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How to evaluate polynomial in a polynomial ring at a particular value

Apologies in advance if this question is too simple. I have the following situation: I have a vector space over a polynomial ring, and at some point in my program I need to sub in a value for the indeterminate $t$, and evaluate the polynomial. The set up is as follows:

P.<x> = QQ[]
R.<t> = QuotientRing(P, P.ideal(x^2 - 2))
v = VectorSpace(R,4)

Then for example I have the vector:

(2*t, 3, 2, 0)

I simply want to evaluate $2*t$ at $t = sqrt(2)$ as a function from $\mathbb{R}$ to $\mathbb{R}$.

What is the easiest way to go about this?