Using a linear combination of dataframe columns as a functional input


I have a dataframe whose column names represent polynomial portions such as ‘xy’ and as such, are symbols. I want to take all of these column names, which include:


and add them together using a linear combination to put into an exponential function and evaluate it for any given x and y:

f(x, y) = exp(c1x + c2y + c3xy + c4xx + c5yy)

I was wondering if this is possible with something like SymPy or another package. Thank you so much for your help.