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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Views: 418346# This file was created automatically, do not edit!
#############################################################################
##
#W docxpl.tst GAP 4 package AtlasRep Thomas Breuer
##
#Y Copyright (C) 2016, Lehrstuhl D für Mathematik, RWTH Aachen, Germany
##
## This file contains the GAP code of the examples in the package
## documentation files.
##
## In order to run the tests, one starts GAP from the `tst' subdirectory
## of the `pkg/atlasrep' directory, and calls `Test( "docxpl.tst" );'.
##
gap> LoadPackage( "AtlasRep", false );
true
gap> save:= SizeScreen();;
gap> SizeScreen( [ 72 ] );;
gap> START_TEST( "Input file: docxpl.tst" );
##
gap> if IsBound( BrowseData ) then
> oldinterval:= BrowseData.defaults.dynamic.replayDefaults.replayInterval;
> BrowseData.defaults.dynamic.replayDefaults.replayInterval:= 1;
> fi;
## ./tutorial.xml (43-50)
gap> LoadPackage( "AtlasRep" );
true
gap> LoadPackage( "CTblLib" );
true
gap> LoadPackage( "TomLib" );
true
## ./tutorial.xml (113-122)
gap> g:= AtlasGroup( "M24" );
Group([ (1,4)(2,7)(3,17)(5,13)(6,9)(8,15)(10,19)(11,18)(12,21)(14,16)
(20,24)(22,23), (1,4,6)(2,21,14)(3,9,15)(5,18,10)(13,17,16)
(19,24,23) ])
gap> IsPermGroup( g ); NrMovedPoints( g ); Size( g );
true
24
244823040
## ./tutorial.xml (140-148)
gap> g:= AtlasSubgroup( "M24", 1 );
Group([ (2,10)(3,12)(4,14)(6,9)(8,16)(15,18)(20,22)(21,24), (1,7,2,9)
(3,22,10,23)(4,19,8,12)(5,14)(6,18)(13,16,17,24) ])
gap> IsPermGroup( g ); NrMovedPoints( g ); Size( g );
true
23
10200960
## ./tutorial.xml (176-185)
gap> s:= AtlasSubgroup( "ON", 3 );
<permutation group of size 175560 with 2 generators>
gap> NrMovedPoints( s ); Size( s );
122760
175560
gap> hom:= SmallerDegreePermutationRepresentation( s );;
gap> NrMovedPoints( Image( hom ) );
1540
## ./tutorial.xml (194-199)
gap> j1:= AtlasGroup( "J1" );
<permutation group of size 175560 with 2 generators>
gap> NrMovedPoints( j1 );
266
## ./tutorial.xml (208-217)
gap> g:= AtlasGroup( "ON" );
<permutation group of size 460815505920 with 2 generators>
gap> s:= AtlasSubgroup( g, 3 );
<permutation group of size 175560 with 2 generators>
gap> IsSubset( g, s );
true
gap> IsSubset( g, j1 );
false
## ./tutorial.xml (234-265)
gap> DisplayAtlasInfo( "A5" );
Representations for G = A5: (all refer to std. generators 1)
---------------------------
1: G <= Sym(5) 3-trans., on cosets of A4 (1st max.)
2: G <= Sym(6) 2-trans., on cosets of D10 (2nd max.)
3: G <= Sym(10) rank 3, on cosets of S3 (3rd max.)
4: G <= GL(4a,2)
5: G <= GL(4b,2)
6: G <= GL(4,3)
7: G <= GL(6,3)
8: G <= GL(2a,4)
9: G <= GL(2b,4)
10: G <= GL(3,5)
11: G <= GL(5,5)
12: G <= GL(3a,9)
13: G <= GL(3b,9)
14: G <= GL(4,Z)
15: G <= GL(5,Z)
16: G <= GL(6,Z)
17: G <= GL(3a,Field([Sqrt(5)]))
18: G <= GL(3b,Field([Sqrt(5)]))
Programs for G = A5: (all refer to std. generators 1)
--------------------
presentation
std. gen. checker
maxes (all 3):
1: A4
2: D10
3: S3
## ./tutorial.xml (273-276)
gap> AtlasGroup( "A5", Position, 1 );
Group([ (1,2)(3,4), (1,3,5) ])
## ./tutorial.xml (287-292)
gap> AtlasGroup( "A5", NrMovedPoints, 10 );
Group([ (2,4)(3,5)(6,8)(7,10), (1,2,3)(4,6,7)(5,8,9) ])
gap> AtlasGroup( "A5", Dimension, 4, Ring, GF(2) );
<matrix group of size 60 with 2 generators>
## ./tutorial.xml (307-315)
gap> AtlasSubgroup( "A5", Dimension, 4, Ring, GF(2), 1 );
<matrix group of size 12 with 2 generators>
gap> g:= AtlasSubgroup( "A5", NrMovedPoints, 10, 3 );
Group([ (2,4)(3,5)(6,8)(7,10), (1,4)(3,8)(5,7)(6,10) ])
gap> Size( g ); NrMovedPoints( g );
6
9
## ./tutorial.xml (363-379)
gap> info:= OneAtlasGeneratingSetInfo( "A5", NrMovedPoints, 10 );
rec( groupname := "A5", id := "",
identifier := [ "A5", [ "A5G1-p10B0.m1", "A5G1-p10B0.m2" ], 1, 10 ],
isPrimitive := true, maxnr := 3, p := 10, rankAction := 3,
repname := "A5G1-p10B0", repnr := 3, size := 60, stabilizer := "S3",
standardization := 1, transitivity := 1, type := "perm" )
gap> info2:= AtlasGenerators( info );
rec( generators := [ (2,4)(3,5)(6,8)(7,10), (1,2,3)(4,6,7)(5,8,9) ],
groupname := "A5", id := "",
identifier := [ "A5", [ "A5G1-p10B0.m1", "A5G1-p10B0.m2" ], 1, 10 ],
isPrimitive := true, maxnr := 3, p := 10, rankAction := 3,
repname := "A5G1-p10B0", repnr := 3, size := 60, stabilizer := "S3",
standardization := 1, transitivity := 1, type := "perm" )
gap> info2.generators;
[ (2,4)(3,5)(6,8)(7,10), (1,2,3)(4,6,7)(5,8,9) ]
## ./tutorial.xml (411-431)
gap> prginfo:= AtlasProgramInfo( "A5", "maxes", 1 );
rec( groupname := "A5", identifier := [ "A5", "A5G1-max1W1", 1 ],
size := 12, standardization := 1, subgroupname := "A4" )
gap> prg:= AtlasProgram( prginfo.identifier );
rec( groupname := "A5", identifier := [ "A5", "A5G1-max1W1", 1 ],
program := <straight line program>, size := 12,
standardization := 1, subgroupname := "A4" )
gap> Display( prg.program );
# input:
r:= [ g1, g2 ];
# program:
r[3]:= r[1]*r[2];
r[4]:= r[2]*r[1];
r[5]:= r[3]*r[3];
r[1]:= r[5]*r[4];
# return values:
[ r[1], r[2] ]
gap> ResultOfStraightLineProgram( prg.program, info2.generators );
[ (1,10)(2,3)(4,9)(7,8), (1,2,3)(4,6,7)(5,8,9) ]
## ./tutorial.xml (453-458)
gap> tbl:= CharacterTable( "M11" );;
gap> modtbl:= tbl mod 2;;
gap> CharacterDegrees( modtbl );
[ [ 1, 1 ], [ 10, 1 ], [ 16, 2 ], [ 44, 1 ] ]
## ./tutorial.xml (474-483)
gap> DisplayAtlasInfo( "M11", Characteristic, 2 );
Representations for G = M11: (all refer to std. generators 1)
----------------------------
6: G <= GL(10,2) character 10a
7: G <= GL(32,2) character 16ab
8: G <= GL(44,2) character 44a
16: G <= GL(16a,4) character 16a
17: G <= GL(16b,4) character 16b
## ./tutorial.xml (497-507)
gap> info:= OneAtlasGeneratingSetInfo( "M11", Characteristic, 2,
> Dimension, 10 );;
gap> gens:= AtlasGenerators( info.identifier );;
gap> ccls:= AtlasProgram( "M11", gens.standardization, "classes" );
rec( groupname := "M11", identifier := [ "M11", "M11G1-cclsW1", 1 ],
outputs := [ "1A", "2A", "3A", "4A", "5A", "6A", "8A", "8B", "11A",
"11B" ], program := <straight line program>,
standardization := 1 )
gap> reps:= ResultOfStraightLineProgram( ccls.program, gens.generators );;
## ./tutorial.xml (519-526)
gap> ord8prg:= RestrictOutputsOfSLP( ccls.program,
> Filtered( [ 1 .. 10 ], i -> ccls.outputs[i][1] = '8' ) );
<straight line program>
gap> ord8reps:= ResultOfStraightLineProgram( ord8prg, gens.generators );;
gap> List( ord8reps, m -> Position( reps, m ) );
[ 7, 8 ]
## ./tutorial.xml (534-537)
gap> List( reps, Order ) = OrdersClassRepresentatives( tbl );
true
## ./tutorial.xml (552-556)
gap> fus:= GetFusionMap( modtbl, tbl );
[ 1, 3, 5, 9, 10 ]
gap> modreps:= reps{ fus };;
## ./tutorial.xml (566-571)
gap> char:= List( modreps, BrauerCharacterValue );
[ 10, 1, 0, -1, -1 ]
gap> Position( Irr( modtbl ), char );
2
## ./tutorial.xml (588-594)
gap> grp:= Group( gens.generators );;
gap> v:= GF(2)^10;;
gap> orbs:= Orbits( grp, AsList( v ) );;
gap> List( orbs, Length );
[ 1, 396, 55, 330, 66, 165, 11 ]
## ./tutorial.xml (616-618)
gap> gens:= AtlasGenerators( "M11", 6, 1 );;
## ./tutorial.xml (622-628)
gap> id:= IdentityMat( 10, GF(2) );;
gap> sub1:= Subspace( v, NullspaceMat( gens.generators[1] - id ) );;
gap> sub2:= Subspace( v, NullspaceMat( gens.generators[2] - id ) );;
gap> fix:= Intersection( sub1, sub2 );
<vector space of dimension 1 over GF(2)>
## ./tutorial.xml (637-641)
gap> orb:= Orbit( grp, Basis( fix )[1] );;
gap> act:= Action( grp, orb );; Print( act, "\n" );
Group( [ ( 1, 2)( 4, 6)( 5, 8)( 7,10), ( 1, 3, 5, 9)( 2, 4, 7,11) ] )
## ./tutorial.xml (652-660)
gap> permgrp:= Group( AtlasGenerators( "M11", 1 ).generators );;
gap> Print( permgrp, "\n" );
Group( [ ( 2,10)( 4,11)( 5, 7)( 8, 9), ( 1, 4, 3, 8)( 2, 5, 6, 9) ] )
gap> permgrp = act;
false
gap> IsConjugate( SymmetricGroup(11), permgrp, act );
true
## ./tutorial.xml (675-700)
gap> DisplayAtlasInfo( "G2(3)", IsStraightLineProgram );
Programs for G = G2(3): (all refer to std. generators 1)
-----------------------
class repres.
