// Example code from paper 8:
// _Support varieties for modules_ by Jon F. Carlson
//
print "Examples from: Support varieties for modules";
load "Paper08_funcs";
ei := GetEchoInput();
SetEchoInput(true);
// Section 6: Varieties of truncated syzygy modules
E  := ExtraSpecialGroup(2, 2);
S  := TrivialModule(E, GF(2));
kE := PermutationModule(E, sub< E | >, GF(2));
O1 := SyzygyModule(S, kE);
O2 := SyzygyModule(O1, kE);
O3 := SyzygyModule(O2, kE);
O4 := SyzygyModule(O3, kE);
Z := ActionGenerator(O2, 5) - Representation(O2)(E!1);
N := sub< O2 | RowSpace(Z) >;
G := AbelianGroup(GrpPerm, [ 2, 2, 2, 2 ]);
L2 := GModule(G, [ ActionGenerator(N, i) : i in [1..4] ]);
var2 := SupportVariety(L2);
var2;
Z4 := ActionGenerator(O4, 5) - Representation(O4)(E!1);
N4 := sub< O4 | RowSpace(Z4) >;
L4 := GModule(G, [ ActionGenerator(N4, i) : i in [1..4] ]);
time var4 := SupportVariety(L4);
var4;
SetEchoInput(ei);