1############################################################################## 2## 3#W gpdaut.tst groupoids Package Chris Wensley 4## 5#Y Copyright (C) 2000-2019, Chris Wensley, 6#Y School of Computer Science, Bangor University, U.K. 7## 8gap> START_TEST( "groupoids package: gpdaut.tst" ); 9gap> gpd_infolevel_saved := InfoLevel( InfoGroupoids );; 10gap> SetInfoLevel( InfoGroupoids, 0 );; 11 12## make gpdaut.tst independent of other tests 13gap> s4 := Group( (1,2,3,4), (3,4) );; 14gap> d8 := Subgroup( s4, [ (1,2,3,4), (1,3) ] );; 15gap> SetName( s4, "s4" ); SetName( d8, "d8" ); 16gap> Gs4 := SinglePieceGroupoid( s4, [-15 .. -11] );; 17gap> Gd8 := Groupoid( d8, [-9,-8,-7] );; 18gap> Hs4 := SubgroupoidByObjects( Gs4, [-14,-13,-12] );; 19gap> SetName( Hs4, "Hs4" ); 20gap> Hd8b := SubgroupoidWithRays( Hs4, d8, [(),(1,2,3),(1,2,4)] );; 21gap> SetName( Hd8b, "Hd8b" ); 22gap> gend12 := [ (15,16,17,18,19,20), (15,20)(16,19)(17,18) ];; 23gap> d12 := Group( gend12 );; 24gap> Gd12 := Groupoid( d12, [-37,-36,-35,-34] );; 25gap> SetName( d12, "d12" ); 26gap> SetName( Gd12, "Gd12" ); 27gap> s3 := Subgroup( d12, [ (15,17,19)(16,18,20), (15,20)(16,19)(17,18) ] );; 28gap> Gs3 := SubgroupoidByPieces( Gd12, [ [ s3, [-36,-35,-34] ] ] );; 29gap> SetName( s3, "s3" ); 30gap> SetName( Gs3, "Gs3" ); 31 32## Section 5.6, Groupoid automorphisms 33 34## SubSection 5.6.1 35gap> a4 := Subgroup( s4, [(1,2,3),(2,3,4)] );; 36gap> SetName( a4, "a4" ); 37gap> gensa4 := GeneratorsOfGroup( a4 );; 38gap> Ga4 := SubgroupoidByPieces( Gs4, [ [a4, [-15,-13,-11]] ] ); 39single piece groupoid: < a4, [ -15, -13, -11 ] > 40gap> SetName( Ga4, "Ga4" ); 41gap> d := Arrow( Ga4, (1,3,4), -11, -13 ); 42[(1,3,4) : -11 -> -13] 43gap> aut1 := GroupoidAutomorphismByObjectPerm( Ga4, [-13,-11,-15] );; 44gap> Display( aut1 ); 45 groupoid mapping: [ Ga4 ] -> [ Ga4 ] 46root homomorphism: [ [ (1,2,3), (2,3,4) ], [ (1,2,3), (2,3,4) ] ] 47images of objects: [ -13, -11, -15 ] 48 images of rays: [ [() : -13 -> -13], [() : -13 -> -11], [() : -13 -> -15] ] 49gap> d1 := ImageElm( aut1, d ); 50[(1,3,4) : -15 -> -11] 51gap> h2 := GroupHomomorphismByImages( a4, a4, gensa4, [(2,3,4), (1,3,4)] );; 52gap> aut2 := GroupoidAutomorphismByGroupAuto( Ga4, h2 );; 53gap> Display( aut2 ); 54 groupoid mapping: [ Ga4 ] -> [ Ga4 ] 55root homomorphism: [ [ (1,2,3), (2,3,4) ], [ (2,3,4), (1,3,4) ] ] 56images of objects: [ -15, -13, -11 ] 57 images of rays: [ [() : -15 -> -15], [() : -15 -> -13], [() : -15 -> -11] ] 58gap> d2 := ImageElm( aut2, d1 ); 59[(1,2,4) : -15 -> -11] 60gap> im3 := [(), (1,3,2), (2,4,3)];; 61gap> aut3 := GroupoidAutomorphismByRayShifts( Ga4, im3 );; 62gap> Display( aut3 ); 63 groupoid mapping: [ Ga4 ] -> [ Ga4 ] 64root homomorphism: [ [ (1,2,3), (2,3,4) ], [ (1,2,3), (2,3,4) ] ] 65images of objects: [ -15, -13, -11 ] 66 images of rays: [ [() : -15 -> -15], [(1,3,2) : -15 -> -13], 67 [(2,4,3) : -15 -> -11] ] 68gap> d3 := ImageElm( aut3, d2 ); 69[(1,4)(2,3) : -15 -> -11] 70gap> d0 := Arrow( Ga4, (2,3,4), -11, -13 );; 71gap> aut4 := GroupoidInnerAutomorphism( Ga4, d0 );; 72gap> Display( aut4 ); 73 groupoid mapping: [ Ga4 ] -> [ Ga4 ] 74root homomorphism: [ [ (1,2,3), (2,3,4) ], [ (1,2,3), (2,3,4) ] ] 75images of objects: [ -15, -11, -13 ] 76 images of rays: [ [() : -15 -> -15], [(2,4,3) : -15 -> -11], 77 [(2,3,4) : -15 -> -13] ] 78gap> d4 := ImageElm( aut4, d3 ); 79[(1,2,4) : -15 -> -13] 80gap> aut1234 := aut1*aut2*aut3*aut4;; 81gap> Display( aut1234 ); 82 groupoid mapping: [ Ga4 ] -> [ Ga4 ] 83root homomorphism: [ [ (1,2,3), (2,3,4) ], [ (1,4,3), (2,4,3) ] ] 84images of objects: [ -11, -13, -15 ] 85 images of rays: [ [() : -11 -> -11], [(1,2)(3,4) : -11 -> -13], 86 [(1,2)(3,4) : -11 -> -15] ] 87gap> d4 = ImageElm( aut1234, d ); 88true 89gap> inv1234 := InverseGeneralMapping( aut1234 );; 90gap> Display( inv1234 ); 91 groupoid mapping: [ Ga4 ] -> [ Ga4 ] 92root homomorphism: [ [ (1,2,3), (2,3,4) ], [ (1,2,4), (1,2,3) ] ] 93images of objects: [ -11, -13, -15 ] 94 images of rays: [ [() : -11 -> -11], [() : -11 -> -13], 95 [(1,4)(2,3) : -11 -> -15] ] 96 97# Subsection 5.6.2 98gap> s4c := Group( (1,2,3,4), (3,4) );; 99gap> SetName( s4c, "s4c" ); 100gap> s3c := Subgroup( s4c, [ (1,2), (2,3) ] );; 101gap> SetName( s3c, "s3c" ); 102gap> Gs4c := SinglePieceGroupoid( s4c, [-9,-8,-7,-6] );; 103gap> SetName( Gs4c, "Gs4c" ); 104gap> Hs3c := SubgroupoidWithRays( Gs4c, s3c, [ (), (1,4), (2,4), (3,4) ] );; 105gap> SetName( Hs3c, "Hs3c" ); 106gap> ## (1) automorphism by group auto 107gap> a1 := GroupHomomorphismByImages( s3c, s3c, [(1,2),(2,3)], [(1,3),(2,3)] );; 108gap> aut1 := GroupoidAutomorphismByGroupAuto( Hs3c, a1 ); 109groupoid homomorphism : Hs3c -> Hs3c 110[ [ [(1,2) : -9 -> -9], [(2,3) : -9 -> -9], [(1,4) : -9 -> -8], 111 [(2,4) : -9 -> -7], [(3,4) : -9 -> -6] ], 112 [ [(1,3) : -9 -> -9], [(2,3) : -9 -> -9], [(1,4) : -9 -> -8], 113 [(2,4) : -9 -> -7], [(3,4) : -9 -> -6] ] ] 114gap> a := Arrow( Hs3c, (2,3,4), -8, -8 ); 115[(2,3,4) : -8 -> -8] 116gap> ImageElm( aut1, a ); 117[(2,4,3) : -8 -> -8] 118gap> b := Arrow( Hs3c, (1,2,3,4), -7, -6 ); 119[(1,2,3,4) : -7 -> -6] 120gap> ## b = (2,4)(1,2)(3,4) -> (2,4)(1,3)(3,4) 121gap> ImageElm( aut1, b ); 122[(1,4,2,3) : -7 -> -6] 123gap> ## (2) automorphism by object perm 124gap> aut2 := GroupoidAutomorphismByObjectPerm( Hs3c, [-8,-7,-6,-9] ); 