|
###########################################################################
##
#W extreme/misc.tst
#Y Copyright (C) 2011-15 James D. Mitchell
##
## Licensing information can be found in the README file of this package.
##
#############################################################################
##
#@local D, H, K18g, L, P, a1, a2, a3, a4, a5, a6, acting, cosets, d, data, dd
#@local e, enum, f, g, gens, h, hh, i, iter, l, lambda_schutz, lambda_stab, m
#@local o, p, r, rep, reps, rho_schutz, rho_stab, rr, s, scc, schutz
gap> START_TEST("Semigroups package: extreme/misc.tst");
gap> LoadPackage("semigroups", false);;
#
gap> SEMIGROUPS.StartTest();
gap> SEMIGROUPS.DefaultOptionsRec.acting := true;;
# MiscTest0
gap> gens := [Transformation([2, 8, 3, 7, 1, 5, 2, 6]),
> Transformation([3, 5, 7, 2, 5, 6, 3, 8]),
> Transformation([4, 1, 8, 3, 5, 7, 3, 5]),
> Transformation([4, 3, 4, 5, 6, 4, 1, 2]),
> Transformation([5, 4, 8, 8, 5, 6, 1, 5]),
> Transformation([6, 7, 4, 1, 4, 1, 6, 2]),
> Transformation([7, 1, 2, 2, 2, 7, 4, 5]),
> Transformation([8, 8, 5, 1, 7, 5, 2, 8])];;
gap> s := Semigroup(gens);
<transformation semigroup of degree 8 with 8 generators>
gap> Size(s);
597369
gap> f := Transformation([8, 1, 5, 5, 8, 3, 7, 8]);;
gap> l := LClassNC(s, f);
<Green's L-class: Transformation( [ 8, 1, 5, 5, 8, 3, 7, 8 ] )>
gap> Transformation([8, 1, 5, 5, 8, 3, 7, 8]) in last;
true
gap> RhoOrbStabChain(l);
true
gap> Size(l);
4560
gap> RhoOrbSCC(l);
[ 1, 2, 5, 9, 10, 13, 14, 18, 24, 25, 22, 28, 34, 21, 11, 16, 12, 33, 32, 36,
3, 6, 39, 35, 37, 38, 29, 17, 23, 4, 7, 15, 19, 26, 30, 31, 27, 20 ]
gap> SchutzenbergerGroup(l);
Sym( [ 1, 3, 5, 7, 8 ] )
gap> ForAll(l, x -> x in l);
true
gap> d := DClass(s, f);
<Green's D-class: Transformation( [ 8, 1, 5, 5, 8, 3, 7, 8 ] )>
gap> Transformation([8, 1, 5, 5, 8, 3, 7, 8]) in last;
true
gap> iter := Iterator(d);
<iterator>
gap> for i in iter do od;
# MiscTest1
gap> gens := [PartialPermNC([1, 2, 3, 5, 7, 10], [12, 3, 1, 11, 9, 5]),
> PartialPermNC([1, 2, 3, 4, 5, 7, 8], [4, 3, 11, 12, 6, 2, 1]),
> PartialPermNC([1, 2, 3, 4, 5, 9, 11], [11, 6, 9, 2, 4, 8, 12]),
> PartialPermNC([1, 2, 3, 4, 7, 9, 12], [7, 1, 12, 2, 9, 4, 5]),
> PartialPermNC([1, 2, 3, 5, 7, 8, 9], [5, 4, 8, 11, 6, 12, 1]),
> PartialPermNC([1, 2, 4, 6, 8, 9, 10], [8, 5, 2, 12, 4, 7, 11])];;
gap> s := Semigroup(gens);
<partial perm semigroup of rank 12 with 6 generators>
gap> f := PartialPermNC([3, 4, 5, 11], [4, 1, 2, 5]);;
gap> l := LClassNC(s, f);
<Green's L-class: [3,4,1][11,5,2]>
gap> l := LClass(s, f);
<Green's L-class: [3,4,1][11,5,2]>
gap> d := DClass(s, f);
<Green's D-class: [3,4,1][11,5,2]>
gap> Size(l);
1
gap> Number(d, x -> x in l);
1
gap> Number(s, x -> x in l);
1
gap> s := Semigroup(gens);
<partial perm semigroup of rank 12 with 6 generators>
gap> l := LClass(s, f);
<Green's L-class: [3,4,1][11,5,2]>
gap> d := DClass(s, f);
<Green's D-class: [3,4,1][11,5,2]>
gap> Number(d, x -> x in l);
1
gap> Number(s, x -> x in l);
1
gap> SchutzenbergerGroup(l);
Group(())
gap> ForAll(l, x -> x in l);
true
gap> d := DClassNC(s, f);
<Green's D-class: [3,4,1][11,5,2]>
gap> d := DClassNC(s, Representative(l));
<Green's D-class: [3,4,1][11,5,2]>
gap> ForAll(l, x -> x in d);
true
gap> Number(d, x -> x in l);
1
gap> Number(s, x -> x in l);
1
# MiscTest2
gap> gens := [Transformation([2, 8, 3, 7, 1, 5, 2, 6]),
> Transformation([3, 5, 7, 2, 5, 6, 3, 8]),
> Transformation([6, 7, 4, 1, 4, 1, 6, 2]),
> Transformation([8, 8, 5, 1, 7, 5, 2, 8])];;
gap> s := Semigroup(gens);
<transformation semigroup of degree 8 with 4 generators>
gap> f := Transformation([5, 2, 7, 2, 7, 2, 5, 8]);;
gap> l := LClassNC(s, f);
<Green's L-class: Transformation( [ 5, 2, 7, 2, 7, 2, 5 ] )>
gap> Transformation([5, 2, 7, 2, 7, 2, 5]) in last;
true
gap> enum := Enumerator(l);
<enumerator of <Green's L-class: Transformation( [ 5, 2, 7, 2, 7, 2, 5 ] )>>
gap> enum[1];
Transformation( [ 5, 2, 7, 2, 7, 2, 5 ] )
gap> enum[2];
Transformation( [ 5, 8, 7, 8, 7, 8, 5, 2 ] )
gap> Position(enum, enum[2]);
2
gap> Position(enum, enum[1]);
1
gap> ForAll(enum, x -> enum[Position(enum, x)] = x);
true
gap> ForAll([1 .. Length(enum)], x -> Position(enum, enum[x]) = x);
true
gap> Length(enum);
1728
gap> ForAll(enum, x -> x in s);
true
gap> ForAll(l, x -> x in enum);
true
gap> Number(s, x -> x in enum);
1728
gap> Number(s, x -> x in l);
1728
gap> AsSet(l) = AsSet(enum);
true
gap> f := Transformation([7, 2, 4, 2, 2, 1, 7, 6]);;
gap> Position(enum, f);
fail
gap> GreensHClasses(l);
[ <Green's H-class: Transformation( [ 5, 2, 7, 2, 7, 2, 5 ] )>,
<Green's H-class: Transformation( [ 2, 8, 7, 5, 5, 7, 2, 2 ] )>,
<Green's H-class: Transformation( [ 8, 2, 7, 2, 2, 5, 8, 7 ] )>,
<Green's H-class: Transformation( [ 2, 7, 7, 8, 8, 2, 2, 5 ] )>,
<Green's H-class: Transformation( [ 8, 8, 7, 5, 5, 7, 2, 8 ] )>,
<Green's H-class: Transformation( [ 7, 5, 2, 8, 5, 7, 7, 8 ] )>,
<Green's H-class: Transformation( [ 5, 8, 2, 7, 7, 5, 5, 7 ] )>,
<Green's H-class: Transformation( [ 8, 7, 2, 5, 5, 7, 8, 5 ] )>,
<Green's H-class: Transformation( [ 7, 5, 2, 8, 8, 5, 7, 7 ] )>,
<Green's H-class: Transformation( [ 7, 2, 8, 2, 2, 5, 7, 7 ] )>,
<Green's H-class: Transformation( [ 2, 7, 8, 7, 7, 2, 2, 5 ] )>,
<Green's H-class: Transformation( [ 2, 5, 7, 5, 5, 7, 2 ] )>,
<Green's H-class: Transformation( [ 5, 8, 7, 2, 2, 5, 5, 7 ] )>,
<Green's H-class: Transformation( [ 8, 7, 7, 5, 5, 2, 8, 5 ] )>,
<Green's H-class: Transformation( [ 7, 5, 7, 8, 8, 5, 7, 2 ] )>,
<Green's H-class: Transformation( [ 5, 2, 7, 7, 7, 8, 5, 5 ] )>,
<Green's H-class: Transformation( [ 7, 8, 7, 5, 8, 5, 7, 2 ] )>,
<Green's H-class: Transformation( [ 8, 2, 7, 7, 7, 8, 8, 5 ] )>,
<Green's H-class: Transformation( [ 2, 5, 7, 8, 8, 7, 2, 8 ] )>,
<Green's H-class: Transformation( [ 5, 8, 7, 2, 2, 8, 5, 7 ] )>,
<Green's H-class: Transformation( [ 8, 7, 7, 5, 5, 2, 8, 8 ] )>,
<Green's H-class: Transformation( [ 7, 8, 7, 8, 8, 5, 7, 2 ] )>,
<Green's H-class: Transformation( [ 7, 5, 8, 7, 5, 2, 7, 8 ] )>,
<Green's H-class: Transformation( [ 7, 2, 5, 8, 2, 8, 7, 7 ] )>,
<Green's H-class: Transformation( [ 7, 5, 8, 7, 5, 2, 7, 5 ] )>,
<Green's H-class: Transformation( [ 5, 5, 8, 2, 2, 5, 5, 7 ] )>,
<Green's H-class: Transformation( [ 5, 7, 8, 5, 5, 2, 5, 5 ] )>,
<Green's H-class: Transformation( [ 7, 5, 8, 5, 5, 5, 7, 2 ] )>,
<Green's H-class: Transformation( [ 5, 2, 8, 7, 7, 5, 5, 5 ] )>,
<Green's H-class: Transformation( [ 8, 5, 2, 5, 5, 7, 8, 5 ] )>,
<Green's H-class: Transformation( [ 8, 7, 5, 2, 7, 5, 8, 5 ] )>,
<Green's H-class: Transformation( [ 8, 5, 5, 7, 5, 2, 8, 5 ] )>,
<Green's H-class: Transformation( [ 8, 2, 5, 5, 2, 5, 8, 7 ] )>,
<Green's H-class: Transformation( [ 7, 2, 5, 8, 2, 5, 7, 7 ] )>,
<Green's H-class: Transformation( [ 2, 8, 7, 5, 8, 5, 2, 7 ] )>,
<Green's H-class: Transformation( [ 2, 5, 8, 7, 5, 7, 2, 5 ] )>,
<Green's H-class: Transformation( [ 2, 7, 5, 8, 7, 5, 2, 7 ] )>,
<Green's H-class: Transformation( [ 7, 2, 5, 8, 5, 8, 7, 8 ] )>,
<Green's H-class: Transformation( [ 2, 8, 5, 7, 7, 5, 2, 8 ] )>,
<Green's H-class: Transformation( [ 8, 8, 5, 2, 2, 7, 8, 5 ] )>,
<Green's H-class: Transformation( [ 8, 5, 5, 8, 8, 2, 8, 7 ] )>,
<Green's H-class: Transformation( [ 5, 7, 5, 8, 8, 8, 5, 2 ] )>,
<Green's H-class: Transformation( [ 7, 2, 5, 5, 5, 8, 7, 8 ] )>,
<Green's H-class: Transformation( [ 5, 8, 8, 5, 8, 2, 5, 7 ] )>,
<Green's H-class: Transformation( [ 7, 8, 7, 5, 5, 7, 7, 2 ] )>,
<Green's H-class: Transformation( [ 8, 2, 7, 7, 7, 5, 8, 7 ] )>,
<Green's H-class: Transformation( [ 2, 7, 7, 8, 8, 7, 2, 5 ] )>,
<Green's H-class: Transformation( [ 7, 5, 7, 2, 2, 8, 7, 7 ] )>,
<Green's H-class: Transformation( [ 5, 7, 7, 7, 7, 2, 5 ] )>,
<Green's H-class: Transformation( [ 7, 7, 5, 7, 7, 2, 7 ] )>,
<Green's H-class: Transformation( [ 7, 8, 5, 7, 7, 7, 7, 2 ] )>,
<Green's H-class: Transformation( [ 8, 2, 5, 7, 7, 7, 8, 7 ] )>,
