# polynomial evaluation

If I have a polynomial p in variables $x_0,...,x_n$, how do I specialize the algebra appropriately to substitute values for $x_i$'s? For example, how do I compute $p(1,1,...,1)$? Or replace $x_i$ by $q^i$ ($q$ a parameter) so to compute $p(1,q,...,q^n)$? In Mathematica, if the variables were x[[i]], one could do "./x[[i]] -> q^i //Simplify" and it is the equivalent of this replace and simplify that I am looking for.

This is coming from symmetric polynomials/functions theory and I know some of the specializations are built in, but at the end of the day I want to try small examples with different specializations than what is already built in.