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what is the command to find the rank of a polynomial?

actually i do not know the definition of rank of polynomial

i guess rank of x*y = 2 rank of x^3*z^2 = 5

i guess rank of  x*y+ x^3*z^2 is the maximum of above ranks, so it is 5

if i am wrong, please tell me, as i can not find in google, and there is no definition in my book

i calculate a polynomial as following

yn := f(x) = _C1*hypergeom([-(1/2)*n, 3/2+(1/2)*n], [1/2], x^2)+_C2*hypergeom([2+(1/2)*n, 1/2-(1/2)*n], [3/2], x^2)*x


want to get the polynomial with degree n  for  summation_n_from_0_to_infinity y_n*z^n/n!

such as n = 1 n = 0 n = 3, but above yn is hypergeom, is n represent degree, if so, i use subs, then is finished, if not, how to get polynomial with degree n?

u = -1/2*ln(-2*t*x+x^2+1)/x;

what is command to find x in terms of u of above formula? i.e. x = u^2+u+1

How to output a list when writing a procedure

i want to get the list c in the procedure, but "return" c not work

z := [x1, x2, x3];

symMonomial := proc(test)
h := 0;
for i from 1 to nops(test) do
    h[i] := choose(z,i);

c := 0;
for k from 1 to nops(test) do
    c[k] := 0;
    for i from 1 to nops(h[k]) do
        ki := 1;

i use symmetric function package


i would like to know after calculating the basis toS(....)

which function can be used to convert into polynomials?

as i expect to get the sequence from any polynomials generated from it

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