coefficients of a polynomial in two or more variables

Hello,

I have experimented on your suggestions and came across the following problem:

(%i1) p1:a*x^2+b*x*y+c*y^2+d*x+e*y+f;
ratcoef(p1,x*y);
hipow(p1,x*y);
bothcoef(p1,x*y);
hipow(p1,b*x*y);
bothcoef(p1,b*x*y);
(%o1) c*y^2+b*x*y+e*y+a*x^2+d*x+f
(%o2) b
(%o3) 0
(%o4) [0,c*y^2+b*x*y+e*y+a*x^2+d*x+f]
(%o5) 1
(%o6) [1,c*y^2+e*y+a*x^2+d*x+f]

ratcoef recognizes x*y as "partial monomial", whereas hipow and bothcoef don't. This means that

[d,eq]: bothcoef(eq,kn)

instead of

d : ratcoef(eq, kn),
eq : eq - d * kn,

does not work.

It seems to me that hipow und bothcoef only work for "full subexpressions". Is this different behaviour of ratcoef, hipow and bothcoef intended? Can someone explain me the reason for it?

With the sum x+y instead of the product x*y hipow und bothcoef work as I would expect it:

(%i7) p2:a*(x+y)^2+b*(x+y)+c;
ratcoef(p2,x+y);
hipow(p2,x+y);
bothcoef(p2,x+y);
(%o7) a*(y+x)^2+b*(y+x)+c
(%o8) b
(%o9) 2
(%o10) [b,a*(y+x)^2+c]

Thanks for your help,
Christian