125groupoid homomorphism : Hs3c -> Hs3c 126[ [ [(1,2) : -9 -> -9], [(2,3) : -9 -> -9], [(1,4) : -9 -> -8], 127 [(2,4) : -9 -> -7], [(3,4) : -9 -> -6] ], 128 [ [(2,4) : -8 -> -8], [(2,3) : -8 -> -8], [(1,2,4) : -8 -> -7], 129 [(1,3,4) : -8 -> -6], [(1,4) : -8 -> -9] ] ] 130gap> ImageElm( aut2, a ); 131[(1,4,3) : -7 -> -7] 132gap> ImageElm( aut2, b ); 133[(1,2)(3,4) : -6 -> -9] 134gap> ## (3) automorphism by ray shifts 135gap> aut3 := GroupoidAutomorphismByRayShifts( Hs3c, [(),(2,3),(1,3),(1,2)] ); 136groupoid homomorphism : Hs3c -> Hs3c 137[ [ [(1,2) : -9 -> -9], [(2,3) : -9 -> -9], [(1,4) : -9 -> -8], 138 [(2,4) : -9 -> -7], [(3,4) : -9 -> -6] ], 139 [ [(1,2) : -9 -> -9], [(2,3) : -9 -> -9], [(1,4)(2,3) : -9 -> -8], 140 [(1,3)(2,4) : -9 -> -7], [(1,2)(3,4) : -9 -> -6] ] ] 141gap> ImageElm( aut3, a ); 142[(2,4,3) : -8 -> -8] 143gap> ImageElm( aut3, b ); 144[(1,4,2,3) : -7 -> -6] 145gap> ## (4) combine these three automorphisms 146gap> aut := aut1 * aut2 * aut3; 147groupoid homomorphism : Hs3c -> Hs3c 148[ [ [(1,2) : -9 -> -9], [(2,3) : -9 -> -9], [(1,4) : -9 -> -8], 149 [(2,4) : -9 -> -7], [(3,4) : -9 -> -6] ], 150 [ [(2,4) : -8 -> -8], [(2,3) : -8 -> -8], [(1,2)(3,4) : -8 -> -7], 151 [(1,3)(2,4) : -8 -> -6], [(1,4)(2,3) : -8 -> -9] ] ] 152gap> ImageElm( aut, a ); 153[(1,4,3) : -7 -> -7] 154gap> ImageElm( aut, b ); 155[(1,2,3,4) : -6 -> -9] 156gap> e86 := Arrow( Hs3c, (1,3,2,4), -8, -6 );; 157gap> aut86 := GroupoidInnerAutomorphism( Hs3c, e86 ); 158groupoid homomorphism : Hs3c -> Hs3c 159[ [ [(1,2) : -9 -> -9], [(2,3) : -9 -> -9], [(1,4) : -9 -> -8], 160 [(2,4) : -9 -> -7], [(3,4) : -9 -> -6] ], 161 [ [(1,2) : -9 -> -9], [(2,3) : -9 -> -9], [(2,4,3) : -9 -> -6], 162 [(2,4) : -9 -> -7], [(1,4)(2,3) : -9 -> -8] ] ] 163 164# Subsection 5.6.3 165gap> AGa4 := AutomorphismGroupOfGroupoid( Ga4 ); 166Aut(Ga4) 167gap> Length( GeneratorsOfGroup( AGa4 ) ); 1688 169gap> AGgens := GeneratorsOfGroup( AGa4);; 170gap> NGa4 := NiceObject( AGa4 );; 171gap> MGa4 := NiceMonomorphism( AGa4 );; 172gap> Size( AGa4 ); 17320736 174gap> SetName( AGa4, "AGa4" ); 175gap> SetName( NGa4, "NGa4" ); 176gap> ## cannot test images of AGgens because of random variations 177gap> ## Now do some tests! 178gap> mgi := MappingGeneratorsImages( MGa4 );; 179gap> autgen := mgi[1];; 180gap> pcgen := mgi[2];; 181gap> ngen := Length( autgen );; 182gap> ForAll( [1..ngen], i -> Order(autgen[i]) = Order(pcgen[i]) ); 183true 184 185## SubSection 5.6.4 186gap> AGa40 := Groupoid( AGa4, [0] ); 187single piece groupoid: < Aut(Ga4), [ 0 ] > 188gap> conj := function(a) 189> return ArrowNC( true, GroupoidInnerAutomorphism(Ga4,a), 0, 0 ); 190> end;; 