<Green's H-class: Transformation( [ 2, 7, 5, 8, 8, 7, 2, 7 ] )>,
<Green's H-class: Transformation( [ 7, 7, 5, 2, 2, 8, 7, 7 ] )>,
<Green's H-class: Transformation( [ 5, 2, 7, 7, 2, 8, 5, 7 ] )>,
<Green's H-class: Transformation( [ 5, 8, 2, 7, 8, 7, 5, 7 ] )>,
<Green's H-class: Transformation( [ 8, 7, 2, 5, 5, 8, 8, 7 ] )>,
<Green's H-class: Transformation( [ 7, 7, 2, 8, 8, 5, 7, 8 ] )>,
<Green's H-class: Transformation( [ 7, 8, 2, 7, 7, 8, 7, 5 ] )>,
<Green's H-class: Transformation( [ 8, 5, 2, 7, 7, 7, 8, 8 ] )>,
<Green's H-class: Transformation( [ 2, 8, 5, 8, 8, 7, 2, 7 ] )>,
<Green's H-class: Transformation( [ 2, 7, 7, 8, 7, 8, 2, 5 ] )>,
<Green's H-class: Transformation( [ 2, 8, 7, 7, 8, 5, 2, 8 ] )>,
<Green's H-class: Transformation( [ 2, 5, 8, 7, 5, 8, 2, 7 ] )>,
<Green's H-class: Transformation( [ 7, 2, 7, 5, 2, 8, 7, 7 ] )>,
<Green's H-class: Transformation( [ 7, 8, 2, 7, 8, 7, 7, 5 ] )>,
<Green's H-class: Transformation( [ 5, 2, 8, 8, 2, 7, 5, 5 ] )>,
<Green's H-class: Transformation( [ 7, 5, 7, 2, 2, 8, 7, 2 ] )>,
<Green's H-class: Transformation( [ 5, 2, 7, 7, 7, 2, 5 ] )>,
<Green's H-class: Transformation( [ 7, 7, 5, 2, 7, 2, 7 ] )>,
<Green's H-class: Transformation( [ 7, 2, 7, 5, 2, 8, 7, 2 ] )>,
<Green's H-class: Transformation( [ 7, 8, 2, 7, 8, 2, 7, 5 ] )> ]
gap> Length(last);
72
# MiscTest3
gap> gens := [
> PartialPermNC([1, 2, 3, 5, 7, 10], [12, 3, 1, 11, 9, 5]),
> PartialPermNC([1, 2, 3, 4, 5, 7, 8], [4, 3, 11, 12, 6, 2, 1]),
> PartialPermNC([1, 2, 3, 4, 5, 9, 11], [11, 6, 9, 2, 4, 8, 12]),
> PartialPermNC([1, 2, 3, 4, 7, 9, 12], [7, 1, 12, 2, 9, 4, 5]),
> PartialPermNC([1, 2, 3, 5, 7, 8, 9], [5, 4, 8, 11, 6, 12, 1]),
> PartialPermNC([1, 2, 4, 6, 8, 9, 10], [8, 5, 2, 12, 4, 7, 11])];;
gap> s := Semigroup(gens);
<partial perm semigroup of rank 12 with 6 generators>
gap> Size(s);
4857
gap> f := PartialPerm([6, 9], [12, 6]);;
gap> l := LClass(s, f);
<Green's L-class: [9,6,12]>
gap> NrHClasses(l);
66
gap> Size(l);
66
gap> SchutzenbergerGroup(l);
Group([ (6,12) ])
gap> o := RhoOrb(l);
<closed orbit, 147 points with Schreier tree with log>
gap> d := DClassOfLClass(l);
<Green's D-class: [2,6][7,12]>
gap> Size(d);
66
gap> NrLClasses(d);
1
gap> NrRClasses(d);
66
gap> SchutzenbergerGroup(d);
Group(())
gap> Length(RhoOrbSCC(l));
33
gap> HClasses(l);
[ <Green's H-class: [2,6][7,12]>, <Green's H-class: [4,6][9,12]>,
<Green's H-class: [7,12][9,6]>, <Green's H-class: [1,12][7,6]>,
<Green's H-class: [1,12][2,6]>, <Green's H-class: [7,6][8,12]>,
<Green's H-class: [1,6][9,12]>, <Green's H-class: [2,12][4,6]>,
<Green's H-class: [4,12][8,6]>, <Green's H-class: [2,12][3,6]>,
<Green's H-class: [1,6][8,12]>, <Green's H-class: [3,12][9,6]>,
<Green's H-class: [5,12][9,6]>, <Green's H-class: [7,6](12)>,
<Green's H-class: [1,6][3,12]>, <Green's H-class: [2,6][8,12]>,
<Green's H-class: [1,12][4,6]>, <Green's H-class: [2,12][9,6]>,
<Green's H-class: [3,6][4,12]>, <Green's H-class: [4,12][7,6]>,
<Green's H-class: [8,12][9,6]>, <Green's H-class: [9,6,12]>,
<Green's H-class: [4,12][5,6]>, <Green's H-class: [9,12,6]>,
<Green's H-class: [3,12][11,6]>, <Green's H-class: [2,12][5,6]>,
<Green's H-class: [4,12,6]>, <Green's H-class: [5,12][11,6]>,
<Green's H-class: [1,12][5,6]>, <Green's H-class: [2,12,6]>,
<Green's H-class: [4,12](6)>, <Green's H-class: [4,12][11,6]>,
<Green's H-class: [8,12](6)>, <Green's H-class: [2,12][7,6]>,
<Green's H-class: [4,12][9,6]>, <Green's H-class: [7,6][9,12]>,
<Green's H-class: [1,6][7,12]>, <Green's H-class: [1,6][2,12]>,
<Green's H-class: [7,12][8,6]>, <Green's H-class: [1,12][9,6]>,
<Green's H-class: [2,6][4,12]>, <Green's H-class: [4,6][8,12]>,
<Green's H-class: [2,6][3,12]>, <Green's H-class: [1,12][8,6]>,
<Green's H-class: [3,6][9,12]>, <Green's H-class: [5,6][9,12]>,
<Green's H-class: [7,12,6]>, <Green's H-class: [1,12][3,6]>,
<Green's H-class: [2,12][8,6]>, <Green's H-class: [1,6][4,12]>,
<Green's H-class: [2,6][9,12]>, <Green's H-class: [3,12][4,6]>,
<Green's H-class: [4,6][7,12]>, <Green's H-class: [8,6][9,12]>,
<Green's H-class: [9,12](6)>, <Green's H-class: [4,6][5,12]>,
<Green's H-class: [9,6](12)>, <Green's H-class: [3,6][11,12]>,
<Green's H-class: [2,6][5,12]>, <Green's H-class: [4,6](12)>,
<Green's H-class: [5,6][11,12]>, <Green's H-class: [1,6][5,12]>,
<Green's H-class: [2,6](12)>, <Green's H-class: [4,6,12]>,
<Green's H-class: [4,6][11,12]>, <Green's H-class: [8,6,12]> ]
gap> IsDuplicateFreeList(last);
true
gap> IsRegularGreensClass(l);
false
gap> H := HClasses(l);;
gap> ForAll(H, x -> Representative(x) in l);
true
gap> ForAll(H, x -> Representative(x) in d);
true
gap> d;
<Green's D-class: [2,6][7,12]>
gap> Representative(l) in d;
true
gap> First(H, x -> not Representative(x) in d);
fail
gap> ForAll(l, x -> x in d);
true
gap> rep := Representative(d);
[2,6][7,12]
gap> s := Parent(d);
<partial perm semigroup of size 4857, rank 12 with 6 generators>
gap> ElementsFamily(FamilyObj(s)) <> FamilyObj(f)
> or RankOfPartialPerm(f) <> RankOfPartialPerm(rep);
false
gap> g := f;
[9,6,12]
gap> m := LambdaOrbSCCIndex(d);
54
gap> o := LambdaOrb(d);
<closed orbit, 184 points with Schreier tree with log>
gap> scc := OrbSCC(o);
[ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ], [ 8 ], [ 9 ], [ 10 ],
[ 11 ], [ 12 ], [ 14 ], [ 15 ], [ 16 ], [ 17 ], [ 18 ], [ 19 ], [ 21 ],
[ 22 ], [ 23 ], [ 24 ], [ 25 ], [ 26 ], [ 27 ], [ 28 ], [ 29 ], [ 30 ],
[ 31 ], [ 32 ], [ 33 ], [ 34 ], [ 35 ], [ 36 ], [ 37 ], [ 38 ], [ 39 ],
[ 40 ], [ 41 ], [ 42 ], [ 43, 46, 44, 50, 20, 47, 69, 61, 63, 86, 78 ],
[ 45 ], [ 48 ],
[ 49, 83, 66, 82, 108, 87, 99, 80, 145, 84, 56, 64, 133, 147, 74, 96, 85,
146, 135, 62, 107, 110, 13, 154, 125, 101, 168, 159, 152, 137, 134,
171, 175 ], [ 51 ], [ 52 ], [ 53, 127, 121, 164, 177 ], [ 54 ], [ 55 ],
[ 57 ], [ 58 ], [ 59 ], [ 60 ], [ 65 ], [ 67 ], [ 68 ], [ 70 ], [ 71 ],
[ 72 ], [ 73 ], [ 75 ], [ 76 ], [ 77 ], [ 79 ], [ 81 ], [ 88 ], [ 89 ],
[ 90 ], [ 91 ], [ 94 ], [ 95 ], [ 97 ], [ 98 ], [ 100 ], [ 102 ], [ 103 ],
[ 104 ], [ 105 ], [ 106 ], [ 109 ], [ 111 ], [ 113 ], [ 114 ], [ 115 ],
[ 116 ], [ 117 ], [ 118 ], [ 119 ], [ 120 ], [ 122 ], [ 123 ], [ 124 ],
[ 126 ], [ 128 ], [ 129 ], [ 130 ], [ 131 ], [ 132 ], [ 136 ], [ 138 ],
[ 139 ], [ 140 ], [ 141 ], [ 142, 173, 179, 92, 150 ], [ 143 ],
[ 144, 112, 93 ], [ 148 ], [ 149 ], [ 151 ], [ 153 ], [ 155 ], [ 156 ],
[ 157 ], [ 158 ], [ 160 ], [ 161 ], [ 162 ], [ 163 ], [ 165 ], [ 166 ],
[ 167 ], [ 169 ], [ 170 ], [ 172 ], [ 174 ], [ 176 ], [ 178 ], [ 180 ],
[ 181 ], [ 182 ], [ 183 ], [ 184 ] ]
gap> l := Position(o, LambdaFunc(s)(g));
65
gap> l = fail or OrbSCCLookup(o)[l] <> m ;
false
gap> l <> scc[m][1];
false
gap> m := RhoOrbSCCIndex(d);
38
gap> o := RhoOrb(d);
<closed orbit, 147 points with Schreier tree with log>
gap> scc := OrbSCC(o);
[ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ], [ 8 ], [ 9 ],
[ 10, 42, 45, 50, 48, 52, 53, 51, 115, 134, 144 ], [ 11 ], [ 14 ], [ 15 ],
[ 16 ], [ 17 ], [ 18 ], [ 19 ], [ 20 ], [ 21 ], [ 22 ], [ 23 ], [ 24 ],
[ 25 ], [ 26 ], [ 27 ], [ 28 ], [ 29 ], [ 30 ], [ 31 ], [ 32 ], [ 33 ],
[ 34 ], [ 36 ], [ 37 ], [ 38 ], [ 40 ], [ 41 ],
[ 43, 46, 102, 59, 69, 63, 12, 89, 62, 81, 103, 65, 112, 143, 54, 70, 47,
98, 74, 100, 120, 123, 121, 94, 122, 145, 132, 124, 93, 133, 128, 138,
125 ], [ 44 ], [ 49, 113, 85, 84, 75 ], [ 55 ], [ 56, 95, 135 ],
[ 57 ], [ 58 ], [ 60 ], [ 61, 119, 108, 64, 13 ], [ 66 ], [ 67 ], [ 68 ],
[ 71 ], [ 72 ], [ 73 ], [ 76 ], [ 77 ], [ 78 ], [ 79 ], [ 80 ], [ 82 ],
[ 83 ], [ 86 ], [ 87 ], [ 88 ], [ 90 ], [ 91 ], [ 92 ], [ 96 ], [ 97 ],
[ 99 ], [ 101 ], [ 104 ], [ 105 ], [ 106 ], [ 107 ], [ 109 ], [ 110 ],
[ 111, 129, 147, 35, 39 ], [ 114 ], [ 116 ], [ 117 ], [ 118 ], [ 126 ],
[ 127 ], [ 130 ], [ 131 ], [ 136 ], [ 137 ], [ 139 ], [ 140 ], [ 141 ],
[ 142 ], [ 146 ] ]
gap> l := Position(o, RhoFunc(s)(g));
123
gap> l = fail or OrbSCCLookup(o)[l] <> m;
false
gap> g := RhoOrbMult(o, m, l)[2] * g;;
