Re: [Maxima-discuss] draw2d parametric fails on a function defined by cases

[Eduardo O. <edu...@gm...>]

On Wed, 9 Oct 2024 at 21:48, Robert Dodier <rob...@gm...> wrote:
> On Wed, Oct 9, 2024 at 2:33 PM Eduardo Ochs <edu...@gm...> wrote:
>
> >   P(t) := if t <= 6 then [t,4] else [6,10-t];
> >   draw2d(explicit(P(t)[1], t,0,10),
> >          explicit(P(t)[2], t,0,10));
> >   draw2d(parametric(P(t)[1], P(t)[2], t,0,10));
> >
> > The first three "draw2d"s work perfectly, but the last one
> > yields this error:
> >
> >   draw2d (parametric): non defined variable
>
> This is due to a bug in the way that parametric verifies that the
> first two arguments are functions of the parameter t alone.
> `listofvars` is called, but listofvars(foo(x)[1]) returns [foo(x)[1]],
> not [x] as one might hope.
>
> I guess this could be interpreted as a bug in listofvars. It is
> supposed to return [x[1]] for listofvars(x[1] + 2), for example, but
> maybe if the expression looks like listofvars(foo(x)[1] + 2) it should
> return [x].
>
> As a workaround, one could say something like
>
> P1(t) := if t <= 6 then t else 6;
> P2(t) := if t <= 6 then 4 else 10 - t;
> draw2d (parametric (P1(t), P2(t), t, 0, 10));
>
> I know that's less elegant in a way.
>
> Robert


Perfect, thanks!

Here is a way to write that workaround that I find more readable:

  P(t) :=  if t <= 6 then [t,4] else [6,10-t];   /* redefine as: */
  P(t) := [if t <= 6 then  t    else  6,         /* x */
           if t <= 6 then    4  else    10-t];   /* y */

  draw2d(xrange=[-1,8], yrange=[-1,8],
         parametric(P(t)[1],P(t)[2], t,0,10));

Solved! Cheers =),
  Eduardo Ochs