit form of the curve is defined by f =