Can Maxima calculate discontinuity points on a function on multiple parts?

Question

I could do it step by step checking for limits, the same way i would do it by hand, but i was wondering if i could get Maxima to analyze a function and give me discontinuity points.

Also, if there is no way to do so in a 'click-n-go' way, what would be the way to make use of Maxima capabilities to do so in an easier way?

Answer 1

Look at the following graph:

wxplot2d(1-signum(x-1)+signum(x),[x,-1,2],[y,0,4]);

As we can see, discontinuities occur when there are jumps on this graph. Formally such a boken line is not a graph of any function. So, our conjecture is that vertical lines on the graph mean jumps.

Another situation:

wxplot2d(sin(1/x),[x,-%pi/2,%pi/2]);

There is a discontinuity of the 2nd kind at $0$: there is no one-sided limits here.