hom<F -> R | cf, g> : FldFun, Rng, Map, RngElt -> Map
The homomorphism from the function field F to any ring R where
g is the image of the generator of F
in R and cf is a map from the coefficient field of F into R.
hom< O -> R | cf, g > : RngFunOrd, Rng, Map, RngElt -> Map
Create the map from the order O of an algebraic function field to R using
g as the image of the primitive element of O. If the map cf is given
it should be from the coefficient ring of O into R, otherwise the
coefficient ring of O should be automatically coercible into R.
Return whether the vector space homomorphism m is a homomorphism of rings.
A simple use of homomorphisms is shown.
> PR<x> := PolynomialRing(Rationals());
> P<y> := PolynomialRing(PR);
> FR1<a> := FunctionField(y^3 - x*y + 1);
> P<y> := PolynomialRing(FR1);
> FR2<c> := FunctionField(y^2 - a^5*x^3*y + 1);
> EFR2F := EquationOrderFinite(FR2);
> cf := hom<FR1 -> EFR2F | a + 1>;
> h := hom<FR2 -> EFR2F | cf, c + 1>;
> h(c) eq c + 1;
true
> h(a*c) eq a*c + a + c + 1;
true
hom< O -> R | m, b1, ..., bn > : RngFunOrd, Rng, Map, RngElt, ..., RngElt -> Map
Return the map from the order O of an algebraic function field into the
ring R which maps the basis elements of O to b1, ..., bn. The map
m, if given, should be from the coefficient ring of O into R and will
be used to map the coefficients of the basis elements. If not given, the
coefficient ring of O should automatically coerce into R.
V2.28, 13 July 2023