gap> schutz := RhoOrbStabChain(d);
<stabilizer chain record, Base [ 12 ], Orbit length 2, Size: 2>
gap> l <> scc[m][1];
true
gap> cosets := LambdaCosets(d);
<enumerator of perm group>
gap> LambdaOrbStabChain(LambdaOrb(d), LambdaOrbSCCIndex(d));
false
gap> g := LambdaPerm(s)(rep, g);
()
gap> schutz <> false;
true
gap> o := LambdaOrb(d);
<closed orbit, 184 points with Schreier tree with log>
gap> m := LambdaOrbSCCIndex(d);
54
gap> lambda_schutz := LambdaOrbSchutzGp(o, m);
Group(())
gap> lambda_stab := LambdaOrbStabChain(o, m);
false
gap> o := RhoOrb(d);
<closed orbit, 147 points with Schreier tree with log>
gap> m := RhoOrbSCCIndex(d);
38
gap> rho_schutz := RhoOrbSchutzGp(o, m);
Group([ (1,12) ])
gap> rho_stab := RhoOrbStabChain(o, m);
true
gap> rho_stab = true;
true
gap> schutz := lambda_schutz;
Group(())
gap> lambda_stab = true;
false
gap> Parent(d) = s;
true
gap> PartialPerm([1, 9], [6, 12]) in d;
true
gap> RhoOrbRep(o, m);
[2,12][7,1]
gap> Representative(d);
[2,6][7,12]
gap> p := LambdaConjugator(Parent(d))(RhoOrbRep(o, m), Representative(d));;
gap> LambdaFunc(s)(RhoOrbRep(o, m));
[ 1, 12 ]
gap> OnSets(last, p);
[ 6, 12 ]
gap> LambdaFunc(s)(Representative(d));
[ 6, 12 ]
gap> rho_schutz := rho_schutz ^ p;
Group([ (6,12) ])
gap> f := PartialPermNC([6, 9], [12, 6]);
[9,6,12]
gap> s := Semigroup(gens);
<partial perm semigroup of rank 12 with 6 generators>
gap> l := LClass(s, f);
<Green's L-class: [9,6,12]>
gap> d := DClassOfLClass(l);
<Green's D-class: [9,6,12]>
gap> ForAll(l, x -> x in d);
true
gap> NrHClasses(l);
66
gap> RhoCosets(d);
<enumerator of perm group>
gap> Length(last);
2
gap> H := HClasses(l);;
gap> ForAll(H, x -> Representative(x) in l);
true
gap> ForAll(H, x -> Representative(x) in d);
true
gap> ForAll(H, x -> Representative(x) in s);
true
gap> ForAll(l, x -> x in l);
true
# MiscTest4
gap> gens := [Transformation([2, 8, 3, 7, 1, 5, 2, 6]),
> Transformation([3, 5, 7, 2, 5, 6, 3, 8]),
> Transformation([6, 7, 4, 1, 4, 1, 6, 2]),
> Transformation([8, 8, 5, 1, 7, 5, 2, 8])];;
gap> s := Semigroup(gens);
<transformation semigroup of degree 8 with 4 generators>
gap> Size(s);
95540
gap> f := Transformation([2, 2, 7, 7, 7, 1, 2, 7]);;
gap> l := LClassNC(s, f);
<Green's L-class: Transformation( [ 2, 2, 7, 7, 7, 1, 2, 7 ] )>
gap> Transformation([2, 2, 7, 7, 7, 1, 2, 7]) in last;
true
gap> g := Transformation([2, 2, 7, 7, 7, 1, 2, 1]);;
gap> Size(l);
936
gap> h := GreensHClassOfElement(l, g);
<Green's H-class: Transformation( [ 2, 2, 7, 7, 7, 1, 2, 1 ] )>
gap> Transformation([2, 2, 7, 7, 7, 1, 2, 1]) in last;
true
gap> Size(h);
1
gap> SchutzenbergerGroup(l);
Sym( [ 1, 2, 7 ] )
gap> IsRegularGreensClass(l);
false
gap> IsGreensClassNC(h);
true
gap> ForAll(h, x -> x in l);
true
gap> ForAll(h, x -> x in s);
true
gap> SchutzenbergerGroup(h);
Group(())
gap> Idempotents(h);
[ ]
gap> IsGroupHClass(h);
false
gap> IsGreensHClass(h);
true
gap> GreensHRelation(s) = EquivalenceClassRelation(h);
true
gap> gens := [PartialPermNC([1, 2, 4, 5, 9], [3, 6, 2, 10, 5]),
> PartialPermNC([1, 2, 3, 4, 7, 8], [10, 6, 7, 9, 4, 1]),
> PartialPermNC([1, 2, 3, 4, 5, 6, 7, 9], [7, 2, 5, 6, 9, 3, 8, 10]),
> PartialPermNC([1, 2, 3, 5, 6, 7, 8, 9], [10, 3, 7, 1, 5, 9, 2, 6]),
> PartialPermNC([2, 3, 5, 6, 10], [4, 1, 9, 2, 5]),
> PartialPermNC([1, 4, 6, 7, 9, 10], [8, 7, 2, 3, 4, 1])];;
gap> s := Semigroup(gens);
<partial perm semigroup of rank 10 with 6 generators>
gap> f := PartialPerm([]);;
gap> l := LClass(s, f);
<Green's L-class: <empty partial perm>>
gap> Size(s);
55279
gap> NrIdempotents(s);
141
gap> NrDClasses(s);
2064
gap> NrRClasses(s);
9568
gap> NrLClasses(s);
8369
gap> NrHClasses(s);
25175
gap> IsRegularSemigroup(s);
false
gap> l := LClass(s, f);
<Green's L-class: <empty partial perm>>
gap> h := HClassNC(l, f);
<Green's H-class: <empty partial perm>>
gap> Size(h);
1
gap> ForAll(h, x -> x in l);
true
gap> ForAll(h, x -> x in s);
true
gap> IsGreensClassNC(h);
true
gap> f := PartialPermNC([2, 8, 9], [8, 10, 5]);;
gap> l := LClass(s, f);
<Green's L-class: [2,8,10][9,5]>
gap> h := HClassNC(l, f);
<Green's H-class: [2,8,10][9,5]>
gap> ForAll(h, x -> x in s);
true
gap> ForAll(h, x -> x in l);
true
gap> Size(h);
1
# MiscTest5
gap> gens := [Transformation([2, 6, 7, 2, 6, 1, 1, 5]),
> Transformation([3, 8, 1, 4, 5, 6, 7, 1]),
> Transformation([4, 3, 2, 7, 7, 6, 6, 5]),
> Transformation([7, 1, 7, 4, 2, 5, 6, 3])];;
gap> s := Monoid(gens);
<transformation monoid of degree 8 with 4 generators>
gap> f := Transformation([5, 4, 7, 2, 2, 2, 2, 5]);;
gap> f in s;
true
gap> l := LClass(s, f);
<Green's L-class: Transformation( [ 5, 4, 7, 2, 2, 2, 2, 5 ] )>
gap> Transformation([5, 4, 7, 2, 2, 2, 2, 5]) in last;
true
gap> IsGreensClassNC(l);
false
gap> Size(l);
1
gap> f := Transformation([4, 3, 2, 7, 7, 6, 6, 5]);;
gap> l := LClass(s, f);
<Green's L-class: Transformation( [ 4, 3, 2, 7, 7, 6, 6, 5 ] )>
gap> Transformation([4, 3, 2, 7, 7, 6, 6, 5]) in last;
true
gap> Size(l);
1
# MiscTest6
gap> gens := [PartialPermNC([1, 2, 3], [1, 4, 3]),
> PartialPermNC([1, 2, 3], [2, 3, 4]),
> PartialPermNC([1, 2, 3], [4, 2, 1]),
> PartialPermNC([1, 2, 4], [1, 4, 3])];;
gap> s := Semigroup(gens);
<partial perm semigroup of rank 4 with 4 generators>
gap> List(LClasses(s), IsRegularGreensClass);
[ false, false, false, false, true, true, false, false, true, true, false,
false, false, false, true, true, true, true, false, true ]
gap> Number(last, x -> x = true);
9
gap> GroupOfUnits(s);
fail
gap> List(LClasses(s), NrIdempotents);
[ 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1 ]
gap> NrIdempotents(s);
9
gap> List(LClasses(s), Size);
[ 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 4, 4, 4, 4, 4, 1 ]
gap> Sum(last);
62
gap> Size(s);
62
gap> f := PartialPerm([2, 3], [2, 4]);;
gap> l := LClassNC(s, f);
<Green's L-class: [3,4](2)>
gap> HClassReps(l);
[ [3,4](2), [1,2,4], [3,2,4], [1,4](2) ]
gap> IsRegularGreensClass(l);
false
gap> NrHClasses(l);
4
gap> l := LClass(s, f);
<Green's L-class: [3,4](2)>
gap> HClassReps(l);
[ [1,4](2), [3,4](2), [1,2,4], [3,2,4] ]
gap> IsRegularGreensClass(l);
false
gap> ForAll(HClassReps(l), x -> x in l);
true
gap> d := DClassOfLClass(l);
<Green's D-class: [1,4](2)>
gap> Size(d);
4
gap> Size(l);
4
gap> AsSSortedList(l) = AsSortedList(d);
true
gap> AsSSortedList(d) = AsSSortedList(l);
true
gap> l < d;
false
gap> ForAll(l, x -> x in d);
true
gap> ForAll(d, x -> x in l);
true
gap> HClassReps(d) = HClassReps(l);
true
gap> NrRClasses(d);
4
gap> NrLClasses(d);
1
gap> NrHClasses(d);
4
# MiscTest7
gap> gens := [Transformation([1, 5, 6, 2, 5, 2, 1]),
> Transformation([1, 7, 5, 4, 3, 5, 7]),
> Transformation([2, 7, 7, 2, 4, 1, 1]),
> Transformation([3, 2, 2, 4, 1, 7, 6]),
> Transformation([3, 3, 5, 1, 7, 1, 6]),
> Transformation([3, 3, 6, 1, 7, 5, 2]),
> Transformation([3, 4, 6, 5, 4, 4, 7]),
> Transformation([5, 2, 4, 5, 1, 4, 5]),
> Transformation([5, 5, 2, 2, 6, 7, 2]),
> Transformation([7, 7, 5, 4, 5, 3, 2])];;
gap> s := Semigroup(gens);;
gap> l := LClasses(s)[1154];
<Green's L-class: Transformation( [ 7, 2, 2, 3, 6, 1, 2 ] )>
gap> Transformation([7, 2, 2, 3, 6, 1, 2]) in last;
true
gap> IsRegularGreensClass(l);
false
gap> d := DClassOfLClass(l);
<Green's D-class: Transformation( [ 7, 2, 2, 3, 6, 1, 2 ] )>
gap> Transformation([7, 2, 2, 3, 6, 1, 2]) in last;
true
gap> Size(l);
1
gap> Size(d);
1
gap> NrHClasses(d);
1
gap> NrLClasses(d);
1
gap> NrRClasses(d);
1
gap> l := LClasses(s)[523];
<Green's L-class: Transformation( [ 5, 5, 5, 1, 7, 3, 6 ] )>
gap> Transformation([5, 5, 5, 1, 7, 3, 6]) in last;
true
gap> Size(l);
1
# MiscTest8
gap> gens := [PartialPermNC([1, 2, 3, 5], [5, 7, 3, 4]),
> PartialPermNC([1, 2, 3, 4, 5], [6, 4, 1, 2, 7]),
> PartialPermNC([1, 2, 3, 4, 7], [2, 7, 4, 5, 8]),
> PartialPermNC([1, 2, 3, 5, 6], [5, 6, 1, 4, 3]),
> PartialPermNC([1, 2, 4, 6, 7], [2, 1, 6, 7, 4]),
> PartialPermNC([1, 3, 5, 6, 7], [6, 2, 3, 5, 7]),
