"I couldn't quite remember (hadn't come up in some time) and wanted to
derive its meaning from an implementation."
Maybe this might help. Treating diracdelta() as a limiting case of a spike
distrubution:
assume(b>0);
[b > 0]
almostdiracdelta(x):=''(pwsimp(max(0,b-b^2*abs(x)),x))$
pwlimit(pwint(x^3*almostdiracdelta(x-t),x,minf,inf),b,inf);
t^3
pwint(x^3*pwdelta(x-t),x,minf,inf);
t^3
almostdiracdelta(x)$
diff(%,x)$
diff_almostdiracdelta(x):=''(%)$
pwlimit(pwint(x^3*diff_almostdiracdelta(x-t),x,minf,inf),b,inf);
-3*t^2
pwint(x^3*diff_pwdelta(1,x-t),x,minf,inf);
-3*t^2
This doesn't work for higher order derivatives, I am not sure why. I got it
to work another way but it took a long time and it was a fairly messy
process.
Rich