presentation
repr. cyc. subg.
std. gen. checker
automorphisms:
2
maxes (all 10):
1: U3(3).2
2: U3(3).2
3: (3^(1+2)+x3^2):2S4
4: (3^(1+2)+x3^2):2S4
5: L3(3).2
6: L3(3).2
7: L2(8).3
8: 2^3.L3(2)
9: L2(13)
10: 2^(1+4)+:3^2.2
gap> prog:= AtlasProgram( "G2(3)", "automorphism", "2" ).program;;
gap> info:= OneAtlasGeneratingSetInfo( "G2(3)", Dimension, 7 );;
gap> gens:= AtlasGenerators( info ).generators;;
gap> imgs:= ResultOfStraightLineProgram( prog, gens );;
## ./tutorial.xml (713-717)
gap> g:= Group( gens );;
gap> aut:= GroupHomomorphismByImagesNC( g, g, gens, imgs );;
gap> SetIsBijective( aut, true );
## ./tutorial.xml (726-730)
gap> aut:= GroupHomomorphismByImages( g, g, gens, imgs );;
gap> IsBijective( aut );
true
## ./tutorial.xml (753-758)
gap> max1:= AtlasProgram( "G2(3)", 1 ).program;;
gap> mgens:= ResultOfStraightLineProgram( max1, gens );;
gap> comp:= CompositionOfStraightLinePrograms( max1, prog );;
gap> mimgs:= ResultOfStraightLineProgram( comp, gens );;
## ./tutorial.xml (773-776)
gap> mimgs = List( mgens, x -> x^aut );
true
## ./tutorial.xml (807-820)
gap> info:= OneAtlasGeneratingSetInfo( "M12", NrMovedPoints, 12 );
rec( charactername := "1a+11a", groupname := "M12", id := "a",
identifier := [ "M12", [ "M12G1-p12aB0.m1", "M12G1-p12aB0.m2" ], 1,
12 ], isPrimitive := true, maxnr := 1, p := 12, rankAction := 2,
repname := "M12G1-p12aB0", repnr := 1, size := 95040,
stabilizer := "M11", standardization := 1, transitivity := 5,
type := "perm" )
gap> gensM12:= AtlasGenerators( info.identifier );;
gap> restM11:= AtlasProgram( "M12", "maxes", 1 );;
gap> gensM11:= ResultOfStraightLineProgram( restM11.program,
> gensM12.generators );
[ (3,9)(4,12)(5,10)(6,8), (1,4,11,5)(2,10,8,3) ]
## ./tutorial.xml (832-838)
gap> checkM11:= AtlasProgram( "M11", "check" );
rec( groupname := "M11", identifier := [ "M11", "M11G1-check1", 1, 1 ]
, program := <straight line decision>, standardization := 1 )
gap> ResultOfStraightLineDecision( checkM11.program, gensM11 );
true
## ./tutorial.xml (847-854)
gap> restL211:= AtlasProgram( "M11", "maxes", 2 );;
gap> gensL211:= ResultOfStraightLineProgram( restL211.program, gensM11 );
[ (3,9)(4,12)(5,10)(6,8), (1,11,9)(2,12,8)(3,6,10) ]
gap> G:= Group( gensL211 );; Size( G ); IsSimple( G );
660
true
## ./tutorial.xml (864-870)
gap> G:= MathieuGroup( 11 );;
gap> gens:= GeneratorsOfGroup( G );
[ (1,2,3,4,5,6,7,8,9,10,11), (3,7,11,8)(4,10,5,6) ]
gap> ResultOfStraightLineDecision( checkM11.program, gens );
false
## ./tutorial.xml (880-895)
gap> find:= AtlasProgram( "M11", "find" );
rec( groupname := "M11", identifier := [ "M11", "M11G1-find1", 1, 1 ],
program := <black box program>, standardization := 1 )
gap> stdgens:= ResultOfBBoxProgram( find.program, Group( gens ) );;
gap> List( stdgens, Order );
[ 2, 4 ]
gap> ResultOfStraightLineDecision( checkM11.program, stdgens );
true
gap> gensL211:= ResultOfStraightLineProgram( restL211.program, stdgens );;
gap> List( gensL211, Order );
[ 2, 3 ]
gap> G:= Group( gensL211 );; Size( G ); IsSimple( G );
660
true
## ./tutorial.xml (917-925)
gap> tom:= TableOfMarks( "A5" );
TableOfMarks( "A5" )
gap> info:= StandardGeneratorsInfo( tom );
[ rec( ATLAS := true, description := "|a|=2, |b|=3, |ab|=5",
generators := "a, b",
script := [ [ 1, 2 ], [ 2, 3 ], [ 1, 1, 2, 1, 5 ] ],
standardization := 1 ) ]
## ./tutorial.xml (942-966)
gap> info:= OneAtlasGeneratingSetInfo( "A5", Ring, Integers, Dimension, 4 );;
gap> stdgens:= AtlasGenerators( info.identifier );
rec( dim := 4,
generators :=
[
[ [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 1, 0, 0 ],
[ -1, -1, -1, -1 ] ],
[ [ 0, 1, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ],
[ 1, 0, 0, 0 ] ] ], groupname := "A5", id := "",
identifier := [ "A5", "A5G1-Zr4B0.g", 1, 4 ],
repname := "A5G1-Zr4B0", repnr := 14, ring := Integers, size := 60,
standardization := 1, type := "matint" )
gap> orders:= OrdersTom( tom );
[ 1, 2, 3, 4, 5, 6, 10, 12, 60 ]
gap> pos:= Position( orders, 4 );
4
gap> sub:= RepresentativeTomByGeneratorsNC( tom, pos, stdgens.generators );
<matrix group of size 4 with 2 generators>
gap> GeneratorsOfGroup( sub );
[ [ [ 1, 0, 0, 0 ], [ -1, -1, -1, -1 ], [ 0, 0, 0, 1 ],
[ 0, 0, 1, 0 ] ],
[ [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 1, 0, 0 ],
[ -1, -1, -1, -1 ] ] ]
## ./tutorial.xml (981-989)
gap> tom:= TableOfMarks( "M22" );
TableOfMarks( "M22" )
gap> subord:= Size( UnderlyingGroup( tom ) ) / 770;
576
gap> ord:= OrdersTom( tom );;
gap> tomstabs:= Filtered( [ 1 .. Length( ord ) ], i -> ord[i] = subord );
[ 144 ]
## ./tutorial.xml (998-1003)
gap> DisplayAtlasInfo( "M22", NrMovedPoints, 770 );
Representations for G = M22: (all refer to std. generators 1)
----------------------------
12: G <= Sym(770) rank 9, on cosets of (A4xA4):4 < 2^4:A6
## ./tutorial.xml (1012-1018)
gap> maxtom:= MaximalSubgroupsTom( tom );
[ [ 155, 154, 153, 152, 151, 150, 146, 145 ],
[ 22, 77, 176, 176, 231, 330, 616, 672 ] ]
gap> List( tomstabs, i -> List( maxtom[1], j -> ContainedTom( tom, i, j ) ) );
[ [ 0, 10, 0, 0, 0, 0, 0, 0 ] ]
## ./tutorial.xml (1037-1043)
gap> g:= AtlasGroup( "M22", NrMovedPoints, 770 );
<permutation group of size 443520 with 2 generators>
gap> allbl:= AllBlocks( g );;
gap> List( allbl, Length );
[ 10 ]
## ./tutorial.xml (1052-1060)
gap> stab:= Stabilizer( g, 1 );;
gap> StructureDescription( stab );
"(A4 x A4) : C4"
gap> blocks:= Orbit( g, allbl[1], OnSets );;
gap> act:= Action( g, blocks, OnSets );;
gap> StructureDescription( Stabilizer( act, 1 ) );
"(C2 x C2 x C2 x C2) : A6"
