In the beginning section $1.4$ from Stichtenoth's Algebraic Function Fields and Codes, the author says:
"From here on, $F/K$ will always denote an algebraic function field of one variable such that $K$ is the full constant field of $F/K$."
(here the "full constant field" is the field of elements $z\in F$ which are algebraic over $K$)
In short, section $1.4$ deals with divisors, Weil differentials and Riemann-Roch theorem.
I couldn't notice in any part of the text why this assumption was needed, or at least convenient.
But in the exercises, at least three of the problems involved findind the full constant field, so it seems like a big deal.
What am I missing?