I've experimented a bit with using J- or APL-like notation for pencil
and paper math, with some mixed success.  Has anyone else tried this
much?

I found my most recent experiment unsatisfying.  I was just working
through (for the nth time) the RSS=TSS+ESS decomposition of the
sum-of-squares in fit residuals, which involve splitting something like:

  +/(y-ym)^2

into

  +/((y-f)-(ym-f))^2
  (+/(y-f)^2)+(+/(f-ym)^2)+2*+/(y-f)*(f-ym)
  (+/(y-f)^2)+(+/(f-ym)^2)+2*+/(y*f)+(f*ym)-(y*ym)+f*f
  etc.

This starts to feel "noisy" to me, compared to the more "classical"
version of:

  sum ((y-f)-(ym-f))^2
  (sum (y-f)^2)+(sum (f-y)^2)+2*sum (y*f-y*ym-f^2+f*ym)

where really I'm using sigmas and superscripts and dots.

Mostly this boils down to the traditional order-of-operations being
optmized for polynomials.  I found that it took more thinking than it
should to turn (a-b)*(c-d) into (a*c)+(b*d)-(a*d)+(b*c), since it cuts
across the grain of my usual mental ordering.

Writing (a*c)-(a*d)+(b*c)-b*d is a little brain-twisting.
"(a*c)+(a*-d)+(-b*c)+(b*d)" is mentally nicer.

Has anyone else tried APL notation for paper math?  Did you like the
experience?

Regards,
Johann

----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm

Reply via email to