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### Function

AbelianExtension ( map() M ) -> fld^abl

### Description

<shortdoc> Construct the RayClassField definined by the map.. </shortdoc>

### Examples

x_R := PolynomialAlgebra( IntegerRing() ); x_x := Generator(x_R, 1); x_O := MaximalOrder( x_x^5-5*x_x^3+7*x_x^2-15*x_x+16 ); x_I := Factorization(7*x_O)[1][1]; x_G := RayClassGroup(x_I); x_f := x_G.ext1; x_A := AbelianExtension(x_f);
x_R := PolynomialAlgebra( IntegerRing() ); x_x := Generator(x_R, 1); x_O := MaximalOrder( x_x^5-5*x_x^3+7*x_x^2-15*x_x+16 ); x_I := Factorization(7*x_O)[1][1]; x_G := RayClassGroup(x_I); x_f := x_G.ext1; x_H := Sub(x_G, [ 2*x_G.1 ] ); x_g := x_H.ext1; x_h := x_g * x_f; x_A := AbelianExtension(x_h);
x_R := PolynomialAlgebra( IntegerRing() ); x_x := Generator(x_R, 1); x_O := MaximalOrder( x_x^5-5*x_x^3+7*x_x^2-15*x_x+16 ); x_I := Factorization(11*x_O)[1][1]^10; x_G := RayClassGroup(x_I); x_f := x_G.ext1; x_A := AbelianExtension(x_f);

| Built: Mon Nov 14 21:12:39 UTC 2005 on mack