# FiniteFieldHomomorphisms(F1, GF, F2)ΒΆ

- F1: FiniteAlgebraicExtensionField GF
- GF: FiniteFieldCategory
- F2: FiniteAlgebraicExtensionField GF

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: F1 -> F2
`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: F2 -> F1
`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.