> PartialPermNC([1, 2, 3, 4, 5, 7], [4, 1, 6, 2, 8, 5]),
> PartialPermNC([1, 2, 3, 4, 5, 8], [5, 6, 3, 8, 2, 7]),
> PartialPermNC([1, 2, 3, 4, 6, 7], [1, 5, 2, 6, 7, 4]),
> PartialPermNC([1, 2, 3, 4, 5, 6, 8], [7, 5, 2, 8, 4, 1, 3])];;
gap> s := Semigroup(gens);
<partial perm semigroup of rank 8 with 10 generators>
gap> Size(s);
72713
gap> NrRClasses(s);
25643
gap> NrDClasses(s);
4737
gap> NrLClasses(s);
11323
gap> NrIdempotents(s);
121
gap> IsRegularSemigroup(s);
false
gap> f := PartialPerm([3, 4, 7], [4, 7, 8]);;
gap> d := DClass(s, f);
<Green's D-class: [3,4,7,8]>
gap> Size(d);
282
gap> NrRClasses(d);
282
gap> NrLClasses(d);
1
gap> IsRegularDClass(d);
false
gap> RhoCosets(d);
<enumerator of perm group>
gap> Length(last);
6
gap> AsList(last2);
[ (), (4,8), (4,7,8), (7,8), (4,8,7), (4,7) ]
gap> SchutzenbergerGroup(d);
Group(())
gap> RhoOrbStabChain(d);
<stabilizer chain record, Base [ 7, 8 ], Orbit length 3, Size: 6>
gap> data := SemigroupData(Parent(d));
<closed semigroup data with 25643 reps, 178 lambda-values, 150 rho-values>
gap> OrbSCC(data)[OrbSCCLookup(data)[SemigroupDataIndex(d)]];
[ 33, 144, 340, 568, 35, 151, 353, 540, 1088, 1900, 1342, 2195, 1043, 1151,
1336, 2189, 1361, 1902, 713, 1346, 561, 711, 1343, 519, 706, 1333, 553,
720, 539, 1086, 571, 1158, 560, 1134, 1973, 1337, 1842, 1040, 725, 1362,
1904, 1357, 1202, 1102, 1367, 2196, 1840, 717, 1181, 1339, 2192, 544, 1103,
1932, 2888, 1360, 729, 1366, 1124, 1958, 2214, 1126, 715, 1352, 2204, 1340,
1013, 1368, 503, 1014, 1801, 2750, 3674, 1335, 2188, 2997, 1344, 356, 727,
1090, 1905, 358, 731, 1139, 1911, 1041, 712, 1347, 1371, 721, 1359, 2213,
1838, 2788, 1045, 1837, 357, 728, 1364, 1349, 2052, 2009, 1903, 2859, 2873,
707, 718, 341, 708, 1338, 345, 719, 147, 344, 1356, 2208, 1978, 2203, 1369,
2217, 2862, 1091, 1907, 710, 1341, 2193, 3127, 343, 714, 1351, 2202, 2191,
3126, 724, 2037, 4041, 726, 1363, 2215, 3767, 2057, 2198, 2058, 2039, 2990,
709, 1137, 1976, 1841, 2794, 2936, 2973, 1974, 1089, 1901, 2855, 2210,
1899, 1831, 2209, 3132, 2866, 730, 1370, 2218, 1348, 2199, 1136, 1975,
3137, 1358, 2212, 3133, 4044, 1365, 2795, 1928, 2065, 3019, 2884, 1898,
1909, 1046, 1839, 342, 1977, 2938, 2792, 148, 346, 1908, 2861, 2939, 3850,
2010, 2974, 3891, 2920, 2051, 3003, 1929, 2885, 2216, 3135, 1910, 2863,
3004, 3124, 3704, 3916, 2791, 3708, 4573, 5517, 4042, 2190, 3125, 4040,
2749, 4043, 4703, 4807, 3925, 2889, 3766, 2783, 2782, 3910, 2789, 2206,
3130, 1979, 3706, 1355, 2207, 3131, 2194, 3128, 2856, 3765, 2857, 2201,
2937, 2790, 3707, 2205, 2200, 1092, 2864, 1913, 1345, 2197, 1833, 3136,
3134, 1960, 2921, 3831, 2865, 1906, 2860, 1832, 1918, 1140, 1800, 1353,
1959, 1933, 1354, 2793, 1105, 2211, 1135, 1087, 1334, 1350, 2858, 1157,
3129, 355, 152, 146 ]
gap> Position(DClasses(s), d);
17
gap> d := DClasses(s)[18];
<Green's D-class: [1,2][3,7,5][6,8]>
gap> OrbSCC(data)[OrbSCCLookup(data)[SemigroupDataIndex(d)]];
[ 36 ]
gap> LambdaCosets(d);
<enumerator of perm group>
gap> LambdaOrbSCC(d);
[ 22 ]
gap> RhoOrbSCC(d);
[ 35 ]
gap> ForAll(d, x -> x in d);
true
gap> enum := Enumerator(d);
<enumerator of <Green's D-class: [1,2][3,7,5][6,8]>>
gap> enum[1];
[1,2][3,7,5][6,8]
gap> Length(enum);
1
gap> Size(d);
1
gap> ForAll(enum, x -> enum[Position(enum, x)] = x);
true
gap> s := Semigroup(gens);
<partial perm semigroup of rank 8 with 10 generators>
gap> d := DClass(s, PartialPerm([1, 3, 6], [7, 4, 8]));
<Green's D-class: [1,7][3,4][6,8]>
gap> enum := Enumerator(d);
<enumerator of <Green's D-class: [1,7][3,4][6,8]>>
gap> ForAll(enum, x -> enum[Position(enum, x)] = x);
true
gap> ForAll([1 .. Length(enum)], x -> Position(enum, enum[x]) = x);
true
gap> enum[1];
[1,7][3,4][6,8]
gap> enum[2];
[2,8][3,7][6,4]
gap> Position(enum, enum[2]);
2
gap> Position(enum, enum[3]);
3
gap> enum[3];
[1,4][3,8][5,7]
gap> enum[4];
[2,7][6,4](8)
gap> for d in DClasses(s) do
> enum := Enumerator(d);
> if not ForAll(enum, x -> enum[Position(enum, x)] = x) then
> Print("problem with enumerator of a D-class 1\n");
> fi;
> od;
gap> Size(s);
72713
gap> NrRClasses(s);
25643
gap> NrLClasses(s);
11323
gap> NrDClasses(s);
4737
gap> NrIdempotents(s);
121
# MiscTest9
gap> gens := [Transformation([3, 4, 1, 2, 1]),
> Transformation([4, 2, 1, 5, 5]),
> Transformation([4, 2, 2, 2, 4])];;
gap> s := Semigroup(gens);;
gap> for d in DClasses(s) do
> enum := Enumerator(d);
> if not ForAll(enum, x -> enum[Position(enum, x)] = x) then
> Print("problem with enumerator of a D-class 1\n");
> fi;
> od;
gap> gens := [PartialPermNC([1, 2, 3, 6, 8, 10], [2, 6, 7, 9, 1, 5]),
> PartialPermNC([1, 2, 3, 4, 5, 8, 10], [7, 1, 4, 3, 2, 6, 5]),
> PartialPermNC([1, 2, 3, 4, 6, 7, 8, 10], [3, 8, 1, 9, 4, 10, 5, 6])];;
gap> s := Semigroup(gens);;
gap> f := PartialPerm([2, 4], [6, 5]);;
gap> d := DClassNC(s, f);
<Green's D-class: [2,6][4,5]>
gap> GreensHClasses(d);
[ <Green's H-class: [2,6][4,5]> ]
gap> Size(d);
1
# MiscTest10
gap> gens :=
> [PartialPermNC([1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 19,
> 20, 24, 25, 26, 27, 28, 29, 31, 32, 34, 35, 36, 37, 38, 40, 43, 45, 46, 49,
> 50, 51, 53, 55, 56, 57, 58, 59, 60, 61, 64, 66, 68, 69, 70, 72, 73, 74, 77,
> 80, 81, 83, 86, 87, 89, 91, 98], [89, 70, 79, 27, 84, 99, 9, 73, 33, 77,
> 69, 41, 18, 63, 29, 42, 75, 56, 90, 64, 98, 49, 35, 100, 71, 3, 20, 2, 26,
> 11, 39, 7, 48, 85, 8, 10, 61, 25, 55, 92, 62, 21, 34, 57, 44, 14, 53, 59,
> 12, 87, 78, 83, 30, 32, 68, 86, 23, 47, 93, 15, 76, 97, 91]),
> PartialPermNC([1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
> 19, 20, 22, 23, 24, 25, 28, 30, 31, 33, 34, 35, 36, 39, 40, 42, 43, 44, 45,
> 46, 47, 50, 53, 54, 55, 58, 59, 64, 65, 67, 69, 70, 71, 72, 73, 76, 77, 78,
> 81, 82, 84, 85, 86, 87, 89, 92, 94, 95], [5, 13, 94, 44, 80, 54, 99, 81,
> 31, 7, 90, 30, 46, 68, 36, 11, 100, 17, 87, 72, 14, 29, 9, 61, 91, 32, 43,
> 64, 60, 41, 26, 40, 8, 23, 63, 38, 57, 12, 59, 83, 92, 96, 18, 3, 65, 2,
> 37, 21, 49, 16, 75, 24, 27, 1, 48, 6, 35, 79, 82, 51, 39, 25, 77, 62, 22]),
> PartialPermNC([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,
> 18, 19, 20, 21, 23, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
> 40, 42, 44, 48, 51, 52, 53, 55, 56, 57, 58, 60, 63, 64, 65, 66, 67, 71, 73,
> 75, 77, 80, 82, 83, 85, 86, 90, 91, 96, 97, 98, 99],
> [67, 93, 18, 59, 86, 16, 99, 73, 60, 74, 17, 95, 85, 49, 79, 4, 33, 66, 15,
> 44, 77, 41, 55, 84, 68, 69, 94, 31, 2, 29, 5, 42, 10, 63, 58, 34, 72, 53,
> 89, 57, 62, 76, 20, 52, 22, 35, 75, 98, 78, 40, 46, 28, 6, 90, 12, 65, 26,
> 36, 25, 61, 83, 38, 39, 87, 92, 97, 43, 30])];;
gap> s := Semigroup(gens);;
gap> f := PartialPerm([12, 27, 37, 40, 46, 50, 51, 53],
> [98, 3, 84, 99, 100, 21, 70, 89]);;
gap> d := DClassNC(s, f);
<Green's D-class: [12,98][27,3][37,84][40,99][46,100][50,21][51,70][53,89]>
gap> Size(d);
1
gap> GreensHClasses(d);
[ <Green's H-class: [12,98][27,3][37,84][40,99][46,100][50,21][51,70][53,89]>
]
gap> iter := IteratorOfDClasses(s);
<iterator>
gap> repeat d := NextIterator(iter); until Size(d) > 1;
gap> d;
<Green's D-class: [8,63][57,87]>
gap> Size(d);
2036
gap> IsRegularDClass(d);
false
gap> GreensHClasses(d);;
gap> NrHClasses(d);
2036
gap> GreensLClasses(d);
[ <Green's L-class: [8,63][57,87]> ]
# MiscTest11
gap> gens := [Transformation([1, 3, 4, 1]),
> Transformation([2, 4, 1, 2]),
> Transformation([3, 1, 1, 3]),
> Transformation([3, 3, 4, 1])];;
gap> s := Monoid(gens);;
gap> List(GreensDClasses(s), LClasses);
[ [ <Green's L-class: IdentityTransformation> ],
[ <Green's L-class: Transformation( [ 1, 3, 4, 1 ] )>,
<Green's L-class: Transformation( [ 4, 1, 3, 4 ] )>,
<Green's L-class: Transformation( [ 3, 4, 1, 3 ] )> ],
[ <Green's L-class: Transformation( [ 2, 4, 1, 2 ] )> ],
[ <Green's L-class: Transformation( [ 3, 1, 1, 3 ] )>,
<Green's L-class: Transformation( [ 1, 4, 4, 1 ] )>,
<Green's L-class: Transformation( [ 2, 1, 1, 2 ] )>,