## ./tutorial.xml (1075-1082)
gap> DisplayAtlasInfo( "M22", NrMovedPoints, 462 );
Representations for G = M22: (all refer to std. generators 1)
----------------------------
7: G <= Sym(462a) rank 5, on cosets of 2^4:A5 < 2^4:A6
8: G <= Sym(462b) rank 8, on cosets of 2^4:A5 < L3(4), 2^4:S5
9: G <= Sym(462c) rank 8, on cosets of 2^4:A5 < L3(4), 2^4:A6
## ./tutorial.xml (1097-1106)
gap> tom:= TableOfMarks( "M22" );
TableOfMarks( "M22" )
gap> genstom:= GeneratorsOfGroup( UnderlyingGroup( tom ) );;
gap> checkM22:= AtlasProgram( "M22", "check" );
rec( groupname := "M22", identifier := [ "M22", "M22G1-check1", 1, 1 ]
, program := <straight line decision>, standardization := 1 )
gap> ResultOfStraightLineDecision( checkM22.program, genstom );
true
## ./tutorial.xml (1115-1119)
gap> ord:= OrdersTom( tom );;
gap> tomstabs:= Filtered( [ 1 .. Length( ord ) ], i -> ord[i] = 960 );
[ 147, 148, 149 ]
## ./tutorial.xml (1130-1161)
gap> atlasreps:= AllAtlasGeneratingSetInfos( "M22", NrMovedPoints, 462 );
[ rec( charactername := "1a+21a+55a+154a+231a", groupname := "M22",
id := "a",
identifier :=
[ "M22", [ "M22G1-p462aB0.m1", "M22G1-p462aB0.m2" ], 1, 462 ],
isPrimitive := false, p := 462, rankAction := 5,
repname := "M22G1-p462aB0", repnr := 7, size := 443520,
stabilizer := "2^4:A5 < 2^4:A6", standardization := 1,
transitivity := 1, type := "perm" ),
rec( charactername := "1a+21a^2+55a+154a+210a", groupname := "M22",
id := "b",
identifier :=
[ "M22", [ "M22G1-p462bB0.m1", "M22G1-p462bB0.m2" ], 1, 462 ],
isPrimitive := false, p := 462, rankAction := 8,
repname := "M22G1-p462bB0", repnr := 8, size := 443520,
stabilizer := "2^4:A5 < L3(4), 2^4:S5", standardization := 1,
transitivity := 1, type := "perm" ),
rec( charactername := "1a+21a^2+55a+154a+210a", groupname := "M22",
id := "c",
identifier :=
[ "M22", [ "M22G1-p462cB0.m1", "M22G1-p462cB0.m2" ], 1, 462 ],
isPrimitive := false, p := 462, rankAction := 8,
repname := "M22G1-p462cB0", repnr := 9, size := 443520,
stabilizer := "2^4:A5 < L3(4), 2^4:A6", standardization := 1,
transitivity := 1, type := "perm" ) ]
gap> atlasreps:= List( atlasreps, AtlasGroup );;
gap> tomstabreps:= List( atlasreps, G -> List( tomstabs,
> i -> RepresentativeTomByGenerators( tom, i, GeneratorsOfGroup( G ) ) ) );;
gap> List( tomstabreps, x -> List( x, NrMovedPoints ) );
[ [ 462, 462, 461 ], [ 460, 462, 462 ], [ 462, 461, 462 ] ]
## ./tutorial.xml (1177-1183)
gap> stabs:= List( atlasreps, G -> Stabilizer( G, 1 ) );;
gap> List( stabs, IdGroup );
[ [ 960, 11358 ], [ 960, 11357 ], [ 960, 11357 ] ]
gap> List( stabs, PerfectIdentification );
[ [ 960, 2 ], [ 960, 1 ], [ 960, 1 ] ]
## ./tutorial.xml (1193-1200)
gap> maxtom:= MaximalSubgroupsTom( tom );
[ [ 155, 154, 153, 152, 151, 150, 146, 145 ],
[ 22, 77, 176, 176, 231, 330, 616, 672 ] ]
gap> List( tomstabs, i -> List( maxtom[1], j -> ContainedTom( tom, i, j ) ) );
[ [ 21, 0, 0, 0, 1, 0, 0, 0 ], [ 21, 6, 0, 0, 0, 0, 0, 0 ],
[ 0, 6, 0, 0, 0, 0, 0, 0 ] ]
## ./tutorial.xml (1231-1237)
gap> bl:= List( atlasreps, AllBlocks );;
gap> List( bl, Length );
[ 1, 3, 2 ]
gap> List( bl, l -> List( l, Length ) );
[ [ 6 ], [ 21, 21, 2 ], [ 21, 6 ] ]
## ./tutorial.xml (1264-1267)
gap> List( atlasreps, RankAction );
[ 5, 8, 8 ]
## ./tutorial.xml (1280-1290)
gap> t:= CharacterTable( "M22" );;
gap> perms:= PermChars( t, 462 );
[ Character( CharacterTable( "M22" ),
[ 462, 30, 3, 2, 2, 2, 3, 0, 0, 0, 0, 0 ] ),
Character( CharacterTable( "M22" ),
[ 462, 30, 12, 2, 2, 2, 0, 0, 0, 0, 0, 0 ] ) ]
gap> MatScalarProducts( t, Irr( t ), perms );
[ [ 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0 ],
[ 1, 2, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0 ] ]
## ./interfac.xml (35-40)
gap> LoadPackage( "ctbllib" );
true
gap> LoadPackage( "tomlib" );
true
## ./../gap/utils.gd (201-223)
gap> AtlasClassNames( CharacterTable( "L3(4).3" ) );
[ "1A", "2A", "3A", "4ABC", "5A", "5B", "7A", "7B", "3B", "3B'",
"3C", "3C'", "6B", "6B'", "15A", "15A'", "15B", "15B'", "21A",
"21A'", "21B", "21B'" ]
gap> AtlasClassNames( CharacterTable( "U3(5).2" ) );
[ "1A", "2A", "3A", "4A", "5A", "5B", "5CD", "6A", "7AB", "8AB",
"10A", "2B", "4B", "6D", "8C", "10B", "12B", "20A", "20B" ]
gap> AtlasClassNames( CharacterTable( "L2(27).6" ) );
[ "1A", "2A", "3AB", "7ABC", "13ABC", "13DEF", "14ABC", "2B", "4A",
"26ABC", "26DEF", "28ABC", "28DEF", "3C", "3C'", "6A", "6A'",
"9AB", "9A'B'", "6B", "6B'", "12A", "12A'" ]
gap> AtlasClassNames( CharacterTable( "L3(4).3.2_2" ) );
[ "1A", "2A", "3A", "4ABC", "5AB", "7A", "7B", "3B", "3C", "6B",
"15A", "15B", "21A", "21B", "2C", "4E", "6E", "8D", "14A", "14B" ]
gap> AtlasClassNames( CharacterTable( "3.A6" ) );
[ "1A_0", "1A_1", "1A_2", "2A_0", "2A_1", "2A_2", "3A_0", "3B_0",
"4A_0", "4A_1", "4A_2", "5A_0", "5A_1", "5A_2", "5B_0", "5B_1",
"5B_2" ]
gap> AtlasClassNames( CharacterTable( "2.A5.2" ) );
[ "1A_0", "1A_1", "2A_0", "3A_0", "3A_1", "5AB_0", "5AB_1", "2B_0",
"4A_0", "4A_1", "6A_0", "6A_1" ]
## ./../gap/utils.gd (269-272)
gap> AtlasCharacterNames( CharacterTable( "A5" ) );
[ "1a", "3a", "3b", "4a", "5a" ]
## ./../gap/interfac.gd (335-341)
gap> DisplayAtlasInfo( [ "M11", "A5" ] );
group | # | maxes | cl | cyc | out | fnd | chk | prs
------+----+-------+----+-----+-----+-----+-----+----
M11 | 42 | 5 | + | + | | + | + | +
A5 | 18 | 3 | | | | | + | +
## ./../gap/interfac.gd (364-376)
gap> DisplayAtlasInfo( "A5", IsPermGroup, true );
Representations for G = A5: (all refer to std. generators 1)
---------------------------
1: G <= Sym(5) 3-trans., on cosets of A4 (1st max.)
