MaplePrimes - answers and comments on Question, Converting a parametric representation of a function

not quite clear for me

Axel Vogt — Sat, 13 Feb 2010 16:11:00 Z

It is not quite clear for me, what you mean and do, but it seems you think of T as 't is a function of x'.

However that is already part of a correct definition for your (1) and (2).

again

Peter Mond — Sat, 13 Feb 2010 16:23:24 Z

Thank you for your reply.

The task is quite simple:

For each t (element of real numbers) I get a pair of y and x values and I want to plot the function y=f(x), but also I want to get the equation of the function y=f(x) for further processing.

I'm just experimenting with solve, eval, and subs but with no success.

Thanks for considering this.

Peter

implicitize

Thomas Unger — Sat, 13 Feb 2010 17:22:35 Z

Try this:

restart:
with(algcurves);
eqs:= x = 3*t/(t^2+1), y = 3/(t^2+1);
implicitize([eqs], [t = 0 .. 1], 2, symbolic = true, useFNV = false);

Regards

Problem solved

Peter Mond — Sat, 13 Feb 2010 21:34:25 Z

Thank you very much all of you. With your help I got the solution, which is listed below, at least for my sample. I'll now turn to my real problem.

restart;
f1 := x -> x*1/2;
f2 := y -> y+20;
plot([f1(t),f2(t),t=-20..20]);
solve(x=f1(t),t);
f1_inv:= unapply(%,x);
f3 := x -> f2(f1_inv(x));
plot(f3(x),x=-10..10);

Axel, the square brackets have been the solution for the parametric plot problem and solve, unapply, and subsequent substitution help to find the function behind the plot. Consequently both plots show the same result.

Thanks again for your time

Peter

again

Axel Vogt — Sat, 13 Feb 2010 20:32:00 Z

If the task is quite simple then you may write it down as such :-)

Ok: not all implicite functions allow what you want.

Consider a circle plot([cos(t),sin(t),t=-Pi..Pi]) and recognize, that you may have 0 or 1 or 2 real solutions for y, depending on x.