[Maxima-discuss] How do I do just the first half of "plotting contour levels"?

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

Hi list,

a few days ago I had to draw some level curves of

  F(x,y) := 2*x^2 - x*y - y^2;

in TikZ. I was in a hurry, so I wrote something that was an uglier
version of this,

  F(x,y)  := 2*x^2 - x*y - y^2;
  xs(y,z) := solve(F(x,y)=z, x);
  maxsol(sols) := apply('max, map('rhs, sols));
  minsol(sols) := apply('min, map('rhs, sols));
  leftx (y,z)  := minsol(xs(y,z));
  rightx(y,z)  := maxsol(xs(y,z));
  seqn(a,b,n)    := makelist(a + (b-a)*k/n, k, 0, n);
  leftxys (ys,z) := ev(makelist([leftx (y,z), y], y, ys), numer);
  rightxys(ys,z) := ev(makelist([rightx(y,z), y], y, ys), numer);
  leftxys (seqn(2, 0.943, 10), -1);
  rightxys(seqn(0.943, 2, 10), -1);

but with more calls to "leftxys" and "rightxys" at the end, and then I
converted the output to a series of "\draw" commands for TikZ using a
throway-ish Lua program.

I'm not in a hurry anymore, and now I can try to learn better ways to
find the points in level curves.

Questions: 1) I got lots of messages like this one:

  rat: replaced 0.110751 by 110751/1000000 = 0.110751

How do I silence them?

And: 2) plot2d knows how to plot "contour levels". It certainly has
separate functions for calculating the points of a level curve and for
converting those points into commands for, say, gnuplot... is it easy
to call just the function that calculates the points? How do I do
that?

  Thanks in advance!
    Eduardo Ochs
    http://angg.twu.net/eev-maxima.html