"Source: Text/RepThy/ArtRep.text";
"Line: 143";
"Date: Fri Sep 26 12:10:12 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/RepThy/ArtRep.text, line: 143
// Example: H48E1 ()
print "Example: H48E1";
ei := GetEchoInput();
SetEchoInput(true);
K<i> := QuadraticField(-1);
triv, sign := Explode(ArtinRepresentations(K));
sign;
triv,sign:Magma;
PermutationCharacter(K);
$1 eq triv+sign;
assert $1;
L := ext<K|Polynomial([2+i,0,1])>;
G := GaloisGroup(AbsoluteField(L));
GroupName(G);
[Dimension(A): A in ArtinRepresentations(L)];
A := ChangeField(sign,L);
A;
A eq sign;
SetEchoInput(ei);
