"Source: Text/Group/GrpBrd.text";
"Line: 2610";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpBrd.text, line: 2610
// Example: H82E7 ()
print "Example: H82E7";
ei := GetEchoInput();
SetEchoInput(true);
B := BraidGroup(4);
u := B.1*B.2*B.1;
p_Artin := PositiveConjugates(u : Presentation := "Artin");
p_BKL := PositiveConjugates(u : Presentation := "BKL");
s_Artin := SuperSummitSet(u : Presentation := "Artin");
s_BKL := SuperSummitSet(u : Presentation := "BKL");
p_Artin subset p_BKL;
assert $1;
#p_Artin;
assert $1 eq 10;
#p_BKL;
assert $1 eq 36;
s_Artin subset p_Artin;
assert $1;
s_BKL subset p_BKL;
assert $1;
#s_Artin;
assert $1 eq 2;
#s_BKL;
assert $1 eq 12;
u := B.2 * B.1 * B.2^2 * B.1 * B.2;
v := B.2^2 * B.1 * B.3 * B.1 * B.3;
CycleStructure(InducedPermutation(u));                                       
CycleStructure(InducedPermutation(v));
SuperSummitInfimum(u) eq SuperSummitInfimum(v);
assert $1;
SuperSummitSupremum(u) eq SuperSummitSupremum(v);
assert $1;
SuperSummitSet(u) eq SuperSummitSet(v);                       
assert not $1;
B := BraidGroup(8);
x := B.4 * B.3 * B.2 * B.1 * B.5 * B.4 * B.5 *
B.6 * B.7 * B.6 * B.5;
x := x^2;
Sx := SuperSummitSet(x);
#Sx;
assert $1 eq 10972;
Ux := UltraSummitSet(x);
#Ux;
assert $1 eq 36;
x := B.4 * B.3 * B.2 * B.1 * B.5 * B.4 * B.5;
x := x^3;
Sx := SuperSummitSet(x);
#Sx;
assert $1 eq 882;
Ux := UltraSummitSet(x);
#Ux;
assert $1 eq 18;
SetEchoInput(ei);
