# FiniteFieldHomomorphisms(F1, GF, F2)¶

FiniteFieldHomomorphisms(F1, GF, F2) exports coercion functions of elements between the fields F1 and F2, which both must be finite simple algebraic extensions of the finite ground field GF.
coerce(x) is the homomorphic image of x from F1 in F2. Thus coerce is a field homomorphism between the fields extensions F1 and F2 both over ground field GF (the second argument to the package). Error: if the extension degree of F1 doesn't divide the extension degree of F2. Note that the other coercion function in the FiniteFieldHomomorphisms is a left inverse.
coerce(x) is the homomorphic image of x from F2 in F1, where coerce is a field homomorphism between the fields extensions F2 and F1 both over ground field GF (the second argument to the package). Error: if the extension degree of F2 doesn't divide the extension degree of F1. Note that the other coercion function in the FiniteFieldHomomorphisms is a left inverse.