Computing Av and Bv such that Av*(\partial g / \partial u) + Bv*(\partial g / \partial z) = 1.

> gupartial:=diff(g(u,z),u);

> gzpartial:=diff(g(u,z),z);

> g(u,z);

Now before using the gcd function we make the following adjustments. First we let Cv be such that Av = u*Cv. Then we modify gupartial by multiplying it by u and then substituting in for 3u^3. The result is etch.

> etch:=simplify(u*gupartial - 3*g(u,z));

> gcdex(etch,gzpartial,z,'r','q');

> Av:=u*r;

> Bv:=q;

This next line is just to show that Av and Bv really do work on V.

> simplify(Av*gupartial + Bv*gzpartial- (-9*c2*z -3*c1*u + (9/2)*c2*z)*g(u,z));

Lastly, we actually need Av^p and Bv^p, and so the following two definitions are for convenience.

> Avp:=Av^p;

> Bvp:=Bv^p;

>