"Source: Text/Group/GrpCoh.text";
"Line: 698";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpCoh.text, line: 698
// Example: H75E11 ()
print "Example: H75E11";
ei := GetEchoInput();
SetEchoInput(true);
G := PermutationGroup< 4 | (1,2,3,4) >;
invar:=[2,4,4];
mats := [ Matrix(Integers(),3,3,[1,2,0,0,0,1,0,1,2]) ];
X := CohomologyModule(G,invar,mats);
C := CohomologyGroup(X,0);
C;
ZeroCocycle(X,[3]);
$1(X);
IdentifyZeroCocycle(X,func<x|-$1>);
C := CohomologyGroup(X,1);
C;
z1 := OneCocycle(X,[1,0]);
z2 := OneCocycle(X,[0,1]);
z1(<G.1>);
z := func< x | z1(x)+z2(x) >; 
IdentifyOneCocycle(X,z);
C := CohomologyGroup(X,2);
C;
z1 := TwoCocycle(X,[1]);
z1(<G.1,G.1^2>);
z := func< xy | z1(xy)+z1(xy) >; 
IdentifyTwoCocycle(X,z);
SetEchoInput(ei);