2: G <= Sym(6) 2-trans., on cosets of D10 (2nd max.)
3: G <= Sym(10) rank 3, on cosets of S3 (3rd max.)
gap> DisplayAtlasInfo( "A5", NrMovedPoints, [ 4 .. 9 ] );
Representations for G = A5: (all refer to std. generators 1)
---------------------------
1: G <= Sym(5) 3-trans., on cosets of A4 (1st max.)
2: G <= Sym(6) 2-trans., on cosets of D10 (2nd max.)
## ./../gap/interfac.gd (381-400)
gap> DisplayAtlasInfo( "A5", Dimension, [ 1 .. 3 ] );
Representations for G = A5: (all refer to std. generators 1)
---------------------------
8: G <= GL(2a,4)
9: G <= GL(2b,4)
10: G <= GL(3,5)
12: G <= GL(3a,9)
13: G <= GL(3b,9)
17: G <= GL(3a,Field([Sqrt(5)]))
18: G <= GL(3b,Field([Sqrt(5)]))
gap> DisplayAtlasInfo( "A5", Characteristic, 0 );
Representations for G = A5: (all refer to std. generators 1)
---------------------------
14: G <= GL(4,Z)
15: G <= GL(5,Z)
16: G <= GL(6,Z)
17: G <= GL(3a,Field([Sqrt(5)]))
18: G <= GL(3b,Field([Sqrt(5)]))
## ./../gap/interfac.gd (409-417)
gap> DisplayAtlasInfo( "A5", Identifier, "a" );
Representations for G = A5: (all refer to std. generators 1)
---------------------------
4: G <= GL(4a,2)
8: G <= GL(2a,4)
12: G <= GL(3a,9)
17: G <= GL(3a,Field([Sqrt(5)]))
## ./../gap/interfac.gd (422-457)
gap> DisplayAtlasInfo( "A5", NrMovedPoints, IsPrimeInt );
Representations for G = A5: (all refer to std. generators 1)
---------------------------
1: G <= Sym(5) 3-trans., on cosets of A4 (1st max.)
gap> DisplayAtlasInfo( "A5", Characteristic, IsOddInt );
Representations for G = A5: (all refer to std. generators 1)
---------------------------
6: G <= GL(4,3)
7: G <= GL(6,3)
10: G <= GL(3,5)
11: G <= GL(5,5)
12: G <= GL(3a,9)
13: G <= GL(3b,9)
gap> DisplayAtlasInfo( "A5", Dimension, IsPrimeInt );
Representations for G = A5: (all refer to std. generators 1)
---------------------------
8: G <= GL(2a,4)
9: G <= GL(2b,4)
10: G <= GL(3,5)
11: G <= GL(5,5)
12: G <= GL(3a,9)
13: G <= GL(3b,9)
15: G <= GL(5,Z)
17: G <= GL(3a,Field([Sqrt(5)]))
18: G <= GL(3b,Field([Sqrt(5)]))
gap> DisplayAtlasInfo( "A5", Ring, IsFinite and IsPrimeField );
Representations for G = A5: (all refer to std. generators 1)
---------------------------
4: G <= GL(4a,2)
5: G <= GL(4b,2)
6: G <= GL(4,3)
7: G <= GL(6,3)
10: G <= GL(3,5)
11: G <= GL(5,5)
## ./../gap/interfac.gd (467-477)
gap> DisplayAtlasInfo( "A5", IsStraightLineProgram, true );
Programs for G = A5: (all refer to std. generators 1)
--------------------
presentation
std. gen. checker
maxes (all 3):
1: A4
2: D10
3: S3
## ./../gap/interfac.gd (576-601)
gap> gens1:= AtlasGenerators( "A5", 1 );
rec( generators := [ (1,2)(3,4), (1,3,5) ], groupname := "A5",
id := "",
identifier := [ "A5", [ "A5G1-p5B0.m1", "A5G1-p5B0.m2" ], 1, 5 ],
isPrimitive := true, maxnr := 1, p := 5, rankAction := 2,
repname := "A5G1-p5B0", repnr := 1, size := 60, stabilizer := "A4",
standardization := 1, transitivity := 3, type := "perm" )
gap> gens8:= AtlasGenerators( "A5", 8 );
rec( dim := 2,
generators := [ [ [ Z(2)^0, 0*Z(2) ], [ Z(2^2), Z(2)^0 ] ],
[ [ 0*Z(2), Z(2)^0 ], [ Z(2)^0, Z(2)^0 ] ] ], groupname := "A5",
id := "a",
identifier := [ "A5", [ "A5G1-f4r2aB0.m1", "A5G1-f4r2aB0.m2" ], 1,
4 ], repname := "A5G1-f4r2aB0", repnr := 8, ring := GF(2^2),
size := 60, standardization := 1, type := "matff" )
gap> gens17:= AtlasGenerators( "A5", 17 );
rec( dim := 3,
generators :=
[ [ [ -1, 0, 0 ], [ 0, -1, 0 ], [ -E(5)-E(5)^4, -E(5)-E(5)^4, 1 ]
], [ [ 0, 1, 0 ], [ 0, 0, 1 ], [ 1, 0, 0 ] ] ],
groupname := "A5", id := "a",
identifier := [ "A5", "A5G1-Ar3aB0.g", 1, 3 ],
repname := "A5G1-Ar3aB0", repnr := 17, ring := NF(5,[ 1, 4 ]),
size := 60, standardization := 1, type := "matalg" )
## ./../gap/interfac.gd (606-619)
gap> gens1max2:= AtlasGenerators( "A5", 1, 2 );
rec( generators := [ (1,2)(3,4), (2,3)(4,5) ], groupname := "D10",
identifier := [ "A5", [ "A5G1-p5B0.m1", "A5G1-p5B0.m2" ], 1, 5, 2 ],
repnr := 1, size := 10, standardization := 1 )
gap> id:= gens1max2.identifier;;
gap> gens1max2 = AtlasGenerators( id );
true
gap> max2:= Group( gens1max2.generators );;
gap> Size( max2 );
10
gap> IdGroup( max2 ) = IdGroup( DihedralGroup( 10 ) );
true
## ./../gap/interfac.gd (839-857)
gap> prog:= AtlasProgram( "A5", 2 );
rec( groupname := "A5", identifier := [ "A5", "A5G1-max2W1", 1 ],
program := <straight line program>, size := 10,
standardization := 1, subgroupname := "D10" )
gap> StringOfResultOfStraightLineProgram( prog.program, [ "a", "b" ] );
"[ a, bbab ]"
gap> gens1:= AtlasGenerators( "A5", 1 );
rec( generators := [ (1,2)(3,4), (1,3,5) ], groupname := "A5",
id := "",
identifier := [ "A5", [ "A5G1-p5B0.m1", "A5G1-p5B0.m2" ], 1, 5 ],
isPrimitive := true, maxnr := 1, p := 5, rankAction := 2,
repname := "A5G1-p5B0", repnr := 1, size := 60, stabilizer := "A4",
standardization := 1, transitivity := 3, type := "perm" )
gap> maxgens:= ResultOfStraightLineProgram( prog.program, gens1.generators );
[ (1,2)(3,4), (2,3)(4,5) ]
gap> maxgens = gens1max2.generators;
true
## ./../gap/interfac.gd (871-881)
gap> prog:= AtlasProgram( "J1", "cyclic" );
rec( groupname := "J1", identifier := [ "J1", "J1G1-cycW1", 1 ],
outputs := [ "6A", "7A", "10B", "11A", "15B", "19A" ],
program := <straight line program>, standardization := 1 )
gap> gens:= GeneratorsOfGroup( FreeGroup( "x", "y" ) );;
gap> ResultOfStraightLineProgram( prog.program, gens );
[ (x*y)^2*((y*x)^2*y^2*x)^2*y^2, x*y, (x*(y*x*y)^2)^2*y,
(x*y*x*(y*x*y)^3*x*y^2)^2*x*y*x*(y*x*y)^2*y, x*y*x*(y*x*y)^2*y,
(x*y)^2*y ]
## ./../gap/interfac.gd (666-670)
gap> AtlasProgramInfo( "J1", "cyclic" );
rec( groupname := "J1", identifier := [ "J1", "J1G1-cycW1", 1 ],
standardization := 1 )
## ./../gap/interfac.gd (956-978)
gap> info:= OneAtlasGeneratingSetInfo( "A5" );
rec( groupname := "A5", id := "",
identifier := [ "A5", [ "A5G1-p5B0.m1", "A5G1-p5B0.m2" ], 1, 5 ],
isPrimitive := true, maxnr := 1, p := 5, rankAction := 2,
repname := "A5G1-p5B0", repnr := 1, size := 60, stabilizer := "A4",
standardization := 1, transitivity := 3, type := "perm" )
gap> gens:= AtlasGenerators( info.identifier );
rec( generators := [ (1,2)(3,4), (1,3,5) ], groupname := "A5",
id := "",
identifier := [ "A5", [ "A5G1-p5B0.m1", "A5G1-p5B0.m2" ], 1, 5 ],
isPrimitive := true, maxnr := 1, p := 5, rankAction := 2,
repname := "A5G1-p5B0", repnr := 1, size := 60, stabilizer := "A4",
