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
