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[hanaki@kissme home]$ gap
игибибибибибибибид GAP, Version 4.5.5 of 16-Jul-2012 (free software, GPL)
ив GAP ив http://www.gap-system.org
ижибибибибибибибие Architecture: i686-pc-linux-gnu-gcc-default32
Libs used: gmp
Loading the library and packages ...
#I You are using an old /home/hanaki/.gaprc file.
#I See '?Ref: The former .gaprc file' for hints to upgrade.
Components: trans 1.0, prim 2.1, small* 1.0, id* 1.0
Packages: AClib 1.2, Alnuth 3.0.0, AutPGrp 1.5, CRISP 1.3.5,
Cryst 4.1.10, CrystCat 1.1.6, CTblLib 1.2.1, FactInt 1.5.3,
FGA 1.1.1, GAPDoc 1.5.1, IRREDSOL 1.2.1, LAGUNA 3.6.1,
Polenta 1.3.1, Polycyclic 2.10.1, RadiRoot 2.6,
ResClasses 3.1.1, Sophus 1.23, TomLib 1.2.2
Try '?help' for help. See also '?copyright' and '?authors'
gap> Read("association_scheme.gap");
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Loading GRAPE 4.6.1 (GRaph Algorithms using PErmutation groups)
by Leonard H. Soicher (http://www.maths.qmul.ac.uk/~leonard/).
Homepage: http://www.maths.qmul.ac.uk/~leonard/grape/
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gap> R := HammingScheme(4,2);;
gap> Display(R);
[ [ 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 ],
[ 1, 0, 2, 1, 2, 1, 3, 2, 2, 1, 3, 2, 3, 2, 4, 3 ],
[ 1, 2, 0, 1, 2, 3, 1, 2, 2, 3, 1, 2, 3, 4, 2, 3 ],
[ 2, 1, 1, 0, 3, 2, 2, 1, 3, 2, 2, 1, 4, 3, 3, 2 ],
[ 1, 2, 2, 3, 0, 1, 1, 2, 2, 3, 3, 4, 1, 2, 2, 3 ],
[ 2, 1, 3, 2, 1, 0, 2, 1, 3, 2, 4, 3, 2, 1, 3, 2 ],
[ 2, 3, 1, 2, 1, 2, 0, 1, 3, 4, 2, 3, 2, 3, 1, 2 ],
[ 3, 2, 2, 1, 2, 1, 1, 0, 4, 3, 3, 2, 3, 2, 2, 1 ],
[ 1, 2, 2, 3, 2, 3, 3, 4, 0, 1, 1, 2, 1, 2, 2, 3 ],
[ 2, 1, 3, 2, 3, 2, 4, 3, 1, 0, 2, 1, 2, 1, 3, 2 ],
[ 2, 3, 1, 2, 3, 4, 2, 3, 1, 2, 0, 1, 2, 3, 1, 2 ],
[ 3, 2, 2, 1, 4, 3, 3, 2, 2, 1, 1, 0, 3, 2, 2, 1 ],
[ 2, 3, 3, 4, 1, 2, 2, 3, 1, 2, 2, 3, 0, 1, 1, 2 ],
[ 3, 2, 4, 3, 2, 1, 3, 2, 2, 1, 3, 2, 1, 0, 2, 1 ],
[ 3, 4, 2, 3, 2, 3, 1, 2, 2, 3, 1, 2, 1, 2, 0, 1 ],
[ 4, 3, 3, 2, 3, 2, 2, 1, 3, 2, 2, 1, 2, 1, 1, 0 ] ]
gap> trad := ThinRadical(R);
[ 0, 4 ]
gap> tres := ThinResidue(R);
[ 0, 2, 4 ]
gap> R2 := RelationMatrixSortedByClosedSubset(R, trad);;
gap> Display(R2);
[ [ 0, 4, 1, 3, 1, 3, 2, 2, 1, 3, 2, 2, 2, 2, 3, 1 ],
[ 4, 0, 3, 1, 3, 1, 2, 2, 3, 1, 2, 2, 2, 2, 1, 3 ],
[ 1, 3, 0, 4, 2, 2, 1, 3, 2, 2, 1, 3, 3, 1, 2, 2 ],
[ 3, 1, 4, 0, 2, 2, 3, 1, 2, 2, 3, 1, 1, 3, 2, 2 ],