standardization := 1, transitivity := 3, type := "perm" )
gap> info = OneAtlasGeneratingSetInfo( "A5", IsPermGroup, true );
true
gap> info = OneAtlasGeneratingSetInfo( "A5", NrMovedPoints, "minimal" );
true
gap> info = OneAtlasGeneratingSetInfo( "A5", NrMovedPoints, [ 1 .. 10 ] );
true
gap> OneAtlasGeneratingSetInfo( "A5", NrMovedPoints, 20 );
fail
## ./../gap/interfac.gd (989-1054)
gap> info:= OneAtlasGeneratingSetInfo( "A5", IsMatrixGroup, true );
rec( dim := 4, groupname := "A5", id := "a",
identifier := [ "A5", [ "A5G1-f2r4aB0.m1", "A5G1-f2r4aB0.m2" ], 1,
2 ], repname := "A5G1-f2r4aB0", repnr := 4, ring := GF(2),
size := 60, standardization := 1, type := "matff" )
gap> gens:= AtlasGenerators( info.identifier );
rec( dim := 4,
generators := [ <an immutable 4x4 matrix over GF2>,
<an immutable 4x4 matrix over GF2> ], groupname := "A5",
id := "a",
identifier := [ "A5", [ "A5G1-f2r4aB0.m1", "A5G1-f2r4aB0.m2" ], 1,
2 ], repname := "A5G1-f2r4aB0", repnr := 4, ring := GF(2),
size := 60, standardization := 1, type := "matff" )
gap> info = OneAtlasGeneratingSetInfo( "A5", Dimension, 4 );
true
gap> info = OneAtlasGeneratingSetInfo( "A5", Characteristic, 2 );
true
gap> info = OneAtlasGeneratingSetInfo( "A5", Ring, GF(2) );
true
gap> OneAtlasGeneratingSetInfo( "A5", Characteristic, [2,5], Dimension, 2 );
rec( dim := 2, groupname := "A5", id := "a",
identifier := [ "A5", [ "A5G1-f4r2aB0.m1", "A5G1-f4r2aB0.m2" ], 1,
4 ], repname := "A5G1-f4r2aB0", repnr := 8, ring := GF(2^2),
size := 60, standardization := 1, type := "matff" )
gap> OneAtlasGeneratingSetInfo( "A5", Characteristic, [2,5], Dimension, 1 );
fail
gap> info:= OneAtlasGeneratingSetInfo( "A5", Characteristic, 0, Dimension, 4 );
rec( dim := 4, groupname := "A5", id := "",
identifier := [ "A5", "A5G1-Zr4B0.g", 1, 4 ],
repname := "A5G1-Zr4B0", repnr := 14, ring := Integers, size := 60,
standardization := 1, type := "matint" )
gap> gens:= AtlasGenerators( info.identifier );
rec( dim := 4,
generators :=
[
[ [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 1, 0, 0 ],
[ -1, -1, -1, -1 ] ],
[ [ 0, 1, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ],
[ 1, 0, 0, 0 ] ] ], groupname := "A5", id := "",
identifier := [ "A5", "A5G1-Zr4B0.g", 1, 4 ],
repname := "A5G1-Zr4B0", repnr := 14, ring := Integers, size := 60,
standardization := 1, type := "matint" )
gap> info = OneAtlasGeneratingSetInfo( "A5", Ring, Integers );
true
gap> info = OneAtlasGeneratingSetInfo( "A5", Ring, CF(37) );
true
gap> OneAtlasGeneratingSetInfo( "A5", Ring, Integers mod 77 );
fail
gap> info:= OneAtlasGeneratingSetInfo( "A5", Ring, CF(5), Dimension, 3 );
rec( dim := 3, groupname := "A5", id := "a",
identifier := [ "A5", "A5G1-Ar3aB0.g", 1, 3 ],
repname := "A5G1-Ar3aB0", repnr := 17, ring := NF(5,[ 1, 4 ]),
size := 60, standardization := 1, type := "matalg" )
gap> gens:= AtlasGenerators( info.identifier );
rec( dim := 3,
generators :=
[ [ [ -1, 0, 0 ], [ 0, -1, 0 ], [ -E(5)-E(5)^4, -E(5)-E(5)^4, 1 ]
], [ [ 0, 1, 0 ], [ 0, 0, 1 ], [ 1, 0, 0 ] ] ],
groupname := "A5", id := "a",
identifier := [ "A5", "A5G1-Ar3aB0.g", 1, 3 ],
repname := "A5G1-Ar3aB0", repnr := 17, ring := NF(5,[ 1, 4 ]),
size := 60, standardization := 1, type := "matalg" )
gap> OneAtlasGeneratingSetInfo( "A5", Ring, GF(17) );
fail
## ./../gap/interfac.gd (1090-1110)
gap> AllAtlasGeneratingSetInfos( "A5", IsPermGroup, true );
[ rec( groupname := "A5", id := "",
identifier := [ "A5", [ "A5G1-p5B0.m1", "A5G1-p5B0.m2" ], 1, 5 ]
, isPrimitive := true, maxnr := 1, p := 5, rankAction := 2,
repname := "A5G1-p5B0", repnr := 1, size := 60,
stabilizer := "A4", standardization := 1, transitivity := 3,
type := "perm" ),
rec( groupname := "A5", id := "",
identifier := [ "A5", [ "A5G1-p6B0.m1", "A5G1-p6B0.m2" ], 1, 6 ]
, isPrimitive := true, maxnr := 2, p := 6, rankAction := 2,
repname := "A5G1-p6B0", repnr := 2, size := 60,
stabilizer := "D10", standardization := 1, transitivity := 2,
type := "perm" ),
rec( groupname := "A5", id := "",
identifier := [ "A5", [ "A5G1-p10B0.m1", "A5G1-p10B0.m2" ], 1,
10 ], isPrimitive := true, maxnr := 3, p := 10,
rankAction := 3, repname := "A5G1-p10B0", repnr := 3,
size := 60, stabilizer := "S3", standardization := 1,
transitivity := 1, type := "perm" ) ]
## ./../gap/interfac.gd (1192-1195)
gap> g:= AtlasGroup( "A5" );
Group([ (1,2)(3,4), (1,3,5) ])
## ./../gap/interfac.gd (1203-1214)
gap> info:= OneAtlasGeneratingSetInfo( "A5" );
rec( groupname := "A5", id := "",
identifier := [ "A5", [ "A5G1-p5B0.m1", "A5G1-p5B0.m2" ], 1, 5 ],
isPrimitive := true, maxnr := 1, p := 5, rankAction := 2,
repname := "A5G1-p5B0", repnr := 1, size := 60, stabilizer := "A4",
standardization := 1, transitivity := 3, type := "perm" )
gap> AtlasGroup( info );
Group([ (1,2)(3,4), (1,3,5) ])
gap> AtlasGroup( info.identifier );
Group([ (1,2)(3,4), (1,3,5) ])
## ./../gap/interfac.gd (1284-1289)
gap> g:= AtlasSubgroup( "A5", NrMovedPoints, 5, 1 );
Group([ (1,5)(2,3), (1,3,5) ])
gap> NrMovedPoints( g );
4
## ./../gap/interfac.gd (1299-1312)
gap> info:= OneAtlasGeneratingSetInfo( "A5" );
rec( groupname := "A5", id := "",
identifier := [ "A5", [ "A5G1-p5B0.m1", "A5G1-p5B0.m2" ], 1, 5 ],
isPrimitive := true, maxnr := 1, p := 5, rankAction := 2,
repname := "A5G1-p5B0", repnr := 1, size := 60, stabilizer := "A4",
standardization := 1, transitivity := 3, type := "perm" )
gap> AtlasSubgroup( info, 1 );
Group([ (1,5)(2,3), (1,3,5) ])
gap> AtlasSubgroup( info.identifier, 1 );
Group([ (1,5)(2,3), (1,3,5) ])
gap> AtlasSubgroup( AtlasGroup( "A5" ), 1 );
Group([ (1,5)(2,3), (1,3,5) ])
## ./../gap/interfac.gd (1145-1152)
gap> AtlasRepInfoRecord( AtlasGroup( "A5" ) );
rec( groupname := "A5", id := "",
identifier := [ "A5", [ "A5G1-p5B0.m1", "A5G1-p5B0.m2" ], 1, 5 ],
isPrimitive := true, maxnr := 1, p := 5, rankAction := 2,
repname := "A5G1-p5B0", repnr := 1, size := 60, stabilizer := "A4",
standardization := 1, transitivity := 3, type := "perm" )
## ./../gap/brmindeg.g (32-47)
gap> if IsBound( BrowseMinimalDegrees ) then
> down:= NCurses.keys.DOWN;; DOWN:= NCurses.keys.NPAGE;;
> right:= NCurses.keys.RIGHT;; END:= NCurses.keys.END;;
> enter:= NCurses.keys.ENTER;; nop:= [ 14, 14, 14 ];;
> # just scroll in the table
> BrowseData.SetReplay( Concatenation( [ DOWN, DOWN, DOWN,
