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

Dear,

It seems the following sequence work on both of your example.

ratsimp(%/(y/x));
ratsubst(H*x^a, y, %);
hipow(expand(factor(%))); => this give:

max(2 a - 4, 3 a - 6) for the first example and
max(-a - 1 / 2, 2 * a + 1) for the second one.

Then you have to solve the system to know if there is a posible "real probably" value for "a"

Hope this help.

Best.

Laurent.


> -----Message d'origine-----
> De?: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu] De la part de NB
> Envoy??: mardi 11 d?cembre 2012 23:40
> ??: maxima at math.utexas.edu
> Objet?: [Maxima] finding out if expr has the form F(y/x^a)
> 
> Dear all,
> 
> 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. The difficulty I
> have here is the generality of the function f. You can have:
> expr:y^3+1/x^(3/2);
> or:
> expr:(y/x)*sin(y^2/x^4 + y^3/x^6);
> 
> I think it reduces to this:
> (after dividing by y/x,) How to find out if there is a constant 'a' for which
> a substitution H=y/x^a leads to an expression free of x and y?
> 
> 
> Best,
> NB
> _______________________________________________
> Maxima mailing list
> Maxima at math.utexas.edu
> http://www.math.utexas.edu/mailman/listinfo/maxima