"Source: Text/Ring/RngOrd.text";
"Line: 2126";
"Date: Fri Sep 26 14:51:59 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/RngOrd.text, line: 2126
// Example: H39E10 ()
print "Example: H39E10";
ei := GetEchoInput();
SetEchoInput(true);
R<x> := PolynomialRing(Integers());
k := NumberField(x^2-2);
l := NumberField(x^2-2);
l eq k;
assert not $1;
HasEmbedding(k, l);
CanComputeEmbedding(k, l);
Embed(k, l, l.1);
l!k.1;           
HasEmbedding(k, l : Print := 1);
HasEmbedding(l, k : Print := 1);
Embed(l, k, k.1);
k!l.1;
HasEmbedding(l, k : Print := 1);
l<a> := NumberField(x^3-2);
L<b> := NumberField(x^6+108);
Root(L!2, 3);
Embed(l, L, $1);
L!l.1;
Roots(PolynomialRing(L)!DefiningPolynomial(l));
Embed(l, L, $1[1][1] : Overwrite := true);
L!l.1;
SetEchoInput(ei);