> right, right, right ], "sedddrrrddd", nop, nop, "Q" ) );
> BrowseMinimalDegrees();;
> # restrict the table to the groups with minimal ordinary degree 6
> BrowseData.SetReplay( Concatenation( "scf6",
> [ down, down, right, enter, enter ] , nop, nop, "Q" ) );
> BrowseMinimalDegrees();;
> BrowseData.SetReplay( false );
> fi;
## ./../gap/brmindeg.g (58-65)
gap> if IsBound( BrowseMinimalDegrees ) then
> # just scroll in the table
> BrowseData.SetReplay( Concatenation( [ DOWN, DOWN, DOWN, END ],
> "rrrrrrrrrrrrrr", nop, nop, "Q" ) );
> BrowseMinimalDegrees( BibliographySporadicSimple.groupNamesJan05 );;
> fi;
## ./../gap/brspor.g (165-178)
gap> if IsBound( BrowseBibliographySporadicSimple ) then
> enter:= NCurses.keys.ENTER;; nop:= [ 14, 14, 14 ];;
> BrowseData.SetReplay( Concatenation(
> # choose the application
> "/Bibliography of Sporadic Simple Groups", [ enter, enter ],
> # search in the title column for the Atlas of Finite Groups
> "scr/Atlas of finite groups", [ enter,
> # and quit
> nop, nop, nop, nop ], "Q" ) );
> BrowseGapData();;
> BrowseData.SetReplay( false );
> fi;
## ./extend.xml (120-123)
gap> level:= InfoLevel( InfoAtlasRep );;
gap> SetInfoLevel( InfoAtlasRep, 1 );
## ./extend.xml (165-182)
gap> prv:= DirectoryTemporary( "privdir" );;
gap> FileString( Filename( prv, "C4G1-p4B0.m1" ),
> MeatAxeString( [ (1,2,3,4) ], 4 ) );;
gap> FileString( Filename( prv, "C4G1-max1W1" ),
> "inp 1\npwr 2 1 2\noup 1 2\n" );;
gap> FileString( Filename( prv, "C4G1-XtestW1" ),
> "inp 1\npwr 2 1 2\noup 1 2\n" );;
gap> FileString( Filename( prv, "C4G1-a2W1" ),
> "inp 1\npwr 3 1 2\noup 1 2\n" );;
gap> FileString( Filename( prv, "C4G1-Ar1aB0.g" ),
> "return rec( generators:= [ [[E(4)]] ] );\n" );;
gap> points:= Elements( AlternatingGroup( 5 ) );;
gap> FileString( Filename( prv, "A5G1-p60B0.m1" ),
> MeatAxeString( [ Permutation( (1,2)(3,4), points, OnRight ) ], 60 ) );;
gap> FileString( Filename( prv, "A5G1-p60B0.m2" ),
> MeatAxeString( [ Permutation( (1,3,5), points, OnRight ) ], 60 ) );;
## ./extend.xml (206-216)
gap> FileString( Filename( prv, "toc.g" ), Concatenation( [
> "AGR.GNAN(\"C4\",\"C4\");\n",
> "AGR.GRS(\"C4\",4);\n",
> "AGR.MXN(\"C4\",1);\n",
> "AGR.MXO(\"C4\",[2]);\n",
> "AGR.MXS(\"C4\",[\"C2\"]);\n",
> "AGR.API(\"C4G1-p4B0\",[1,4,\"imprim\",\"1 < C2\"]);\n",
> "AGR.API(\"A5G1-p60B0\",[1,60,\"imprim\",\"1 < A4\"]);\n",
> ] ) );;
## ./extend.xml (224-227)
gap> AtlasOfGroupRepresentationsNotifyPrivateDirectory( prv, "priv", true );
true
## ./extend.xml (236-312)
gap> DisplayAtlasInfo( [ "C4" ] );
group | # | maxes | cl | cyc | out | fnd | chk | prs
------+---+-------+----+-----+-----+-----+-----+----
C4* | 2 | 1 | | | 2 | | |
gap> DisplayAtlasInfo( "C4" );
Representations for G = C4: (all refer to std. generators 1)
---------------------------
1: G <= Sym(4)* rank 4, on cosets of 1 < C2
2: G <= GL(1a,C)*
Programs for G = C4: (all refer to std. generators 1)
--------------------
automorphisms:
2*
maxes (all 1):
1*: C2
other scripts:
"test"*
gap> DisplayAtlasInfo( "C4", IsPermGroup, true );
Representations for G = C4: (all refer to std. generators 1)
---------------------------
1: G <= Sym(4)* rank 4, on cosets of 1 < C2
gap> DisplayAtlasInfo( "C4", IsMatrixGroup );
Representations for G = C4: (all refer to std. generators 1)
---------------------------
2: G <= GL(1a,C)*
gap> DisplayAtlasInfo( "C4", Dimension, 2 );
gap> DisplayAtlasInfo( "A5", NrMovedPoints, 60 );
Representations for G = A5: (all refer to std. generators 1)
---------------------------
4: G <= Sym(60)* rank 60, on cosets of 1 < A4
gap> info:= OneAtlasGeneratingSetInfo( "C4" );
rec( groupname := "C4", id := "",
identifier := [ [ "priv", "C4" ], [ "C4G1-p4B0.m1" ], 1, 4 ],
isPrimitive := false, p := 4, rankAction := 4,
repname := "C4G1-p4B0", repnr := 1, size := 4,
stabilizer := "1 < C2", standardization := 1, transitivity := 1,
type := "perm" )
gap> AtlasGenerators( info.identifier );
rec( generators := [ (1,2,3,4) ], groupname := "C4", id := "",
identifier := [ [ "priv", "C4" ], [ "C4G1-p4B0.m1" ], 1, 4 ],
isPrimitive := false, p := 4, rankAction := 4,
repname := "C4G1-p4B0", repnr := 1, size := 4,
stabilizer := "1 < C2", standardization := 1, transitivity := 1,
type := "perm" )
gap> AtlasProgram( "C4", 1 );
rec( groupname := "C4",
identifier := [ [ "priv", "C4" ], "C4G1-max1W1", 1 ],
program := <straight line program>, size := 2, standardization := 1,
subgroupname := "C2" )
gap> AtlasProgram( "C4", "maxes", 1 );
rec( groupname := "C4",
identifier := [ [ "priv", "C4" ], "C4G1-max1W1", 1 ],
program := <straight line program>, size := 2, standardization := 1,
subgroupname := "C2" )
gap> AtlasProgram( "C4", "maxes", 2 );
fail
gap> AtlasGenerators( "C4", 1 );
rec( generators := [ (1,2,3,4) ], groupname := "C4", id := "",
identifier := [ [ "priv", "C4" ], [ "C4G1-p4B0.m1" ], 1, 4 ],
isPrimitive := false, p := 4, rankAction := 4,
repname := "C4G1-p4B0", repnr := 1, size := 4,
stabilizer := "1 < C2", standardization := 1, transitivity := 1,
type := "perm" )
gap> AtlasGenerators( "C4", 2 );
rec( dim := 1, generators := [ [ [ E(4) ] ] ], groupname := "C4",
id := "a", identifier := [ [ "priv", "C4" ], "C4G1-Ar1aB0.g", 1, 1 ]
, repname := "C4G1-Ar1aB0", repnr := 2, size := 4,
standardization := 1, type := "matalg" )
gap> AtlasGenerators( "C4", 3 );
fail
gap> AtlasProgram( "C4", "other", "test" );
rec( groupname := "C4",
identifier := [ [ "priv", "C4" ], "C4G1-XtestW1", 1 ],
program := <straight line program>, standardization := 1 )
## ./extend.xml (321-327)
gap> DisplayAtlasInfo( "contents", "priv" );
group | # | maxes | cl | cyc | out | fnd | chk | p*
-------------------------+---+-------+----+-----+-----+-----+-----+--*
A5* | 1 | | | | | | | *
C4* | 2 | 1 | | | 2 | | | *
## ./extend.xml (337-353)
gap> if not IsBound( AGR.Test ) then
> ReadPackage( "atlasrep", "gap/test.g" );
> fi;
gap> AGR.Test.Words( "priv" );
true
gap> AGR.Test.FileHeaders( "priv" );
true
gap> AGR.Test.Files( "priv" );
true
gap> AGR.Test.BinaryFormat( "priv" );
true
gap> AGR.Test.Primitivity( "priv" );
true
gap> AGR.Test.Characters( "priv" );
true
## ./extend.xml (366-369)
gap> AtlasOfGroupRepresentationsForgetPrivateDirectory( "priv" );
gap> SetInfoLevel( InfoAtlasRep, level );