<Green's L-class: Transformation( [ 2, 4, 4, 2 ] )>,
<Green's L-class: Transformation( [ 4, 3, 3, 4 ] )> ],
[ <Green's L-class: Transformation( [ 3, 3, 4, 1 ] )> ],
[ <Green's L-class: Transformation( [ 1, 1, 1, 1 ] )>,
<Green's L-class: Transformation( [ 2, 2, 2, 2 ] )>,
<Green's L-class: Transformation( [ 3, 3, 3, 3 ] )>,
<Green's L-class: Transformation( [ 4, 4, 4, 4 ] )> ] ]
gap> List(Concatenation(last), Size);
[ 1, 1, 1, 1, 1, 10, 10, 10, 10, 10, 3, 1, 1, 1, 1 ]
gap> Sum(last);
62
gap> Size(s);
62
gap> l := Concatenation(List(GreensDClasses(s), LClasses));
[ <Green's L-class: IdentityTransformation>,
<Green's L-class: Transformation( [ 1, 3, 4, 1 ] )>,
<Green's L-class: Transformation( [ 4, 1, 3, 4 ] )>,
<Green's L-class: Transformation( [ 3, 4, 1, 3 ] )>,
<Green's L-class: Transformation( [ 2, 4, 1, 2 ] )>,
<Green's L-class: Transformation( [ 3, 1, 1, 3 ] )>,
<Green's L-class: Transformation( [ 1, 4, 4, 1 ] )>,
<Green's L-class: Transformation( [ 2, 1, 1, 2 ] )>,
<Green's L-class: Transformation( [ 2, 4, 4, 2 ] )>,
<Green's L-class: Transformation( [ 4, 3, 3, 4 ] )>,
<Green's L-class: Transformation( [ 3, 3, 4, 1 ] )>,
<Green's L-class: Transformation( [ 1, 1, 1, 1 ] )>,
<Green's L-class: Transformation( [ 2, 2, 2, 2 ] )>,
<Green's L-class: Transformation( [ 3, 3, 3, 3 ] )>,
<Green's L-class: Transformation( [ 4, 4, 4, 4 ] )> ]
gap> List(last, Elements);
[ [ IdentityTransformation ], [ Transformation( [ 1, 3, 4, 1 ] ) ],
[ Transformation( [ 4, 1, 3, 4 ] ) ], [ Transformation( [ 3, 4, 1, 3 ] ) ],
[ Transformation( [ 2, 4, 1, 2 ] ) ],
[ Transformation( [ 1, 1, 1, 3 ] ), Transformation( [ 1, 1, 3, 1 ] ),
Transformation( [ 1, 1, 3, 3 ] ), Transformation( [ 1, 3, 1, 1 ] ),
Transformation( [ 1, 3, 3, 1 ] ), Transformation( [ 3, 1, 1, 3 ] ),
Transformation( [ 3, 1, 3, 3 ] ), Transformation( [ 3, 3, 1, 1 ] ),
Transformation( [ 3, 3, 1, 3 ] ), Transformation( [ 3, 3, 3, 1 ] ) ],
[ Transformation( [ 1, 1, 1 ] ), Transformation( [ 1, 1, 4, 1 ] ),
Transformation( [ 1, 1, 4, 4 ] ), Transformation( [ 1, 4, 1, 1 ] ),
Transformation( [ 1, 4, 4, 1 ] ), Transformation( [ 4, 1, 1, 4 ] ),
Transformation( [ 4, 1, 4, 4 ] ), Transformation( [ 4, 4, 1, 1 ] ),
Transformation( [ 4, 4, 1, 4 ] ), Transformation( [ 4, 4, 4, 1 ] ) ],
[ Transformation( [ 1, 1, 1, 2 ] ), Transformation( [ 1, 1, 2, 1 ] ),
Transformation( [ 1, 1, 2, 2 ] ), Transformation( [ 1, 2, 1, 1 ] ),
Transformation( [ 1, 2, 2, 1 ] ), Transformation( [ 2, 1, 1, 2 ] ),
Transformation( [ 2, 1, 2, 2 ] ), Transformation( [ 2, 2, 1, 1 ] ),
Transformation( [ 2, 2, 1, 2 ] ), Transformation( [ 2, 2, 2, 1 ] ) ],
[ Transformation( [ 2, 2, 2 ] ), Transformation( [ 2, 2, 4, 2 ] ),
Transformation( [ 2, 2, 4, 4 ] ), Transformation( [ 2, 4, 2, 2 ] ),
Transformation( [ 2, 4, 4, 2 ] ), Transformation( [ 4, 2, 2, 4 ] ),
Transformation( [ 4, 2, 4, 4 ] ), Transformation( [ 4, 4, 2, 2 ] ),
Transformation( [ 4, 4, 2, 4 ] ), Transformation( [ 4, 4, 4, 2 ] ) ],
[ Transformation( [ 3, 3, 3 ] ), Transformation( [ 3, 3, 4, 3 ] ),
Transformation( [ 3, 3, 4, 4 ] ), Transformation( [ 3, 4, 3, 3 ] ),
Transformation( [ 3, 4, 4, 3 ] ), Transformation( [ 4, 3, 3, 4 ] ),
Transformation( [ 4, 3, 4, 4 ] ), Transformation( [ 4, 4, 3, 3 ] ),
Transformation( [ 4, 4, 3, 4 ] ), Transformation( [ 4, 4, 4, 3 ] ) ],
[ Transformation( [ 1, 1 ] ), Transformation( [ 3, 3, 4, 1 ] ),
Transformation( [ 4, 4, 1, 3 ] ) ], [ Transformation( [ 1, 1, 1, 1 ] ) ]
, [ Transformation( [ 2, 2, 2, 2 ] ) ],
[ Transformation( [ 3, 3, 3, 3 ] ) ], [ Transformation( [ 4, 4, 4, 4 ] ) ] ]
gap> Union(last);
[ Transformation( [ 1, 1, 1, 1 ] ), Transformation( [ 1, 1, 1, 2 ] ),
Transformation( [ 1, 1, 1, 3 ] ), Transformation( [ 1, 1, 1 ] ),
Transformation( [ 1, 1, 2, 1 ] ), Transformation( [ 1, 1, 2, 2 ] ),
Transformation( [ 1, 1, 3, 1 ] ), Transformation( [ 1, 1, 3, 3 ] ),
Transformation( [ 1, 1 ] ), Transformation( [ 1, 1, 4, 1 ] ),
Transformation( [ 1, 1, 4, 4 ] ), Transformation( [ 1, 2, 1, 1 ] ),
Transformation( [ 1, 2, 2, 1 ] ), IdentityTransformation,
Transformation( [ 1, 3, 1, 1 ] ), Transformation( [ 1, 3, 3, 1 ] ),
Transformation( [ 1, 3, 4, 1 ] ), Transformation( [ 1, 4, 1, 1 ] ),
Transformation( [ 1, 4, 4, 1 ] ), Transformation( [ 2, 1, 1, 2 ] ),
Transformation( [ 2, 1, 2, 2 ] ), Transformation( [ 2, 2, 1, 1 ] ),
Transformation( [ 2, 2, 1, 2 ] ), Transformation( [ 2, 2, 2, 1 ] ),
Transformation( [ 2, 2, 2, 2 ] ), Transformation( [ 2, 2, 2 ] ),
Transformation( [ 2, 2, 4, 2 ] ), Transformation( [ 2, 2, 4, 4 ] ),
Transformation( [ 2, 4, 1, 2 ] ), Transformation( [ 2, 4, 2, 2 ] ),
Transformation( [ 2, 4, 4, 2 ] ), Transformation( [ 3, 1, 1, 3 ] ),
Transformation( [ 3, 1, 3, 3 ] ), Transformation( [ 3, 3, 1, 1 ] ),
Transformation( [ 3, 3, 1, 3 ] ), Transformation( [ 3, 3, 3, 1 ] ),
Transformation( [ 3, 3, 3, 3 ] ), Transformation( [ 3, 3, 3 ] ),
Transformation( [ 3, 3, 4, 1 ] ), Transformation( [ 3, 3, 4, 3 ] ),
Transformation( [ 3, 3, 4, 4 ] ), Transformation( [ 3, 4, 1, 3 ] ),
Transformation( [ 3, 4, 3, 3 ] ), Transformation( [ 3, 4, 4, 3 ] ),
Transformation( [ 4, 1, 1, 4 ] ), Transformation( [ 4, 1, 3, 4 ] ),
Transformation( [ 4, 1, 4, 4 ] ), Transformation( [ 4, 2, 2, 4 ] ),
Transformation( [ 4, 2, 4, 4 ] ), Transformation( [ 4, 3, 3, 4 ] ),
Transformation( [ 4, 3, 4, 4 ] ), Transformation( [ 4, 4, 1, 1 ] ),
Transformation( [ 4, 4, 1, 3 ] ), Transformation( [ 4, 4, 1, 4 ] ),
Transformation( [ 4, 4, 2, 2 ] ), Transformation( [ 4, 4, 2, 4 ] ),
Transformation( [ 4, 4, 3, 3 ] ), Transformation( [ 4, 4, 3, 4 ] ),
Transformation( [ 4, 4, 4, 1 ] ), Transformation( [ 4, 4, 4, 2 ] ),
Transformation( [ 4, 4, 4, 3 ] ), Transformation( [ 4, 4, 4, 4 ] ) ]
gap> last = AsSSortedList(s);
true
# MiscTest12
gap> gens := [PartialPermNC([1, 2, 3, 4], [5, 7, 1, 6]),
> PartialPermNC([1, 2, 3, 5], [5, 2, 7, 3]),
> PartialPermNC([1, 2, 3, 6, 7], [1, 3, 4, 7, 5]),
> PartialPermNC([1, 2, 3, 4, 5, 7], [3, 2, 4, 6, 1, 5])];;
gap> s := Semigroup(gens);;
gap> Size(s);
840
gap> NrDClasses(s);
176
# MiscTest13
gap> gens := [PartialPermNC([1, 2, 3, 4], [5, 7, 1, 6]),
> PartialPermNC([1, 2, 3, 5], [5, 2, 7, 3]),
> PartialPermNC([1, 2, 3, 6, 7], [1, 3, 4, 7, 5]),
> PartialPermNC([1, 2, 3, 4, 5, 7], [3, 2, 4, 6, 1, 5])];;
gap> s := Semigroup(gens);;
gap> Size(s);
840
gap> NrDClasses(s);
176
gap> List(DClasses(s), RClasses);
[ [ <Green's R-class: [2,7][3,1,5][4,6]> ],
[ <Green's R-class: [1,5,3,7](2)> ],
[ <Green's R-class: [2,3,4][6,7,5](1)> ],
[ <Green's R-class: [7,5,1,3,4,6](2)> ],
[ <Green's R-class: [3,5]>,
<Green's R-class: <identity partial perm on [ 5 ]>>,
<Green's R-class: [1,5]>, <Green's R-class: [7,5]>,
<Green's R-class: [6,5]>, <Green's R-class: [4,5]> ],
[ <Green's R-class: [1,3][2,5]>, <Green's R-class: [2,5,3]>,
<Green's R-class: [2,5][7,3]>, <Green's R-class: [2,5](3)> ],
[ <Green's R-class: [2,1,5,6]>, <Green's R-class: [2,1][7,6](5)>,
<Green's R-class: [2,1,5][3,6]>, <Green's R-class: [2,1,6](5)>,
<Green's R-class: [2,1][7,5,6]>, <Green's R-class: [2,1,6][3,5]> ],
[ <Green's R-class: [2,7][3,6](1)(5)> ],
[ <Green's R-class: [1,3,5]>, <Green's R-class: [1,5,3]>,
<Green's R-class: [1,5][7,3]>, <Green's R-class: [1,5][6,3]>,
<Green's R-class: [4,3,5]>, <Green's R-class: [4,3](5)>,
<Green's R-class: [7,5](3)>, <Green's R-class: (3,5)>,
<Green's R-class: [7,3](5)> ],
[ <Green's R-class: [1,3][5,7](2)>, <Green's R-class: [5,3](2)(7)>,
<Green's R-class: [1,3,7](2)>, <Green's R-class: [1,7][5,3](2)>,
<Green's R-class: [5,7,3](2)>, <Green's R-class: [1,7](2)(3)> ],
[ <Green's R-class: [1,5][2,7,3]> ], [ <Green's R-class: [1,7,3](2)(5)> ],
[ <Green's R-class: [2,5][3,1][4,7]> ], [ <Green's R-class: [2,3,5,4]> ],
[ <Green's R-class: [2,4][6,5](1)> ], [ <Green's R-class: [2,3][5,1,4,7]> ],
[ <Green's R-class: [2,5,3](1)>, <Green's R-class: [2,5,1][7,3]>,
<Green's R-class: [2,5](1)(3)>, <Green's R-class: [2,5,1,3]>,
<Green's R-class: [2,5,3][7,1]>, <Green's R-class: [2,5](1,3)> ],
