How Can I Use plot2d code for presence of singularities?

>>>>> "Richard" == Richard Fateman <fateman at eecs.berkeley.edu> writes:

    Richard> How about evaluating the expression in interval arithmetic and seeing
    Richard> if it is bounded or not.
    Richard> If it is unbounded, bisect the range.  Etc.

That would probably work.  I don't have any interval package for
maxima, but you can get an idea with cmucl and sbcl:

to_lisp();
(defun foo (x)
  (declare (type (double-float 0.0d0 1d0)) x)
  (values (/ x (expt (- 1/2 x) 3)) (expt (- 1/2 x) 3)))

(compile 'foo)
(describe 'foo) ->

Function arguments:
  (x)
Its defined argument types are:
  ((DOUBLE-FLOAT 0.0d0 1.0d0))
Its result type is:
  (VALUES DOUBLE-FLOAT (DOUBLE-FLOAT -0.125d0 0.125d0))

So, indeed, the first expression is unbounded (plain double-float
means unbounded), and we can see that (1/2-x)^3 contains 0 because the
interval is -1/8 to 1/8.

Ray