## ./../gap/bbox.gd (547-554)
gap> dec:= StraightLineDecision( [ [ [ 1, 1, 2, 1 ], 3 ],
> [ "Order", 1, 2 ], [ "Order", 2, 3 ], [ "Order", 3, 5 ] ] );
<straight line decision>
gap> LinesOfStraightLineDecision( dec );
[ [ [ 1, 1, 2, 1 ], 3 ], [ "Order", 1, 2 ], [ "Order", 2, 3 ],
[ "Order", 3, 5 ] ]
## ./../gap/bbox.gd (577-580)
gap> NrInputsOfStraightLineDecision( dec );
2
## ./../gap/scanmtx.gd (635-650)
gap> str:= "inp 2\nchor 1 2\nchor 2 3\nmu 1 2 3\nchor 3 5";;
gap> prg:= ScanStraightLineDecision( str );
rec( program := <straight line decision> )
gap> prg:= prg.program;;
gap> Display( prg );
# input:
r:= [ g1, g2 ];
# program:
if Order( r[1] ) <> 2 then return false; fi;
if Order( r[2] ) <> 3 then return false; fi;
r[3]:= r[1]*r[2];
if Order( r[3] ) <> 5 then return false; fi;
# return value:
true
## ./../gap/bbox.gd (644-649)
gap> dec:= StraightLineDecision( [ ], 1 );
<straight line decision>
gap> ResultOfStraightLineDecision( dec, [ () ] );
true
## ./../gap/bbox.gd (654-665)
gap> dec:= StraightLineDecision( [ [ [ 1, 1, 2, 1 ], 3 ],
> [ "Order", 1, 2 ], [ "Order", 2, 3 ], [ "Order", 3, 5 ] ] );
<straight line decision>
gap> LinesOfStraightLineDecision( dec );
[ [ [ 1, 1, 2, 1 ], 3 ], [ "Order", 1, 2 ], [ "Order", 2, 3 ],
[ "Order", 3, 5 ] ]
gap> ResultOfStraightLineDecision( dec, [ (), () ] );
false
gap> ResultOfStraightLineDecision( dec, [ (1,2)(3,4), (1,4,5) ] );
true
## ./../gap/bbox.gd (759-785)
gap> check:= AtlasProgram( "L2(8)", "check" );
rec( groupname := "L2(8)",
identifier := [ "L2(8)", "L28G1-check1", 1, 1 ],
program := <straight line decision>, standardization := 1 )
gap> gens:= AtlasGenerators( "L2(8)", 1 );
rec( charactername := "1a+8a",
generators := [ (1,2)(3,4)(6,7)(8,9), (1,3,2)(4,5,6)(7,8,9) ],
groupname := "L2(8)", id := "",
identifier := [ "L2(8)", [ "L28G1-p9B0.m1", "L28G1-p9B0.m2" ], 1, 9
], isPrimitive := true, maxnr := 1, p := 9, rankAction := 2,
repname := "L28G1-p9B0", repnr := 1, size := 504,
stabilizer := "2^3:7", standardization := 1, transitivity := 3,
type := "perm" )
gap> ResultOfStraightLineDecision( check.program, gens.generators );
true
gap> gens:= AtlasGenerators( "L3(2)", 1 );
rec( generators := [ (2,4)(3,5), (1,2,3)(5,6,7) ],
groupname := "L3(2)", id := "a",
identifier := [ "L3(2)", [ "L27G1-p7aB0.m1", "L27G1-p7aB0.m2" ], 1,
7 ], isPrimitive := true, maxnr := 1, p := 7, rankAction := 2,
repname := "L27G1-p7aB0", repnr := 1, size := 168,
stabilizer := "S4", standardization := 1, transitivity := 2,
type := "perm" )
gap> ResultOfStraightLineDecision( check.program, gens.generators );
true
## ./../gap/bbox.gd (973-985)
gap> lines:= [ [ "Order", 1, 2 ], [ "Order", 2, 3 ],
> [ [ 1, 1, 2, 1 ], 3 ], [ "Order", 3, 5 ] ];;
gap> dec:= StraightLineDecision( lines, 2 );
<straight line decision>
gap> bboxdec:= AsBBoxProgram( dec );
<black box program>
gap> asdec:= AsStraightLineDecision( bboxdec );
<straight line decision>
gap> LinesOfStraightLineDecision( asdec );
[ [ "Order", 1, 2 ], [ "Order", 2, 3 ], [ [ 1, 1, 2, 1 ], 3 ],
[ "Order", 3, 5 ] ]
## ./../gap/bbox.gd (823-845)
gap> dec:= StraightLineDecision( [ [ [ 1, 1, 2, 1 ], 3 ],
> [ "Order", 1, 2 ], [ "Order", 2, 3 ], [ "Order", 3, 5 ] ] );
<straight line decision>
gap> prog:= StraightLineProgramFromStraightLineDecision( dec );
<straight line program>
gap> Display( prog );
# input:
r:= [ g1, g2 ];
# program:
r[3]:= r[1]*r[2];
r[4]:= r[1]^2;
r[5]:= r[2]^3;
r[6]:= r[3]^5;
# return values:
[ r[4], r[5], r[6] ]
gap> StringOfResultOfStraightLineProgram( prog, [ "a", "b" ] );
"[ a^2, b^3, (ab)^5 ]"
gap> gens:= GeneratorsOfGroup( FreeGroup( "a", "b" ) );
[ a, b ]
gap> ResultOfStraightLineProgram( prog, gens );
[ a^2, b^3, (a*b)^5 ]
## ./../gap/bbox.gd (190-221)
gap> findstr:= "\
> set V 0\n\
> lbl START1\n\
> rand 1\n\
> ord 1 A\n\
> incr V\n\
> if V gt 100 then timeout\n\
> if A notin 1 2 3 5 then fail\n\
> if A noteq 2 then jmp START1\n\
> lbl START2\n\
> rand 2\n\
> ord 2 B\n\
> incr V\n\
> if V gt 100 then timeout\n\
> if B notin 1 2 3 5 then fail\n\
> if B noteq 3 then jmp START2\n\
> # The elements 1 and 2 have the orders 2 and 3, respectively.\n\
> set X 0\n\
> lbl CONJ\n\
> incr X\n\
> if X gt 100 then timeout\n\
> rand 3\n\
> cjr 2 3\n\
> mu 1 2 4 # ab\n\
> ord 4 C\n\
> if C notin 2 3 5 then fail\n\
> if C noteq 5 then jmp CONJ\n\
> oup 2 1 2";;
gap> find:= ScanBBoxProgram( findstr );
rec( program := <black box program> )
## ./../gap/bbox.gd (226-234)
gap> checkstr:= "\
> chor 1 2\n\
> chor 2 3\n\
> mu 1 2 3\n\
> chor 3 5";;
gap> check:= ScanBBoxProgram( checkstr );
rec( program := <black box program> )
## ./../gap/bbox.gd (330-350)
gap> g:= AlternatingGroup( 5 );;
gap> res:= RunBBoxProgram( find.program, g, [], rec() );;
gap> IsBound( res.gens ); IsBound( res.result );
true
false
gap> List( res.gens, Order );
[ 2, 3 ]
gap> Order( Product( res.gens ) );
5
gap> res:= RunBBoxProgram( check.program, "dummy", res.gens, rec() );;
gap> IsBound( res.gens ); IsBound( res.result );
false
true
gap> res.result;
true
gap> othergens:= GeneratorsOfGroup( g );;
gap> res:= RunBBoxProgram( check.program, "dummy", othergens, rec() );;
gap> res.result;
false
## ./../gap/bbox.gd (382-394)
gap> g:= AlternatingGroup( 5 );;
gap> res:= ResultOfBBoxProgram( find.program, g );;
gap> List( res, Order );
[ 2, 3 ]
gap> Order( Product( res ) );
5
gap> res:= ResultOfBBoxProgram( check.program, res );
true
gap> othergens:= GeneratorsOfGroup( g );;
gap> res:= ResultOfBBoxProgram( check.program, othergens );
false
## ./../gap/bbox.gd (879-903)
gap> f:= FreeGroup( "x", "y" );; gens:= GeneratorsOfGroup( f );;
gap> slp:= StraightLineProgram( [ [1,2,2,3], [3,-1] ], 2 );
<straight line program>
gap> ResultOfStraightLineProgram( slp, gens );
y^-3*x^-2
gap> bboxslp:= AsBBoxProgram( slp );
<black box program>
gap> ResultOfBBoxProgram( bboxslp, gens );
[ y^-3*x^-2 ]
gap> lines:= [ [ "Order", 1, 2 ], [ "Order", 2, 3 ],
> [ [ 1, 1, 2, 1 ], 3 ], [ "Order", 3, 5 ] ];;
gap> dec:= StraightLineDecision( lines, 2 );
<straight line decision>
gap> ResultOfStraightLineDecision( dec, [ (1,2)(3,4), (1,3,5) ] );
true
gap> ResultOfStraightLineDecision( dec, [ (1,2)(3,4), (1,3,4) ] );
false
gap> bboxdec:= AsBBoxProgram( dec );
<black box program>
gap> ResultOfBBoxProgram( bboxdec, [ (1,2)(3,4), (1,3,5) ] );
true
