"Source: Text/Module/ModCpx.text";
"Line: 988";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Module/ModCpx.text, line: 988
// Example: H62E3 ()
print "Example: H62E3";
ei := GetEchoInput();
SetEchoInput(true);
ff := GF(3);
p := Characteristic(ff);
FA<e1, e2, y, x, a, b> := FreeAlgebra(ff,6);
rrr := [y^p,x^p,x*y+y*x,x*a*b-a*b*x,y*a*b-a*b*y,(b*a)^2,(b*a)^2];
A := BasicAlgebra(FA,rrr,2,[<1,1>,<1,1>,<1,2>,<2,1>]);
A;
DimensionsOfProjectiveModules(A);
S1 := SimpleModule(A,1);
PP := ProjectiveModule(A,[2,2]);
J1 := JacobsonRadical(PP);
theta1 := Morphism(J1,PP);
J2 := JacobsonRadical(J1);
theta2 := Morphism(J2,J1);
theta := theta2*theta1;
HomPJ := AHom(PP, J2);
HomPJ;
gamma := Random(HomPJ)*theta;
LL := [* gamma *];
for i := 1 to 15 do
    K, phi := Kernel(gamma);
    HomPK := AHom(PP,K);
    gamma := Random(HomPK)*MapToMatrix(phi);
    LL := [* gamma *] cat LL;
end for;
C := Complex(LL,0);
C;
DimensionsOfHomology(C);
a,b := Degrees(C);
S, mu := RandomSubcomplex(C,[2: i in [1 .. a-b+1]]);
S;
DimensionsOfHomology(S);
Q,nu := quo<C|S>;
Q;
DimensionsOfHomology(Q);
IsShortExactSequence(mu,nu);
assert $1;
lll := LongExactSequenceOnHomology(mu,nu);
IsExact(lll);
assert $1;
SetEchoInput(ei);