191gap> inner := MappingWithObjectsByFunction( Ga4, AGa40, conj, [0,0,0] );; 192gap> a1 := Arrow( Ga4, (1,2,3), -15, -13 );; 193gap> inn1 := ImageElm( inner, a1 );; 194gap> a2 := Arrow( Ga4, (2,3,4), -13, -11 );; 195gap> inn2 := ImageElm( inner, a2 );; 196gap> a3 := a1*a2; 197[(1,3)(2,4) : -15 -> -11] 198gap> inn3 := ImageElm( inner, a3 ); 199[groupoid homomorphism : Ga4 -> Ga4 200[ [ [(1,2,3) : -15 -> -15], [(2,3,4) : -15 -> -15], [() : -15 -> -13], 201 [() : -15 -> -11] ], 202 [ [(1,3,4) : -11 -> -11], [(1,2,4) : -11 -> -11], [(1,3)(2,4) : -11 -> -13], 203 [() : -11 -> -15] ] ] : 0 -> 0] 204gap> (inn3 = inn1*inn2*inn1) and (inn3 = inn2*inn1*inn2); 205true 206 207## SubSection 5.6.5 208gap> Hs3 := HomogeneousDiscreteGroupoid( s3, [ -13..-10] ); 209homogeneous, discrete groupoid: < s3, [ -13 .. -10 ] > 210gap> aut4 := GroupoidAutomorphismByObjectPerm( Hs3, [-12,-10,-11,-13] ); 211groupoid homomorphism : morphism from a homogeneous discrete groupoid: 212[ -13, -12, -11, -10 ] -> [ -12, -10, -11, -13 ] 213object homomorphisms: 214IdentityMapping( s3 ) 215IdentityMapping( s3 ) 216IdentityMapping( s3 ) 217IdentityMapping( s3 ) 218 219gap> gens3 := GeneratorsOfGroup( s3 );; 220gap> g1 := gens3[1];; 221gap> g2 := gens3[2];; 222gap> b1 := GroupHomomorphismByImages( s3, s3, gens3, [g1, g2^g1 ] );; 223gap> b2 := GroupHomomorphismByImages( s3, s3, gens3, [g1^g2, g2 ] );; 224gap> b3 := GroupHomomorphismByImages( s3, s3, gens3, [g1^g2, g2^(g1*g2) ] );; 225gap> b4 := GroupHomomorphismByImages( s3, s3, gens3, [g1^(g2*g1), g2^g1 ] );; 226gap> aut5 := GroupoidAutomorphismByGroupAutos( Hs3, [b1,b2,b3,b4] ); 227groupoid homomorphism : morphism from a homogeneous discrete groupoid: 228[ -13, -12, -11, -10 ] -> [ -13, -12, -11, -10 ] 229object homomorphisms: 230GroupHomomorphismByImages( s3, s3, 231[ (15,17,19)(16,18,20), (15,20)(16,19)(17,18) ], 232[ (15,17,19)(16,18,20), (15,18)(16,17)(19,20) ] ) 233GroupHomomorphismByImages( s3, s3, 234[ (15,17,19)(16,18,20), (15,20)(16,19)(17,18) ], 235[ (15,19,17)(16,20,18), (15,20)(16,19)(17,18) ] ) 236GroupHomomorphismByImages( s3, s3, 237[ (15,17,19)(16,18,20), (15,20)(16,19)(17,18) ], 238[ (15,19,17)(16,20,18), (15,16)(17,20)(18,19) ] ) 239GroupHomomorphismByImages( s3, s3, 240[ (15,17,19)(16,18,20), (15,20)(16,19)(17,18) ], 241[ (15,19,17)(16,20,18), (15,18)(16,17)(19,20) ] ) 242 243gap> AHs3 := AutomorphismGroupOfGroupoid( Hs3 ); 244<group with 4 generators> 245gap> Size( AHs3 ); 24631104 247gap> genAHs3 := GeneratorsOfGroup( AHs3 ); 248[ groupoid homomorphism : morphism from a homogeneous discrete groupoid: 249 [ -13, -12, -11, -10 ] -> [ -13, -12, -11, -10 ] 250 object homomorphisms: 