[ <Green's R-class: [3,5,4](1)(2)> ],
[ <Green's R-class: [2,4][7,1,3,6,5]> ],
[ <Green's R-class: [5,3,6][7,1,4](2)> ],
[ <Green's R-class: <empty partial perm>> ], [ <Green's R-class: [2,5]> ],
[ <Green's R-class: [1,5][2,6]>, <Green's R-class: [2,6](5)>,
<Green's R-class: [2,6][7,5]>, <Green's R-class: [2,6][3,5]> ],
[ <Green's R-class: [1,5,6][2,7]>, <Green's R-class: [2,7,6](5)>,
<Green's R-class: [1,5][2,7][3,6]>, <Green's R-class: [1,6][2,7](5)>,
<Green's R-class: [2,7,5,6]>, <Green's R-class: [1,6][2,7][3,5]> ],
[ <Green's R-class: [2,6][7,5](1)> ], [ <Green's R-class: [2,7,5,1,6]> ],
[ <Green's R-class: [1,7](2)>, <Green's R-class: [5,7](2)>,
<Green's R-class: <identity partial perm on [ 2, 7 ]>>,
<Green's R-class: [3,7](2)> ],
[ <Green's R-class: [1,5,7][2,3]>, <Green's R-class: [2,3](5)(7)>,
<Green's R-class: [1,5][2,3,7]>, <Green's R-class: [1,7][2,3](5)>,
<Green's R-class: [2,3](5,7)>, <Green's R-class: [1,7][2,3,5]> ],
[ <Green's R-class: [1,5,3](2)>, <Green's R-class: [7,3](2)(5)>,
<Green's R-class: [1,5](2)(3)>, <Green's R-class: [1,3](2)(5)>,
<Green's R-class: [7,5,3](2)>, <Green's R-class: [1,3,5](2)> ],
[ <Green's R-class: [1,7,5][6,3]> ],
[ <Green's R-class: [1,7](2)(5)>, <Green's R-class: (2)(5,7)>,
<Green's R-class: [1,7][3,5](2)> ],
[ <Green's R-class: [2,5,7](1)>, <Green's R-class: [2,5,1](7)>,
<Green's R-class: [2,5][3,7](1)>, <Green's R-class: [2,5,1,7]>,
<Green's R-class: [2,5,7,1]>, <Green's R-class: [2,5][3,1,7]> ],
[ <Green's R-class: [1,4][2,3](5)>, <Green's R-class: [2,3][7,5,4]>,
<Green's R-class: [1,4][2,3,5]>, <Green's R-class: [1,5,4][2,3]>,
<Green's R-class: [2,3][7,4](5)>, <Green's R-class: [1,5][2,3,4]> ],
[ <Green's R-class: [1,5][2,3][7,4]> ], [ <Green's R-class: [2,4,5,1]> ],
[ <Green's R-class: [3,4](1)>, <Green's R-class: [5,1,4]>,
<Green's R-class: [7,1,4]>, <Green's R-class: [6,1,4]>,
<Green's R-class: [3,4,1]>, <Green's R-class: [5,4,1]>,
<Green's R-class: [3,1][7,4]>, <Green's R-class: [3,4][5,1]>,
<Green's R-class: [5,4][7,1]>, <Green's R-class: [3,1,4]>,
<Green's R-class: [5,4](1)>, <Green's R-class: [7,4](1)>,
<Green's R-class: [6,4](1)>, <Green's R-class: [3,1](4)>,
<Green's R-class: [5,1](4)>, <Green's R-class: [3,4][7,1]>,
<Green's R-class: [3,1][5,4]>, <Green's R-class: [5,1][7,4]> ],
[ <Green's R-class: [3,7,1,4]> ], [ <Green's R-class: [2,3,7,1][5,4]> ],
[ <Green's R-class: [1,4](2)(5)>, <Green's R-class: [7,5,4](2)>,
<Green's R-class: [1,4][3,5](2)>, <Green's R-class: [1,5,4](2)>,
<Green's R-class: [7,4](2)(5)>, <Green's R-class: [1,5][3,4](2)> ],
[ <Green's R-class: [2,5][7,4](1)> ], [ <Green's R-class: [7,4](1,5)(2)> ],
[ <Green's R-class: [2,1][4,5](3)> ], [ <Green's R-class: [2,4][3,1][5,6]> ]
, [ <Green's R-class: [2,6,1,3]> ], [ <Green's R-class: [1,6][2,4,5,3]> ],
[ <Green's R-class: [2,1,3][5,4]>, <Green's R-class: [2,1][5,3][7,4]>,
<Green's R-class: [2,1,3,4]>, <Green's R-class: [2,1,4][5,3]>,
<Green's R-class: [2,1][5,4][7,3]>, <Green's R-class: [2,1,4](3)> ],
[ <Green's R-class: [5,6](1,3)(2)> ], [ <Green's R-class: [2,6,1,4][7,3]> ],
[ <Green's R-class: [1,6][5,4][7,3](2)> ],
[ <Green's R-class: [1,5][3,6]>, <Green's R-class: [1,6](5)>,
<Green's R-class: [1,6][7,5]>, <Green's R-class: [1,6,5]>,
<Green's R-class: [3,6][4,5]>, <Green's R-class: [4,5,6]>,
<Green's R-class: [3,5][7,6]>, <Green's R-class: [3,6](5)>,
<Green's R-class: [7,5,6]>, <Green's R-class: [1,6][3,5]>,
<Green's R-class: [1,5,6]>, <Green's R-class: [1,5][7,6]>,
<Green's R-class: [1,5](6)>, <Green's R-class: [3,5][4,6]>,
<Green's R-class: [4,6](5)>, <Green's R-class: [3,6][7,5]>,
<Green's R-class: [3,5,6]>, <Green's R-class: [7,6](5)> ],
[ <Green's R-class: [1,6][2,7]>, <Green's R-class: [2,7][5,6]>,
<Green's R-class: [2,7,6]>, <Green's R-class: [2,7][3,6]> ],
[ <Green's R-class: [2,5,6](1)>, <Green's R-class: [2,5,1][7,6]>,
<Green's R-class: [2,5][3,6](1)>, <Green's R-class: [2,5,1,6]>,
<Green's R-class: [2,5,6][7,1]>, <Green's R-class: [2,5][3,1,6]> ],
[ <Green's R-class: [2,7](1)(5)>, <Green's R-class: [2,7,5,1]>,
<Green's R-class: [2,7][3,5](1)>, <Green's R-class: [2,7](1,5)>,
<Green's R-class: [2,7,1](5)>, <Green's R-class: [2,7][3,1,5]> ],
[ <Green's R-class: [7,1,6,5]> ],
[ <Green's R-class: [2,7][5,1,6]>, <Green's R-class: [2,7,1][5,6]>,
<Green's R-class: [2,7][3,1,6]>, <Green's R-class: [2,7][5,6](1)>,
<Green's R-class: [2,7,6][5,1]>, <Green's R-class: [2,7][3,6](1)> ],
[ <Green's R-class: <identity partial perm on [ 2 ]>> ],
[ <Green's R-class: [6,3][7,5]> ], [ <Green's R-class: [2,5][4,3,7]> ],
[ <Green's R-class: [2,4](1)>, <Green's R-class: [2,4][5,1]>,
<Green's R-class: [2,4][7,1]>, <Green's R-class: [2,4][3,1]> ],
[ <Green's R-class: [2,4][3,5][7,1]> ],
[ <Green's R-class: [2,1,4]>, <Green's R-class: [2,1][5,4]>,
<Green's R-class: [2,1][7,4]>, <Green's R-class: [2,1][3,4]> ],
[ <Green's R-class: [2,7][6,1,4]> ],
[ <Green's R-class: [1,4][3,7]>, <Green's R-class: [1,7][5,4]>,
<Green's R-class: [1,7,4]>, <Green's R-class: [1,7][6,4]>,
<Green's R-class: [3,7](4)>, <Green's R-class: [5,7](4)>,
<Green's R-class: [3,4](7)>, <Green's R-class: [3,7][5,4]>,
<Green's R-class: [5,7,4]>, <Green's R-class: [1,7][3,4]>,
<Green's R-class: [1,4][5,7]>, <Green's R-class: [1,4](7)>,
<Green's R-class: [1,4][6,7]>, <Green's R-class: [3,4,7]>,
<Green's R-class: [5,4,7]>, <Green's R-class: [3,7,4]>,
<Green's R-class: [3,4][5,7]>, <Green's R-class: [5,4](7)> ],
[ <Green's R-class: [2,3,1,4][5,7]> ], [ <Green's R-class: [2,7,4][6,1]> ],
[ <Green's R-class: [1,7,4][2,3]> ],
[ <Green's R-class: [5,4](1)(2)>, <Green's R-class: [5,1][7,4](2)>,
<Green's R-class: [3,4](1)(2)>, <Green's R-class: [5,1,4](2)>,
<Green's R-class: [5,4][7,1](2)>, <Green's R-class: [3,1,4](2)> ],
[ <Green's R-class: [6,4][7,1,5]> ],
[ <Green's R-class: [2,1,3](5)>, <Green's R-class: [2,1][7,5,3]>,
<Green's R-class: [2,1,3,5]>, <Green's R-class: [2,1,5,3]>,
<Green's R-class: [2,1][7,3](5)>, <Green's R-class: [2,1,5](3)> ],
[ <Green's R-class: [2,4][5,1,6]>, <Green's R-class: [2,4][5,6][7,1]>,
<Green's R-class: [2,4][3,1,6]>, <Green's R-class: [2,4][5,6](1)>,
<Green's R-class: [2,4][5,1][7,6]>, <Green's R-class: [2,4][3,6](1)> ],
[ <Green's R-class: [2,4][7,6](1)> ], [ <Green's R-class: [2,6][4,1][5,3]> ]
,
[ <Green's R-class: [1,3,6]>, <Green's R-class: [1,6][5,3]>,
<Green's R-class: [1,6][7,3]>, <Green's R-class: [1,6,3]>,
<Green's R-class: [4,3,6]>, <Green's R-class: [4,3][5,6]>,
<Green's R-class: [7,6](3)>, <Green's R-class: [5,3,6]>,
<Green's R-class: [5,6][7,3]>, <Green's R-class: [1,6](3)>,
<Green's R-class: [1,3][5,6]>, <Green's R-class: [1,3][7,6]>,
<Green's R-class: [1,3](6)>, <Green's R-class: [4,6](3)>,
<Green's R-class: [4,6][5,3]>, <Green's R-class: [7,3,6]>,
<Green's R-class: [5,6](3)>, <Green's R-class: [5,3][7,6]> ],
[ <Green's R-class: [1,6][7,3,5]> ], [ <Green's R-class: [2,4][7,3,5,6]> ],
[ <Green's R-class: [5,1,6](2)>, <Green's R-class: [5,6][7,1](2)>,
<Green's R-class: [3,1,6](2)>, <Green's R-class: [5,6](1)(2)>,
<Green's R-class: [5,1][7,6](2)>, <Green's R-class: [3,6](1)(2)> ],
[ <Green's R-class: [2,1,3][7,6]> ], [ <Green's R-class: [5,3][7,6](1)(2)> ]
, [ <Green's R-class: [2,3,4,1]> ], [ <Green's R-class: [2,6][5,4,1]> ],
[ <Green's R-class: [1,4][2,3][5,6]>, <Green's R-class: [2,3][5,4][7,6]>,
<Green's R-class: [1,4][2,3,6]>, <Green's R-class: [1,6][2,3][5,4]>,
<Green's R-class: [2,3][5,6][7,4]>, <Green's R-class: [1,6][2,3,4]> ],
[ <Green's R-class: [1,4][5,3](2)>, <Green's R-class: [5,4][7,3](2)>,
<Green's R-class: [1,4](2)(3)>, <Green's R-class: [1,3][5,4](2)>,
<Green's R-class: [5,3][7,4](2)>, <Green's R-class: [1,3,4](2)> ],
[ <Green's R-class: [1,6,3][7,4]> ],
[ <Green's R-class: [1,6][5,4](2)>, <Green's R-class: [5,6][7,4](2)>,
<Green's R-class: [1,6][3,4](2)>, <Green's R-class: [1,4][5,6](2)>,
<Green's R-class: [5,4][7,6](2)>, <Green's R-class: [1,4][3,6](2)> ],
