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

[Stavros M. <mac...@gm...>]

This is not a very good way to plot contours. The purely numerical approach
used by the plotting routines will work much better.

Here are some of the issues:

* Solve is designed to give exact solutions, so you will get solutions in
radicals, not floating-point numbers (even with float inputs and
*keepfloat:true*)
* You can silence the "rat replaced" messages by setting *ratprint:false*,
but those warnings are telling you that Maxima is calculating with
rationals rather than floats. e.g., *solve(x^2=.14,x) *gives the exact
solution *sqrt(7)/(5*sqrt(2)) *rather than 0.374
* At the very least, you should convert everything to numbers before any
further calculations (including *min*).
* It is almost always a bad idea to use *ev* in code. I think you can
replace *ev(...,numer)* with *float(...)*
* Your code isn't robust in the case of imaginary solutions.

But overall, I think you should depend on the plotting packages' contour
plotting capabilities as others have mentioned.

           -s

On Thu, Nov 17, 2022 at 10:07 PM Eduardo Ochs <edu...@gm...> wrote:

> 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
>
>
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