I've been reading the "Pairing for Beginners" tutorial from Craig Costello and have been asking myself about the example given in section 3.3 (Weil Reciprocity page 44, example 3.3.2). It states that if $supp(D)~\cap~supp((f)) \neq \emptyset$, then one could find an equivalent divisor $D'$ such that one is allowed to evaluate $f(D')$ (i.e. both divisors have disjoint supports).
In this example, if $D = (P)+(R)+(T) - 3(\mathcal{O})$ ($P, S, T$ are on the same line), then $D \sim D'$ where $D' = (P+U)+(S+U)+(T+U)-3(U)$ ($U$ is a random point over $E(\mathcal{F}_q)$ that does not belong to $supp(f)$). Hence, one can compute $f(D')$ thanks to this equivalent $D'$.
Let $e$ be the Weil Pairing function. I know that if $D \sim D'$ then $e(D, P) = e(D', P)$ (this can be easily proved thanks to Weil Reciprocity theorem). However, I'm not sure to understand the meaning given to this $f(D')$ evaluation.
What is the relationship between $f(D)$, $f(D')$ and $f(D'+(g))$ where $g$ is a rational function (note that $D$, $D'$ and $D'+(g)$ belong to the same class) ? Does it actually make sense to evaluate these quantities if they are not used for pairing ?