Question: Write a function in Maple

Hello Everybody!
I am working on an interesting problem right now. Please read it and let me know what you think.

Lets assume there is some function f(v) where v is argument-vector with fixed length. It is known, that the function is a rational type of function with integer coefficients from the vector v.

It is required to find analytic expression for this function.

In other words, we can compute the value of the function f at any rational values of the coordinate-vector v (they could be found using a long formula), for instance:

f(1/3, -7/2, 13, -5),
f(-7/13, -7/2,-1/2, 4),
.....

on top of that we know that function f can be expressed as:
                               p(x1,x2,x3,x4)
f(x1,x2,x3,x4) = -------------------------- ,
                               q(x1,x2,x3,x4)

where p,q - are polynomes of (x1,x2,x3,x4) with integer coefficients, notably their power is limited or controlled, for instance, no more than 3.
IT is required to find those polynomes.

If something is not clear in the task above please let me know what and how to correct it.
I need to write a function in Maple in order to be able to find an analytic expression for the function f(v). Can some one help on that matter? Does anyone know to approach this problem? Thank you very much for your advice and attention!
Cheers, Konstantin