[ 1, 3, 2, 2, 0, 4, 1, 3, 2, 2, 3, 1, 1, 3, 2, 2 ],
[ 3, 1, 2, 2, 4, 0, 3, 1, 2, 2, 1, 3, 3, 1, 2, 2 ],
[ 2, 2, 1, 3, 1, 3, 0, 4, 3, 1, 2, 2, 2, 2, 1, 3 ],
[ 2, 2, 3, 1, 3, 1, 4, 0, 1, 3, 2, 2, 2, 2, 3, 1 ],
[ 1, 3, 2, 2, 2, 2, 3, 1, 0, 4, 1, 3, 1, 3, 2, 2 ],
[ 3, 1, 2, 2, 2, 2, 1, 3, 4, 0, 3, 1, 3, 1, 2, 2 ],
[ 2, 2, 1, 3, 3, 1, 2, 2, 1, 3, 0, 4, 2, 2, 1, 3 ],
[ 2, 2, 3, 1, 1, 3, 2, 2, 3, 1, 4, 0, 2, 2, 3, 1 ],
[ 2, 2, 3, 1, 1, 3, 2, 2, 1, 3, 2, 2, 0, 4, 1, 3 ],
[ 2, 2, 1, 3, 3, 1, 2, 2, 3, 1, 2, 2, 4, 0, 3, 1 ],
[ 3, 1, 2, 2, 2, 2, 1, 3, 2, 2, 1, 3, 1, 3, 0, 4 ],
[ 1, 3, 2, 2, 2, 2, 3, 1, 2, 2, 3, 1, 3, 1, 4, 0 ] ]
gap> R3 := RelationMatrixSortedByClosedSubset(R, tres);;
gap> Display(R3);
[ [ 0, 2, 2, 2, 2, 2, 2, 4, 1, 1, 1, 3, 1, 3, 3, 3 ],
[ 2, 0, 2, 2, 2, 2, 4, 2, 1, 1, 3, 1, 3, 1, 3, 3 ],
[ 2, 2, 0, 2, 2, 4, 2, 2, 1, 3, 1, 1, 3, 3, 1, 3 ],
[ 2, 2, 2, 0, 4, 2, 2, 2, 3, 1, 1, 1, 3, 3, 3, 1 ],
[ 2, 2, 2, 4, 0, 2, 2, 2, 1, 3, 3, 3, 1, 1, 1, 3 ],
[ 2, 2, 4, 2, 2, 0, 2, 2, 3, 1, 3, 3, 1, 1, 3, 1 ],
[ 2, 4, 2, 2, 2, 2, 0, 2, 3, 3, 1, 3, 1, 3, 1, 1 ],
[ 4, 2, 2, 2, 2, 2, 2, 0, 3, 3, 3, 1, 3, 1, 1, 1 ],
[ 1, 1, 1, 3, 1, 3, 3, 3, 0, 2, 2, 2, 2, 2, 2, 4 ],
[ 1, 1, 3, 1, 3, 1, 3, 3, 2, 0, 2, 2, 2, 2, 4, 2 ],
[ 1, 3, 1, 1, 3, 3, 1, 3, 2, 2, 0, 2, 2, 4, 2, 2 ],
[ 3, 1, 1, 1, 3, 3, 3, 1, 2, 2, 2, 0, 4, 2, 2, 2 ],
[ 1, 3, 3, 3, 1, 1, 1, 3, 2, 2, 2, 4, 0, 2, 2, 2 ],
[ 3, 1, 3, 3, 1, 1, 3, 1, 2, 2, 4, 2, 2, 0, 2, 2 ],
[ 3, 3, 1, 3, 1, 3, 1, 1, 2, 4, 2, 2, 2, 2, 0, 2 ],
[ 3, 3, 3, 1, 3, 1, 1, 1, 4, 2, 2, 2, 2, 2, 2, 0 ] ]
gap> R4 := Subscheme(R, trad);;
gap> Display(R4);
[ [ 0, 1 ],
[ 1, 0 ] ]
gap> R5 := Subscheme(R, tres, 1);;
gap> Display(R5);
[ [ 0, 1, 1, 1, 1, 1, 1, 2 ],
[ 1, 0, 1, 1, 1, 1, 2, 1 ],
[ 1, 1, 0, 1, 1, 2, 1, 1 ],
[ 1, 1, 1, 0, 2, 1, 1, 1 ],
[ 1, 1, 1, 2, 0, 1, 1, 1 ],
[ 1, 1, 2, 1, 1, 0, 1, 1 ],
[ 1, 2, 1, 1, 1, 1, 0, 1 ],
[ 2, 1, 1, 1, 1, 1, 1, 0 ] ]
gap> R6 := FactorScheme(R, trad);;
gap> Display(R6);
[ [ 0, 1, 1, 2, 1, 2, 2, 1 ],
[ 1, 0, 2, 1, 2, 1, 1, 2 ],
[ 1, 2, 0, 1, 2, 1, 1, 2 ],
[ 2, 1, 1, 0, 1, 2, 2, 1 ],
[ 1, 2, 2, 1, 0, 1, 1, 2 ],
[ 2, 1, 1, 2, 1, 0, 2, 1 ],
[ 2, 1, 1, 2, 1, 2, 0, 1 ],
[ 1, 2, 2, 1, 2, 1, 1, 0 ] ]
gap> R7 := FactorScheme(R, tres);;
gap> Display(R7);
[ [ 0, 1 ],
[ 1, 0 ] ]
gap> IsThin(R6);
false
gap> IsThin(R7);
true
gap> IsQuasiThin(R6);
false
gap> IsQuasiThin(R7);
false
gap> quit;
[hanaki@kissme home]$