Assignment R1 ------------- Consider the algebraic curve given by: x = 3*t^2/(t^2+1), y = t^3/(t^2+1)^2 [*] You can view this curve in Maple by typing: plot( [3*t^2/(t^2+1), t^3/(t^2+1)^2, t=-1000..1000] ,numpoints=1000); Find a polynomial equation F(x,y) for this curve. Hint: We want: one equation F(x,y)=0 in two variables. Given in [*] are: A) One more equation than what we want. B) One more variable than what we want. and in this situation, you always have to eliminate that variable with a resultant. Note that resultant wants polynomial inputs, so the equation x = 3*t^2/(t^2+1) becomes the equation x-3*t^2/(t^2+1) = 0 which becomes the equation numer( x-3*t^2/(t^2+1) ) = 0 so that numer( x-3*t^2/(t^2+1) ) is one of the inputs for resultant. Assignment R2 ------------- Do not type this in Maple, use copy/paste ! f := y^5-2494*y^4+2042158*y^3-761328152*y^2+134266087241*y-9127158539954+474*y^4*x- 660492*y^3*x+128361096*y^2*x+15052058268*y*x-3212722859346*x+84366*y^3*x^2- 47970216*y^2*x^2-12024807786*y*x^2-228715574724*x^2+6697080*y^2*x^3-506101284* y*x^3+34263110700*x^3+202172841*y*x^4+5431439286*x^4+201803238*x^5; g := diff(f,x); h := diff(f,y); Find all solutions of {f,g,h} (i.e. f=0, g=0, h=0) using the Maple commands: resultant, gcd, factor, subs, etc. You may use Maple's solve command only on univariate equations.