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.
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.
> 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
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.[Next][Prev] [Right] [Left] [Up] [Index] [Root]