"Source: Text/Ring/FldNum.text";
"Line: 1850";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/FldNum.text, line: 1850
// Example: H36E12 ()
print "Example: H36E12";
ei := GetEchoInput();
SetEchoInput(true);
_<x> := PolynomialRing(Integers());
K := NumberField(x^3-7);
suc, L := EmbeddedNumberField(K,7^(1/3));
ComplexImage(L.1 + L.1^2);
Reconstruction(L,1/2 + 7^(1/3) + 5 * 7^(2/3));
Reconstruction(L,Sqrt(-1));
_<x> := PolynomialRing(Integers());
suc, K := EmbeddedNumberField(x^6-3,3^(1/6));
suc, L := EmbeddedNumberField(x^9-3,3^(1/9));
K meet L;
Composite(K,L);
_<x> := PolynomialRing(Integers());
suc, K := EmbeddedNumberField(x^2-2,Sqrt(2));
suc, L := EmbeddedNumberField(Polynomial([-K.1,0,1]),2^(1/4));
ComplexImage(L.1);
ComplexImage(L!(K.1));
SetEchoInput(ei);