[ <Green's R-class: [1,6][2,5]>, <Green's R-class: [2,5,6]>,
<Green's R-class: [2,5][7,6]>, <Green's R-class: [2,5][3,6]> ],
[ <Green's R-class: [7,6,5]> ], [ <Green's R-class: [7,5](6)> ],
[ <Green's R-class: [2,1][3,6][4,5]> ], [ <Green's R-class: [2,5][4,3]> ],
[ <Green's R-class: [1,7][2,5,3]>, <Green's R-class: [2,5,7,3]>,
<Green's R-class: [1,7][2,5](3)>, <Green's R-class: [1,3][2,5,7]>,
<Green's R-class: [2,5,3](7)>, <Green's R-class: [1,3,7][2,5]> ],
[ <Green's R-class: [2,3][6,5]> ], [ <Green's R-class: [2,4][3,1](5)> ],
[ <Green's R-class: [2,7][5,4,1]> ],
[ <Green's R-class: [2,3][5,1,7]>, <Green's R-class: [2,3][5,7,1]>,
<Green's R-class: [2,3,1,7]>, <Green's R-class: [2,3][5,7](1)>,
<Green's R-class: [2,3][5,1](7)>, <Green's R-class: [2,3,7](1)> ],
[ <Green's R-class: [2,1,4](7)> ], [ <Green's R-class: [2,3][5,4](1)(7)> ],
[ <Green's R-class: [2,4,1]> ],
[ <Green's R-class: [1,7][2,4]>, <Green's R-class: [2,4][5,7]>,
<Green's R-class: [2,4](7)>, <Green's R-class: [2,4][3,7]> ],
[ <Green's R-class: [2,4](1,5)>, <Green's R-class: [2,4][7,1](5)>,
<Green's R-class: [2,4][3,1,5]>, <Green's R-class: [2,4](1)(5)>,
<Green's R-class: [2,4][7,5,1]>, <Green's R-class: [2,4][3,5](1)> ],
[ <Green's R-class: [2,1][3,5](4)> ],
[ <Green's R-class: [1,3][2,6]>, <Green's R-class: [2,6][5,3]>,
<Green's R-class: [2,6][7,3]>, <Green's R-class: [2,6](3)> ],
[ <Green's R-class: [2,6][7,3,1]> ],
[ <Green's R-class: [1,6][2,3]>, <Green's R-class: [2,3][5,6]>,
<Green's R-class: [2,3][7,6]>, <Green's R-class: [2,3,6]> ],
[ <Green's R-class: [1,6,3][2,5]> ], [ <Green's R-class: [1,6][2,4](3)(5)> ]
, [ <Green's R-class: [2,5][7,6,3]> ],
[ <Green's R-class: [1,5][2,4][7,6]> ],
[ <Green's R-class: [1,3][5,6](2)>, <Green's R-class: [5,3][7,6](2)>,
<Green's R-class: [1,3,6](2)>, <Green's R-class: [1,6][5,3](2)>,
<Green's R-class: [5,6][7,3](2)>, <Green's R-class: [1,6](2)(3)> ],
[ <Green's R-class: [7,3](1)(6)> ],
[ <Green's R-class: [1,4][2,6]>, <Green's R-class: [2,6][5,4]>,
<Green's R-class: [2,6][7,4]>, <Green's R-class: [2,6][3,4]> ],
[ <Green's R-class: [2,6][3,1][7,4]> ], [ <Green's R-class: [2,4,3,6]> ],
[ <Green's R-class: [1,6][2,4]>, <Green's R-class: [2,4][5,6]>,
<Green's R-class: [2,4][7,6]>, <Green's R-class: [2,4][3,6]> ],
[ <Green's R-class: [7,6,4]> ],
[ <Green's R-class: [1,6](2)>, <Green's R-class: [5,6](2)>,
<Green's R-class: [7,6](2)>, <Green's R-class: [3,6](2)> ],
[ <Green's R-class: [2,6][4,5]> ], [ <Green's R-class: [2,5][4,6]> ],
[ <Green's R-class: [2,4][7,5](1)> ], [ <Green's R-class: [6,1][7,4]> ],
[ <Green's R-class: [1,4][2,7]>, <Green's R-class: [2,7][5,4]>,
<Green's R-class: [2,7,4]>, <Green's R-class: [2,7][3,4]> ],
[ <Green's R-class: [2,7,4][3,1]> ], [ <Green's R-class: [6,4](7)> ],
[ <Green's R-class: [1,4][2,3][5,7]>, <Green's R-class: [2,3][5,4](7)>,
<Green's R-class: [1,4][2,3,7]>, <Green's R-class: [1,7][2,3][5,4]>,
<Green's R-class: [2,3][5,7,4]>, <Green's R-class: [1,7][2,3,4]> ],
[ <Green's R-class: [6,7,4](1)> ],
[ <Green's R-class: [2,3][5,4](1)>, <Green's R-class: [2,3][5,1][7,4]>,
<Green's R-class: [2,3,4](1)>, <Green's R-class: [2,3][5,1,4]>,
<Green's R-class: [2,3][5,4][7,1]>, <Green's R-class: [2,3,1,4]> ],
[ <Green's R-class: [6,4][7,1]> ],
[ <Green's R-class: [1,4](2)>, <Green's R-class: [5,4](2)>,
<Green's R-class: [7,4](2)>, <Green's R-class: [3,4](2)> ],
[ <Green's R-class: [2,1,5,4]>, <Green's R-class: [2,1][7,4](5)>,
<Green's R-class: [2,1,5][3,4]>, <Green's R-class: [2,1,4](5)>,
<Green's R-class: [2,1][7,5,4]>, <Green's R-class: [2,1,4][3,5]> ],
[ <Green's R-class: [2,6][5,1](3)> ], [ <Green's R-class: [2,5,6][4,3]> ],
[ <Green's R-class: [1,5,3][2,4]>, <Green's R-class: [2,4][7,3](5)>,
<Green's R-class: [1,5][2,4](3)>, <Green's R-class: [1,3][2,4](5)>,
<Green's R-class: [2,4][7,5,3]>, <Green's R-class: [1,3,5][2,4]> ],
[ <Green's R-class: [1,6][2,3][7,5]> ],
[ <Green's R-class: [1,3][2,4][7,5,6]> ], [ <Green's R-class: [2,6][4,3]> ],
[ <Green's R-class: [2,6][5,3](1)>, <Green's R-class: [2,6][5,1][7,3]>,
<Green's R-class: [2,6](1)(3)>, <Green's R-class: [2,6][5,1,3]>,
<Green's R-class: [2,6][5,3][7,1]>, <Green's R-class: [2,6](1,3)> ],
[ <Green's R-class: [2,3,1][4,6]> ], [ <Green's R-class: [2,1][6,4]> ],
[ <Green's R-class: [2,6][3,4][5,1]> ],
[ <Green's R-class: [1,4][3,6]>, <Green's R-class: [1,6][5,4]>,
<Green's R-class: [1,6][7,4]>, <Green's R-class: [1,6,4]>,
<Green's R-class: [3,6](4)>, <Green's R-class: [5,6](4)>,
<Green's R-class: [3,4][7,6]>, <Green's R-class: [3,6][5,4]>,
<Green's R-class: [5,6][7,4]>, <Green's R-class: [1,6][3,4]>,
<Green's R-class: [1,4][5,6]>, <Green's R-class: [1,4][7,6]>,
<Green's R-class: [1,4](6)>, <Green's R-class: [3,4,6]>,
<Green's R-class: [5,4,6]>, <Green's R-class: [3,6][7,4]>,
<Green's R-class: [3,4][5,6]>, <Green's R-class: [5,4][7,6]> ],
[ <Green's R-class: [2,6](4)> ], [ <Green's R-class: [2,5](6)> ],
[ <Green's R-class: [2,7][3,4][5,1]> ], [ <Green's R-class: [2,7](4)> ],
[ <Green's R-class: [2,7][5,4](1)>, <Green's R-class: [2,7,4][5,1]>,
<Green's R-class: [2,7][3,4](1)>, <Green's R-class: [2,7][5,1,4]>,
<Green's R-class: [2,7,1][5,4]>, <Green's R-class: [2,7][3,1,4]> ],
[ <Green's R-class: [2,4,7][3,1]> ], [ <Green's R-class: [2,1](4)> ],
[ <Green's R-class: [2,4][6,1]> ], [ <Green's R-class: [2,6][7,1,3]> ],
[ <Green's R-class: [7,6,3]> ], [ <Green's R-class: [2,5][7,6](3)> ],
[ <Green's R-class: [1,6][2,4](5)>, <Green's R-class: [2,4][7,5,6]>,
<Green's R-class: [1,6][2,4][3,5]>, <Green's R-class: [1,5,6][2,4]>,
<Green's R-class: [2,4][7,6](5)>, <Green's R-class: [1,5][2,4][3,6]> ],
[ <Green's R-class: [1,3][7,6,5]> ],
[ <Green's R-class: [1,3][2,4][5,6]>, <Green's R-class: [2,4][5,3][7,6]>,
<Green's R-class: [1,3,6][2,4]>, <Green's R-class: [1,6][2,4][5,3]>,
<Green's R-class: [2,4][5,6][7,3]>, <Green's R-class: [1,6][2,4](3)> ],
[ <Green's R-class: [7,3](6)> ],
[ <Green's R-class: [2,3][5,6](1)>, <Green's R-class: [2,3][5,1][7,6]>,
<Green's R-class: [2,3,6](1)>, <Green's R-class: [2,3][5,1,6]>,
<Green's R-class: [2,3][5,6][7,1]>, <Green's R-class: [2,3,1,6]> ],
[ <Green's R-class: [2,6][5,4](1)>, <Green's R-class: [2,6][5,1][7,4]>,
<Green's R-class: [2,6][3,4](1)>, <Green's R-class: [2,6][5,1,4]>,
<Green's R-class: [2,6][5,4][7,1]>, <Green's R-class: [2,6][3,1,4]> ],
[ <Green's R-class: [2,6][7,1,4]> ], [ <Green's R-class: [2,3](6)> ],
[ <Green's R-class: [2,6,5]> ], [ <Green's R-class: [2,7,1,4]> ],
[ <Green's R-class: [6,7,4]> ],
[ <Green's R-class: [2,4][5,7](1)>, <Green's R-class: [2,4][5,1](7)>,
<Green's R-class: [2,4][3,7](1)>, <Green's R-class: [2,4][5,1,7]>,
<Green's R-class: [2,4][5,7,1]>, <Green's R-class: [2,4][3,1,7]> ],
[ <Green's R-class: [2,4][6,7]> ], [ <Green's R-class: [2,5,3,6]> ],
[ <Green's R-class: [1,3][2,5,6]>, <Green's R-class: [2,5,3][7,6]>,
<Green's R-class: [1,3,6][2,5]>, <Green's R-class: [1,6][2,5,3]>,
<Green's R-class: [2,5,6][7,3]>, <Green's R-class: [1,6][2,5](3)> ],
[ <Green's R-class: [2,6][4,5](3)> ], [ <Green's R-class: [2,3][4,6]> ],
[ <Green's R-class: [2,6,3]> ], [ <Green's R-class: [2,4](6)> ],
[ <Green's R-class: [7,4](6)> ], [ <Green's R-class: [2,4,7]> ],
[ <Green's R-class: [2,7][6,4]> ], [ <Green's R-class: [1,6][2,5][7,3]> ],
[ <Green's R-class: [1,3][2,6](5)>, <Green's R-class: [2,6][7,5,3]>,
<Green's R-class: [1,3,5][2,6]>, <Green's R-class: [1,5,3][2,6]>,
<Green's R-class: [2,6][7,3](5)>, <Green's R-class: [1,5][2,6](3)> ],
[ <Green's R-class: [2,4,6]> ], [ <Green's R-class: [2,6,4]> ] ]
gap> ForAll(Union(List(Union(last), Elements)), x -> x in s);
true
gap> Union(List(last2, Elements));
[ <Green's R-class: [2,7][3,1,5][4,6]>, <Green's R-class: [1,5,3,7](2)>,
<Green's R-class: [2,3,4][6,7,5](1)>, <Green's R-class: [7,5,1,3,4,6](2)>,
<Green's R-class: [3,5]>, <Green's R-class: [2,5,3]>,
<Green's R-class: [2,1,5][3,6]>, <Green's R-class: [2,7][3,6](1)(5)>,
