Get Coefficient of polynomial excluding variables

Question

I'd like to write a function that returns the coefficient of a polynomial, but excludes some 'cross-term' coefficients.

The function could be called CoefficientExclude, and the first argument would take a variable, then the second argument would be a list of variables to exclude.

So for p defined as p=a1*x1 + a2*x1/y1+a2*y1, this function would return:

CoefficientExclude[p,{x1},{y1}] = a1

CoefficientExclude[p,{y1},{x1}] = a2

CoefficientExclude[p,{x1/y1},{}] = a2

Answer 1

I think you need SeriesCoefficient.

For example

p = a1*x1 + a2*x1/y1 + a2*y1
SeriesCoefficient[p, {x1, 0, n}, {y1, 0, m}]

gives

$\begin{cases} \text{a2} & (m=-1 \&\& n=1) || (m=1 \&\& n=0) \\ 0 & (m\neq -1 \&\& m\neq 0) || n\neq 1 \\ \text{a1} & \text{True} \end{cases}$

For a cross term both m and n will be nonzero. Avoid that condition and you are done.

In your case [...,{x1^c},{y1}] is equivalent to m=c and n=0

SeriesCoefficient[p, {x1, 0, 1}, {y1, 0, 0}]

Or say you explicitly want the coefficient of x1/y1, (m=1,n=-1)

SeriesCoefficient[p, {x1, 0, 1}, {y1, 0, -1}]