251 ConjugatorAutomorphism( s3, (15,19,17)(16,20,18) ) 252 IdentityMapping( s3 ) 253 IdentityMapping( s3 ) 254 IdentityMapping( s3 ) 255 , groupoid homomorphism : morphism from a homogeneous discrete groupoid: 256 [ -13, -12, -11, -10 ] -> [ -13, -12, -11, -10 ] 257 object homomorphisms: 258 ConjugatorAutomorphism( s3, (15,20)(16,19)(17,18) ) 259 IdentityMapping( s3 ) 260 IdentityMapping( s3 ) 261 IdentityMapping( s3 ) 262 , groupoid homomorphism : morphism from a homogeneous discrete groupoid: 263 [ -13, -12, -11, -10 ] -> [ -12, -11, -10, -13 ] 264 object homomorphisms: 265 IdentityMapping( s3 ) 266 IdentityMapping( s3 ) 267 IdentityMapping( s3 ) 268 IdentityMapping( s3 ) 269 , groupoid homomorphism : morphism from a homogeneous discrete groupoid: 270 [ -13, -12, -11, -10 ] -> [ -12, -13, -11, -10 ] 271 object homomorphisms: 272 IdentityMapping( s3 ) 273 IdentityMapping( s3 ) 274 IdentityMapping( s3 ) 275 IdentityMapping( s3 ) 276 ] 277gap> nobAHs3 := NiceObject( AHs3 );; 278gap> nmonAHs3 := NiceMonomorphism( AHs3 );; 279gap> w := genAHs3[1];; 280gap> w1 := ImageElm( nmonAHs3, w );; 281gap> x := genAHs3[2];; 282gap> x1 := ImageElm( nmonAHs3, x );; 283gap> y := genAHs3[3];; 284gap> y1 := ImageElm( nmonAHs3, y );; 285gap> z := genAHs3[4];; 286gap> z1 := ImageElm( nmonAHs3, z );; 287gap> u := z*w*y*x*z; 288groupoid homomorphism : morphism from a homogeneous discrete groupoid: 289[ -13, -12, -11, -10 ] -> [ -11, -13, -10, -12 ] 290object homomorphisms: 291IdentityMapping( s3 ) 292ConjugatorAutomorphism( s3, (15,19,17)(16,20,18) ) 293IdentityMapping( s3 ) 294ConjugatorAutomorphism( s3, (15,20)(16,19)(17,18) ) 295 296gap> u1 := z1*w1*y1*x1*z1; 297(1,2,4,3)(5,17,23,16,8,20,26,13)(6,18,24,15,7,19,25,14)(9,21,27,12,10,22,28, 29811) 299gap> imu := ImageElm( nmonAHs3, u );; 300gap> u1 = imu; 301true 302 303## SubSection 5.6.5 304gap> Hd8 := HomogeneousGroupoid( Gd8, 305> [ [-20,-19,-18], [-12,-11,-10], [-16,-15,-14] ] );; 306gap> SetName( Hd8, "Hd8" ); 307gap> AHd8 := AutomorphismGroupoidOfGroupoid( Hd8 ); 308Aut(Hd8) 309gap> ObjectList( AHd8 ); 310[ [ -20, -19, -18 ], [ -16, -15, -14 ], [ -12, -11, -10 ] ] 311gap> RaysOfGroupoid( AHd8 ){[2..3]}; 312[ groupoid homomorphism : 313 [ [ [(1,2,3,4) : -20 -> -20], [(1,3) : -20 -> -20], [() : -20 -> -19], 314 [() : -20 -> -18] ], 315 [ [(1,2,3,4) : -16 -> -16], [(1,3) : -16 -> -16], [() : -16 -> -15], 316 [() : -16 -> -14] ] ], groupoid homomorphism : 317 [ [ [(1,2,3,4) : -20 -> -20], [(1,3) : -20 -> -20], [() : -20 -> -19], 318 [() : -20 -> -18] ], 319 [ [(1,2,3,4) : -12 -> -12], [(1,3) : -12 -> -12], [() : -12 -> -11], 320 [() : -12 -> -10] ] ] ] 321gap> ObjectGroup( AHd8, [ -12, -11, -10 ] ); 322<group with 8 generators> 323 324## Section 5.7 325gap> reps := IrreducibleRepresentations( s4 );; 326gap> rep4 := reps[4];; 327gap> Rs4 := Groupoid( Image( rep4 ), Gs4!.objects ); 328single piece groupoid: < Group([ [ [ 0, 1, 0 ], [ 1, 0, 0 ], [ 0, 0, 1 ] ], 329 [ [ 0, 0, 1 ], [ 1, 0, 0 ], [ 0, 1, 0 ] ], 330 [ [ -1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, -1 ] ], 331 [ [ 1, 0, 0 ], [ 0, -1, 0 ], [ 0, 0, -1 ] ] ]), [ -15, -14, -13, -12, -11 332 ] > 333gap> gens := GeneratorsOfGroupoid( Gs4 ); 334[ [(1,2,3,4) : -15 -> -15], [(3,4) : -15 -> -15], [() : -15 -> -14], 335 [() : -15 -> -13], [() : -15 -> -12], [() : -15 -> -11] ] 336gap> images := List( gens, 337> g -> Arrow( Rs4, ImageElm(rep4,g![1]), g![2], g![3] ) ); 338[ [[ [ -1, 0, 0 ], [ 0, 0, 1 ], [ 0, -1, 0 ] ] : -15 -> -15], 339 [[ [ 0, 1, 0 ], [ 1, 0, 0 ], [ 0, 0, 1 ] ] : -15 -> -15], 340 [[ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] : -15 -> -14], 341 [[ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] : -15 -> -13], 342 [[ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] : -15 -> -12], 343 [[ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] : -15 -> -11] ] 344gap> mor := GroupoidHomomorphismFromSinglePiece( Gs4, Rs4, gens, images ); 345groupoid homomorphism : 346[ [ [(1,2,3,4) : -15 -> -15], [(3,4) : -15 -> -15], [() : -15 -> -14], 347 [() : -15 -> -13], [() : -15 -> -12], [() : -15 -> -11] ], 348 [ [[ [ -1, 0, 0 ], [ 0, 0, 1 ], [ 0, -1, 0 ] ] : -15 -> -15], 349 [[ [ 0, 1, 0 ], [ 1, 0, 0 ], [ 0, 0, 1 ] ] : -15 -> -15], 350 [[ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] : -15 -> -14], 351 [[ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] : -15 -> -13], 352 [[ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] : -15 -> -12], 353 [[ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] : -15 -> -11] ] ] 354gap> IsMatrixGroupoid( Rs4 ); 355true 356gap> a := Arrow( Hs4, (1,4,2), -12, -13 ); 357[(1,4,2) : -12 -> -13] 358gap> ImageElm( mor, a ); 359[[ [ 0, 0, -1 ], [ -1, 0, 0 ], [ 0, 1, 0 ] ] : -12 -> -13] 360gap> rmor := RestrictedMappingGroupoids( mor, Hd8b ); 361groupoid homomorphism : 362[ [ [(1,2,3,4) : -14 -> -14], [(1,3) : -14 -> -14], [(1,2,3) : -14 -> -13], 363 [(1,2,4) : -14 -> -12] ], 364 [ [[ [ -1, 0, 0 ], [ 0, 0, 1 ], [ 0, -1, 0 ] ] : -14 -> -14], 365 [[ [ 1, 0, 0 ], [ 0, 0, -1 ], [ 0, -1, 0 ] ] : -14 -> -14], 366 [[ [ 0, 0, 1 ], [ -1, 0, 0 ], [ 0, -1, 0 ] ] : -14 -> -13], 367 [[ [ 0, -1, 0 ], [ 0, 0, 1 ], [ -1, 0, 0 ] ] : -14 -> -12] ] ] 368gap> # 369gap> SetInfoLevel( InfoGroupoids, gpd_infolevel_saved );; 370gap> STOP_TEST( "gpdaut.tst", 10000 ); 371