<Green's R-class: [1,3,5]>, <Green's R-class: [1,3][5,7](2)>,
<Green's R-class: [1,5][2,7,3]>, <Green's R-class: [1,7,3](2)(5)>,
<Green's R-class: [2,5][3,1][4,7]>, <Green's R-class: [2,3,5,4]>,
<Green's R-class: [2,4][6,5](1)>, <Green's R-class: [2,3][5,1,4,7]>,
<Green's R-class: [2,5](1)(3)>, <Green's R-class: [3,5,4](1)(2)>,
<Green's R-class: [2,4][7,1,3,6,5]>, <Green's R-class: [5,3,6][7,1,4](2)>,
<Green's R-class: <empty partial perm>>,
<Green's R-class: <identity partial perm on [ 5 ]>>,
<Green's R-class: [2,5]>, <Green's R-class: [1,5]>,
<Green's R-class: [1,3][2,5]>, <Green's R-class: [7,5]>,
<Green's R-class: [2,5][7,3]>, <Green's R-class: [1,5][2,6]>,
<Green's R-class: [2,1,6](5)>, <Green's R-class: [1,5,6][2,7]>,
<Green's R-class: [2,6][7,5](1)>, <Green's R-class: [2,7,5,1,6]>,
<Green's R-class: [1,5,3]>, <Green's R-class: [1,7](2)>,
<Green's R-class: [1,5][7,3]>, <Green's R-class: [5,3](2)(7)>,
<Green's R-class: [2,5](3)>, <Green's R-class: [1,5][6,3]>,
<Green's R-class: [1,5][2,3,7]>, <Green's R-class: [1,5](2)(3)>,
<Green's R-class: [1,7,5][6,3]>, <Green's R-class: (2)(5,7)>,
<Green's R-class: [2,5][3,7](1)>, <Green's R-class: [1,4][2,3](5)>,
<Green's R-class: [1,5][2,3][7,4]>, <Green's R-class: [4,3,5]>,
<Green's R-class: [2,4,5,1]>, <Green's R-class: [3,4](1)>,
<Green's R-class: [3,7,1,4]>, <Green's R-class: [2,3,7,1][5,4]>,
<Green's R-class: [2,5,1,3]>, <Green's R-class: [3,1,4]>,
<Green's R-class: [1,4](2)(5)>, <Green's R-class: [2,5][7,4](1)>,
<Green's R-class: [7,4](1,5)(2)>, <Green's R-class: [2,1][4,5](3)>,
<Green's R-class: [2,4][3,1][5,6]>, <Green's R-class: [2,6,1,3]>,
<Green's R-class: [1,6][2,4,5,3]>, <Green's R-class: [2,1,3,4]>,
<Green's R-class: [5,6](1,3)(2)>, <Green's R-class: [2,6,1,4][7,3]>,
<Green's R-class: [1,6][5,4][7,3](2)>, <Green's R-class: [6,5]>,
<Green's R-class: [2,6](5)>, <Green's R-class: [1,5][3,6]>,
<Green's R-class: [1,6][7,5]>, <Green's R-class: [2,1][7,5,6]>,
<Green's R-class: [1,6][3,5]>, <Green's R-class: [1,6][2,7]>,
<Green's R-class: [1,5][7,6]>, <Green's R-class: [2,7,6](5)>,
<Green's R-class: [2,6][3,5]>, <Green's R-class: [2,5][3,6](1)>,
<Green's R-class: [2,7][3,5](1)>, <Green's R-class: [7,1,6,5]>,
<Green's R-class: [2,7,1][5,6]>, <Green's R-class: [7,3](5)>,
<Green's R-class: <identity partial perm on [ 2 ]>>,
<Green's R-class: [5,7](2)>, <Green's R-class: [1,3,7](2)>,
<Green's R-class: [6,3][7,5]>,
<Green's R-class: <identity partial perm on [ 2, 7 ]>>,
<Green's R-class: [4,3](5)>, <Green's R-class: [1,7][2,3](5)>,
<Green's R-class: [1,3](2)(5)>, <Green's R-class: [2,5][4,3,7]>,
<Green's R-class: [1,7][3,5](2)>, <Green's R-class: [2,5,1,7]>,
<Green's R-class: [2,3][7,5,4]>, <Green's R-class: [2,4](1)>,
<Green's R-class: [7,5](3)>, <Green's R-class: [2,4][3,5][7,1]>,
<Green's R-class: [5,1,4]>, <Green's R-class: [2,1][3,4]>,
<Green's R-class: (3,5)>, <Green's R-class: [2,7][6,1,4]>,
<Green's R-class: [1,7][5,4]>, <Green's R-class: [2,1,4]>,
<Green's R-class: [2,3,1,4][5,7]>, <Green's R-class: [2,7,4][6,1]>,
<Green's R-class: [1,7,4][2,3]>, <Green's R-class: [2,5,3][7,1]>,
<Green's R-class: [5,4](1)>, <Green's R-class: [7,5,4](2)>,
<Green's R-class: [2,4][3,1]>, <Green's R-class: [6,4](1)>,
<Green's R-class: [2,4][3,5](1)>, <Green's R-class: [3,4](1)(2)>,
<Green's R-class: [6,4][7,1,5]>, <Green's R-class: [2,1,3,5]>,
<Green's R-class: [2,4][5,1,6]>, <Green's R-class: [2,4][7,6](1)>,
<Green's R-class: [2,6][4,1][5,3]>, <Green's R-class: [1,3,6]>,
<Green's R-class: [1,6][7,3,5]>, <Green's R-class: [2,4][7,3,5,6]>,
<Green's R-class: [2,1][5,4]>, <Green's R-class: [2,1,4][5,3]>,
<Green's R-class: [1,6](3)>, <Green's R-class: [5,1,6](2)>,
<Green's R-class: [2,1,3][7,6]>, <Green's R-class: [5,3][7,6](1)(2)>,
<Green's R-class: [2,3,4,1]>, <Green's R-class: [2,6](3)>,
<Green's R-class: [2,6][5,4,1]>, <Green's R-class: [1,4][2,3,6]>,
<Green's R-class: [1,4](2)(3)>, <Green's R-class: [1,6,3][7,4]>,
<Green's R-class: [5,6][7,4](2)>, <Green's R-class: [4,5]>,
<Green's R-class: [2,6][7,5]>, <Green's R-class: [1,6](5)>,
<Green's R-class: [2,5][3,6]>, <Green's R-class: [1,6,5]>,
<Green's R-class: [1,6][2,5]>, <Green's R-class: [2,1,6][3,5]>,
<Green's R-class: [7,6,5]>, <Green's R-class: [1,5,6]>,
<Green's R-class: [2,7][5,6]>, <Green's R-class: [1,5](6)>,
<Green's R-class: [1,5][2,7][3,6]>, <Green's R-class: [7,5](6)>,
<Green's R-class: [2,5,6]>, <Green's R-class: [2,5,1,6]>,
<Green's R-class: [2,7](1,5)>, <Green's R-class: [2,1][3,6][4,5]>,
<Green's R-class: [4,5,6]>, <Green's R-class: [2,7][3,1,6]>,
<Green's R-class: [2,7,6]>, <Green's R-class: [1,7][5,3](2)>,
<Green's R-class: [2,5][4,3]>, <Green's R-class: [3,7](2)>,
<Green's R-class: [2,3](5,7)>, <Green's R-class: [7,5,3](2)>,
<Green's R-class: [1,7][2,5](3)>, <Green's R-class: [1,7](2)(5)>,
<Green's R-class: [2,5,7,1]>, <Green's R-class: [1,4][2,3,5]>,
<Green's R-class: [2,4][5,1]>, <Green's R-class: [2,3][6,5]>,
<Green's R-class: [2,4][3,1](5)>, <Green's R-class: [7,1,4]>,
<Green's R-class: [5,4][7,1]>, <Green's R-class: [3,4,1]>,
<Green's R-class: [2,7][5,4,1]>, <Green's R-class: [1,4][3,7]>,
<Green's R-class: [1,7,4]>, <Green's R-class: [5,7,4]>,
<Green's R-class: [1,7][3,4]>, <Green's R-class: [2,3][5,1,7]>,
<Green's R-class: [2,1,4](7)>, <Green's R-class: [2,3][5,4](1)(7)>,
<Green's R-class: [2,4,1]>, <Green's R-class: [2,7][3,4]>,
<Green's R-class: [2,4][3,7]>, <Green's R-class: [1,7][6,4]>,
<Green's R-class: [2,5](1,3)>, <Green's R-class: [7,4](1)>,
<Green's R-class: [5,1][7,4]>, <Green's R-class: [1,4][3,5](2)>,
<Green's R-class: [7,4](2)>, <Green's R-class: [3,1](4)>,
<Green's R-class: [5,1](4)>, <Green's R-class: [2,4](1,5)>,
<Green's R-class: [5,4](2)>, <Green's R-class: [5,1,4](2)>,
<Green's R-class: [2,1][3,5](4)>, <Green's R-class: [2,1,5,3]>,
<Green's R-class: [2,4][5,6][7,1]>, <Green's R-class: [2,4][3,6]>,
<Green's R-class: [1,3][2,6]>, <Green's R-class: [2,6][7,3,1]>,
<Green's R-class: [1,6][5,3]>, <Green's R-class: [2,3,6]>,
<Green's R-class: [1,6,3][2,5]>, <Green's R-class: [1,6][2,3]>,
<Green's R-class: [1,6][2,4](3)(5)>, <Green's R-class: [2,5][7,6,3]>,
<Green's R-class: [1,5][2,4][7,6]>, <Green's R-class: [2,1][7,4]>,
<Green's R-class: [2,1][5,4][7,3]>, <Green's R-class: [1,3][5,6]>,
<Green's R-class: [5,6][7,1](2)>, <Green's R-class: [1,3](6)>,
<Green's R-class: [2,6](1,3)>, <Green's R-class: [1,3,6](2)>,
<Green's R-class: [7,3](1)(6)>, <Green's R-class: [2,3,1,4]>,
<Green's R-class: [2,6][5,3]>, <Green's R-class: [1,4][2,6]>,
<Green's R-class: [3,1][7,4]>, <Green's R-class: [2,6][3,1][7,4]>,
<Green's R-class: [2,3][5,6]>, <Green's R-class: [1,6][2,3][5,4]>,
<Green's R-class: [1,3][5,4](2)>, <Green's R-class: [2,4,3,6]>,
<Green's R-class: [1,6,4]>, <Green's R-class: [4,3][5,6]>,
<Green's R-class: [1,6][2,4]>, <Green's R-class: [1,6][3,4](2)>,
<Green's R-class: [7,6,4]>, <Green's R-class: [7,6](2)>,
<Green's R-class: [7,5,6]>, <Green's R-class: [3,6][4,5]>,
<Green's R-class: [2,1,5,6]>, <Green's R-class: [2,6][4,5]>,
<Green's R-class: [7,6](5)>, <Green's R-class: [3,5][4,6]>,
<Green's R-class: [4,6](5)>, <Green's R-class: [1,6][2,7](5)>,
<Green's R-class: [2,5][4,6]>, <Green's R-class: [2,5][7,6]>,
<Green's R-class: [2,5,6][7,1]>, <Green's R-class: [2,7,1](5)>,
<Green's R-class: [3,5][7,6]>, <Green's R-class: [2,7][5,6](1)>,
<Green's R-class: [2,7][3,6]>, <Green's R-class: [5,7,3](2)>,
<Green's R-class: [1,7][2,3,5]>, <Green's R-class: [1,3,5](2)>,
<Green's R-class: [1,3][2,5,7]>, <Green's R-class: [2,5][3,1,7]>,
<Green's R-class: [1,5,4][2,3]>, <Green's R-class: [2,4][7,1]>,
<Green's R-class: [2,4][7,5](1)>, <Green's R-class: [6,1,4]>,
<Green's R-class: [6,1][7,4]>, <Green's R-class: [1,4][2,7]>,
<Green's R-class: [2,7,4][3,1]>, <Green's R-class: [1,7][2,4]>,
--> --------------------
--> maximum size reached
--> --------------------
[ Dauer der Verarbeitung: 0.32 Sekunden
(vorverarbeitet)
]
|
