finding out if expr has the form F(y/x^a)

• Subject: finding out if expr has the form F(y/x^a)
• From: Barton Willis
• Date: Wed, 12 Dec 2012 03:09:23 +0000

Assuming differentiability, here is a start at one approach:

 (%i1) load(pdiff)$

 (%i2) g(x,y) = (y/x)*f(y/x^a)$

 (%i3) [%,diff(%,x),diff(%,y)]$

 (%i4) eliminate(%,[f(y/x^a), subst(z=y/x^a,diff(f(z),z))]);
 (%o4) [-x^(a+1)*y^3*(a*g[(0,1)](x,y)*y+x*g[(1,0)](x,y)+(1-a)*g(x,y))]

--Barton

________________________________________

> I would like to find out if an expression is of (or can be written in) the
> general form (y/x)*f(y/x^a), with 'a' a nonzero constant. 

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