gap> ResultOfBBoxProgram( bboxdec, [ (1,2)(3,4), (1,3,4) ] );
false
## ./../gap/bbox.gd (932-945)
gap> Display( AsStraightLineProgram( bboxslp ) );
# input:
r:= [ g1, g2 ];
# program:
r[3]:= r[1]^2;
r[4]:= r[2]^3;
r[5]:= r[3]*r[4];
r[3]:= r[5]^-1;
# return values:
[ r[3] ]
gap> AsStraightLineProgram( bboxdec );
fail
## ./../gap/mindeg.gd (192-203)
gap> MinimalRepresentationInfo( "A5", NrMovedPoints );
rec(
source := [ "computed (alternating group)",
"computed (char. table)", "computed (subgroup tables)",
"computed (subgroup tables, known repres.)",
"computed (table of marks)" ], value := 5 )
gap> MinimalRepresentationInfo( "A5", Characteristic, 2 );
rec( source := [ "computed (char. table)" ], value := 2 )
gap> MinimalRepresentationInfo( "A5", Size, 2 );
rec( source := [ "computed (char. table)" ], value := 4 )
## ./../gap/mindeg.gd (336-355)
gap> SetMinimalRepresentationInfo( "A5", "NrMovedPoints", 5,
> "computed (alternating group)" );
true
gap> SetMinimalRepresentationInfo( "A5", [ "Characteristic", 0 ], 3,
> "computed (char. table)" );
true
gap> SetMinimalRepresentationInfo( "A5", [ "Characteristic", 2 ], 2,
> "computed (char. table)" );
true
gap> SetMinimalRepresentationInfo( "A5", [ "Size", 2 ], 4,
> "computed (char. table)" );
true
gap> SetMinimalRepresentationInfo( "A5", [ "Size", 4 ], 2,
> "computed (char. table)" );
true
gap> SetMinimalRepresentationInfo( "A5", [ "Characteristic", 3 ], 3,
> "computed (char. table)" );
true
## ./../gap/scanmtx.gd (298-317)
gap> mat:= [ [ 1, -1 ], [ 0, 1 ] ] * Z(3)^0;;
gap> str:= MeatAxeString( mat, 3 );
"1 3 2 2\n12\n01\n"
gap> mat = ScanMeatAxeFile( str, "string" );
true
gap> str:= MeatAxeString( mat, 9 );
"1 9 2 2\n12\n01\n"
gap> mat = ScanMeatAxeFile( str, "string" );
true
gap> perms:= [ (1,2,3)(5,6) ];;
gap> str:= MeatAxeString( perms, 6 );
"12 1 6 1\n2\n3\n1\n4\n6\n5\n"
gap> perms = ScanMeatAxeFile( str, "string" );
true
gap> str:= MeatAxeString( perms, 8 );
"12 1 8 1\n2\n3\n1\n4\n6\n5\n7\n8\n"
gap> perms = ScanMeatAxeFile( str, "string" );
true
## ./../gap/scanmtx.gd (323-341)
gap> perm:= (1,2,4);;
gap> str:= MeatAxeString( perm, 3, [ 5, 6 ] );
"2 3 5 6\n2\n4\n3\n1\n5\n"
gap> mat:= ScanMeatAxeFile( str, "string" );; Print( mat, "\n" );
[ [ 0*Z(3), Z(3)^0, 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ],
[ 0*Z(3), 0*Z(3), 0*Z(3), Z(3)^0, 0*Z(3), 0*Z(3) ],
[ 0*Z(3), 0*Z(3), Z(3)^0, 0*Z(3), 0*Z(3), 0*Z(3) ],
[ Z(3)^0, 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ],
[ 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), Z(3)^0, 0*Z(3) ] ]
gap> pref:= UserPreference( "AtlasRep", "WriteMeatAxeFilesOfMode2" );;
gap> SetUserPreference( "AtlasRep", "WriteMeatAxeFilesOfMode2", true );
gap> MeatAxeString( mat, 3 ) = str;
true
gap> SetUserPreference( "AtlasRep", "WriteMeatAxeFilesOfMode2", false );
gap> MeatAxeString( mat, 3 );
"1 3 5 6\n010000\n000100\n001000\n100000\n000010\n"
gap> SetUserPreference( "AtlasRep", "WriteMeatAxeFilesOfMode2", pref );
## ./../gap/scanmtx.gd (104-109)
gap> FFList( GF(4) );
[ 0*Z(2), Z(2)^0, Z(2^2), Z(2^2)^2 ]
gap> IsBound( FFLists[4] );
true
## ./../gap/scanmtx.gd (389-403)
gap> tmpdir:= DirectoryTemporary();;
gap> mat:= Filename( tmpdir, "mat" );;
gap> q:= 4;;
gap> mats:= GeneratorsOfGroup( GL(10,q) );;
gap> CMtxBinaryFFMatOrPerm( mats[1], q, Concatenation( mat, "1" ) );
gap> CMtxBinaryFFMatOrPerm( mats[2], q, Concatenation( mat, "2" ) );
gap> prm:= Filename( tmpdir, "prm" );;
gap> n:= 200;;
gap> perms:= GeneratorsOfGroup( SymmetricGroup( n ) );;
gap> CMtxBinaryFFMatOrPerm( perms[1], n, Concatenation( prm, "1" ) );
gap> CMtxBinaryFFMatOrPerm( perms[2], n, Concatenation( prm, "2" ) );
gap> CMtxBinaryFFMatOrPerm( perms[1], n, Concatenation( prm, "1a" ), 0 );
gap> CMtxBinaryFFMatOrPerm( perms[2], n, Concatenation( prm, "2b" ), 1 );
## ./../gap/scanmtx.gd (430-443)
gap> FFMatOrPermCMtxBinary( Concatenation( mat, "1" ) ) = mats[1];
true
gap> FFMatOrPermCMtxBinary( Concatenation( mat, "2" ) ) = mats[2];
true
gap> FFMatOrPermCMtxBinary( Concatenation( prm, "1" ) ) = perms[1];
true
gap> FFMatOrPermCMtxBinary( Concatenation( prm, "2" ) ) = perms[2];
true
gap> FFMatOrPermCMtxBinary( Concatenation( prm, "1a" ) ) = perms[1];
true
gap> FFMatOrPermCMtxBinary( Concatenation( prm, "2b" ) ) = perms[2];
true
## ./../gap/scanmtx.gd (700-749)
gap> str:= "inp 2\nmu 1 2 3\nmu 3 1 2\niv 2 1\noup 2 1 2";;
gap> prg:= ScanStraightLineProgram( str, "string" );
rec( program := <straight line program> )
gap> prg:= prg.program;;
gap> Display( prg );
# input:
r:= [ g1, g2 ];
# program:
r[3]:= r[1]*r[2];
r[2]:= r[3]*r[1];
r[1]:= r[2]^-1;
# return values:
[ r[1], r[2] ]
gap> StringOfResultOfStraightLineProgram( prg, [ "a", "b" ] );
"[ (aba)^-1, aba ]"
gap> AtlasStringOfProgram( prg );
"inp 2\nmu 1 2 3\nmu 3 1 2\niv 2 1\noup 2\n"
gap> prg:= StraightLineProgram( "(a^2b^3)^-1", [ "a", "b" ] );
<straight line program>
gap> Print( AtlasStringOfProgram( prg ) );
inp 2
pwr 2 1 4
pwr 3 2 5
mu 4 5 3
iv 3 4
oup 1 4
gap> prg:= StraightLineProgram( [ [2,3], [ [3,1,1,4], [1,2,3,1] ] ], 2 );
<straight line program>
gap> Print( AtlasStringOfProgram( prg ) );
inp 2
pwr 3 2 3
pwr 4 1 5
mu 3 5 4
pwr 2 1 6
mu 6 3 5
oup 2 4 5
gap> Print( AtlasStringOfProgram( prg, "mtx" ) );
# inputs are expected in 1 2
zsm pwr3 2 3
zsm pwr4 1 5
zmu 3 5 4
zsm pwr2 1 6
zmu 6 3 5
echo "outputs are in 4 5"
gap> str:= "inp 2\nchor 1 2\nchor 2 3\nmu 1 2 3\nchor 3 5";;
gap> prg:= ScanStraightLineDecision( str );;
gap> AtlasStringOfProgram( prg.program );
"inp 2\nchor 1 2\nchor 2 3\nmu 1 2 3\nchor 3 5\n"
## ./../gap/access.gd (165-176)
gap> format:= [ [ [ IsChar, "G", IsDigitChar ],
> [ "p", IsDigitChar, AGR.IsLowerAlphaOrDigitChar,
> "B", IsDigitChar, ".m", IsDigitChar ] ],
> [ ParseBackwards, ParseForwards ] ];;
gap> AGR.ParseFilenameFormat( "A6G1-p10B0.m1", format );
[ "A6", "G", 1, "p", 10, "", "B", 0, ".m", 1 ]
gap> AGR.ParseFilenameFormat( "A6G1-p15aB0.m1", format );
[ "A6", "G", 1, "p", 15, "a", "B", 0, ".m", 1 ]
gap> AGR.ParseFilenameFormat( "A6G1-f2r16B0.m1", format );
fail
##
gap> if IsBound( BrowseData ) then
> BrowseData.defaults.dynamic.replayDefaults.replayInterval:= oldinterval;
> fi;
##
gap> STOP_TEST( "docxpl.tst", 10000000 );
gap> SizeScreen( save );;
#############################################################################
##
#E