Subject: rule for nn^3*K3(xx,yy) --> K3(nn*xx, nn*yy)?
From: Rhys Pratt
Date: Wed, 24 Nov 2010 10:42:20 +0800
(%i1) K3((b*log(n))/n^2+a/n,(b*log(n-1))/(n-1)^2+a/(n-1));
(%o1) K3((b*log(n))/n^2+a/n,(b*log(n-1))/(n-1)^2+a/(n-1))
K3 is a homogeneous polynomial of order 3.
I want to pull the factor a/n out of its parameters to
make K3() evaluated near (1,1) (assumed that n->infinity)
(%i3) matchdeclare([xx,yy], true, cc, true);
(%o3) done
(%i14) defrule(r1, cc^3*K3(xx,yy), K3(cc*xx, cc*yy));
(%o14) r1:cc^3*K3(xx,yy)->K3(cc*xx,cc*yy)
(%i15) r1((n/a)^3*K3((b*log(n))/n^2+a/n,(b*log(n-1))/(n-1)^2+a/(n-1)));
(%o15) false
==================================
for the sake of convenience, one could save the following lines into a file and open it in wxmaxima.
/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
/* [ Created with wxMaxima version 0.8.5 ] */
/* [wxMaxima: input start ] */
K3((b*log(n))/n^2+a/n,(b*log(n-1))/(n-1)^2+a/(n-1));
/* [wxMaxima: input end ] */
/* [wxMaxima: comment start ]
K3 is a homogeneous polynomial of order 3.
I want to pull the factor a/n out of its parameters to
make K3() evaluated near (1,1)
[wxMaxima: comment end ] */
/* [wxMaxima: input start ] */
matchdeclare([xx,yy], true, cc, true);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
defrule(r1, cc^3*K3(xx,yy), K3(cc*xx, cc*yy));
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
r1((n/a)^3*K3((b*log(n))/n^2+a/n,(b*log(n-1))/(n-1)^2+a/(n-1)));
/* [wxMaxima: input end ] */
/* Maxima can't load/batch files which end with a comment! */
"Created with wxMaxima"$