#3807 plot2d heuristic to detect unbound variables excludes some valid cases

[Robert Dodier]

plot2d has a bit of code to figure out if the expression to be plotted has variables that are unbound, which would lead to many or all values being nonnumeric and therefore unplottable. The heuristic is that if listofvars(f(x)) returns something other than x (where f is the function constructed by COERCE-FLOAT-FUN and x is the plotting variable) then those other variables are unbound and therefore the function is rejected.

This excludes some classes of valid functions, e.g. expressions containing calls to quadpack functions or find_root; there may be others, anything with a dummy variable has the potential to tickle the bug.

(%i1) plot2d (quad_qags (sin(u), u, 0, x)[1], [x, 0, 1]);
plot2d: expression quad_qags(sin(u),u,0,x,epsrel = 1.0E-8,epsabs = 0.0,
                             limit = 200)[
                    1]
    should  depend only on x, or be an expression of 2 variables
    equal another expression of the same variables.
 -- an error. To debug this try: debugmode(true);
(%i2) plot2d (find_root (sin(u) - x, u, 0, %pi/2), [x, 0, 1]);
plot2d: expression find_root(sin(u)-x,u,0.0,1.570796326794897)
    should  depend only on x, or be an expression of 2 variables
    equal another expression of the same variables.
 -- an error. To debug this try: debugmode(true);

These examples worked as expected with Maxima 5.44.

Trying to see what the function does with a trial value is susceptible to mistakes, since the function can do something different when there's a numerical value. I think a preferable solution is to remove the listofvars check, and go ahead with adaptive plotting, and go to a small depth (adapt_depth = 1, 2, or 3, let's say) for a trial run, and if that yields only nonnumeric values, then give up, otherwise keep going.

[Gunter Königsmann]

...or is there a way of making listofvars stronger? I rather like the fact that the plotting functions no more only say that the function that is to be plotted evaluates to a non-number in all points that were tested initially, but can tell which variable one failed to eliminate before plotting. Also one could argue we detect the list of variables in quad_qag expressions wrong...

[Robert Dodier]

I'm inclined to agree with figuring out how to tell listofvars about dummy variables for quadpack functions, find_root, and maybe others, and that would fix the examples I gave.

However, there are other cases which used to work and now they don't, involving functions that don't work for symbolic arguments. For example, length, makelist, for, etc. As it stands, the unbound-variable heuristic requires that expressions be evaluated for symbolic argument; I don't think this restriction is necessary.

Maybe instead of an error, plot2d can just give a warning.

@villate I would be interested to hear what you think about all this.

[Stavros Macrakis]

I agree that a warning is much more appropriate than an error when we're
using an unreliable heuristic.

         -s

On Fri, Jul 2, 2021 at 2:35 PM Robert Dodier via Maxima-bugs maxima-bugs@lists.sourceforge.net wrote:

I'm inclined to agree with figuring out how to tell listofvars about
dummy variables for quadpack functions, find_root, and maybe others, and
that would fix the examples I gave.

However, there are other cases which used to work and now they don't,
involving functions that don't work for symbolic arguments. For example,
length, makelist, for, etc. As it stands, the unbound-variable heuristic
requires that expressions be evaluated for symbolic argument; I don't think
this restriction is necessary.

Maybe instead of an error, plot2d can just give a warning.

@villate https://sourceforge.net/u/villate/ I would be interested to
hear what you think about all this.

---

• [bugs:#3807] https://sourceforge.net/p/maxima/bugs/3807/ plot2d
  heuristic to detect unbound variables excludes some valid cases*

Status: open
Group: None
Labels: plot2d plotting
Created: Fri Jul 02, 2021 05:04 AM UTC by Robert Dodier
Last Updated: Fri Jul 02, 2021 08:05 AM UTC
Owner: nobody

plot2d has a bit of code to figure out if the expression to be plotted has
variables that are unbound, which would lead to many or all values being
nonnumeric and therefore unplottable. The heuristic is that if
listofvars(f(x)) returns something other than x (where f is the function
constructed by COERCE-FLOAT-FUN and x is the plotting variable) then
those other variables are unbound and therefore the function is rejected.

This excludes some classes of valid functions, e.g. expressions containing
calls to quadpack functions or find_root; there may be others, anything
with a dummy variable has the potential to tickle the bug.

(%i1) plot2d (quad_qags (sin(u), u, 0, x)[1], [x, 0, 1]);plot2d: expression quad_qags(sin(u),u,0,x,epsrel = 1.0E-8,epsabs = 0.0,
limit = 200)
1
should depend only on x, or be an expression of 2 variables
equal another expression of the same variables.
-- an error. To debug this try: debugmode(true);(%i2) plot2d (find_root (sin(u) - x, u, 0, %pi/2), [x, 0, 1]);plot2d: expression find_root(sin(u)-x,u,0.0,1.570796326794897)
should depend only on x, or be an expression of 2 variables
equal another expression of the same variables.
-- an error. To debug this try: debugmode(true);

These examples worked as expected with Maxima 5.44.

Trying to see what the function does with a trial value is susceptible to
mistakes, since the function can do something different when there's a
numerical value. I think a preferable solution is to remove the listofvars
check, and go ahead with adaptive plotting, and go to a small depth
(adapt_depth = 1, 2, or 3, let's say) for a trial run, and if that yields
only nonnumeric values, then give up, otherwise keep going.

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[Gunter Königsmann]

A warning would be great: it helps the user debugging the problem and tells where listofvars still isn't perfect.

[Jaime E. Villate]

It is possible to relax the requirement on the number of variables, leaving it to the user to make user the expression leads to numbers (as someone has suggested in another ticket). But in that case I would rather give a warning and let plot2d end with an error if the expression does not give numbers, rather than trying to use some heuristics.

[Robert Dodier]

Another example, collected from the mailing list 2021-10-08:

(%i1) plot2d(sum(w, w, 1, abs(x)), [x, 1, 10]);
plot2d: expression 'sum(w,w,1,abs(x))
    should  depend only on x, or be an expression of 2 variables
    equal another expression of the same variables.

[Jaime E. Villate]

Fixed by commit [558ba7].