I discovered the following, trying to write a check to establish if a student's answer for a series question is a p-series. [As a side note, if anyone has a suggestion for a better way to accomplish this, I'd love to hear it.] Here is a minimal code snippet example of the issue.
$myf= Formula("1/n");
$mydf=$myf->D('n');
$shouldbeminusone = ($myf/$mydf)/Formula("n");
$shouldbezero= $shouldbeminusone ->D('n');
#
BEGIN_PGML
[@$mydf@]
[@$shouldbeminusone@]
[@$shouldbezero@]
END_PGML
This outputs three lines:
(-1)/(n^2)
1/n/[1/(n^2)]/n
([1/(n^2)*1/(n^2)-1/n*2*n/[(n^2)^2]]/[(-[1/(n^2)])^2]*n-1/n/[1/(n^2)])/(n^2)
The top line is the correct derivative of 1/n. The second line should be displaying 1/n/[(-1)/(n^2)]/n but the minus sign is missing. This is issue #1.
Regardless of whether the second line reduces to 1 or -1, the bottom line is defined as its derivative, and should simplify to 0. But it simplifies to -2/n. (Try copying and pasting it into WolframAlpha to see this. In any case, in PG it is being counted as equal to Formula("0").)
This is issue #2.
And so my check that this equals Formula("0") (as a way to check whether the original thing was a p-series) fails. Something about D is not working here. Or I am not using D correctly.
Here is evidence that the D method is altering what you apply it to. For instance, if you comment out the line in the minimal example that calls D on $shouldbeminusone then when $shouldbeminusone is displayed, the minus sign no longer is dropped.
I adopted a less slick process to test if my students' series are p-series that avoids calling D so much. So while I think there is an issue here about D modifying the MathObject that called it, it's not an urgent matter for me at least. Something to look at some time.