### How to solve a linear equation within a field of rational functions?

I have a field of rational functions over the rational numbers in 4 variables:

K = Frac(PolynomialRing(QQ,'x,y,z,w'))

and some explicit elements R[0],...,R[n] in K. Is there a way to solve the equation

a[0]*R[0] + ... + a[n]*R[n] == 0

with a[i] in QQ? That is, I would like to first check if there are any solutions. In the positive case, then I would like an explicit solution.