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#@local M6, L6, M4, L4, M8, L8, L, A, M3, L3, M5, L5;
##############################################################################
##
#W matrix.tst Utils Package
##
#Y Copyright (C) 2015-2023, The GAP Group
##
gap> ReadPackage( "utils", "tst/loadall.g" );;
gap> UtilsLoadingComplete;
true
## SubSection 9.1.1
gap> M6 := [ [1,2,0,0,0,0], [3,4,0,0,0,0], [5,6,0,0,0,0],
> [0,0,9,0,0,0], [0,0,0,1,2,3], [0,0,0,4,5,6] ];;
gap> Display( M6 );
[ [ 1, 2, 0, 0, 0, 0 ],
[ 3, 4, 0, 0, 0, 0 ],
[ 5, 6, 0, 0, 0, 0 ],
[ 0, 0, 9, 0, 0, 0 ],
[ 0, 0, 0, 1, 2, 3 ],
[ 0, 0, 0, 4, 5, 6 ] ]
gap> L6 := DirectSumDecompositionMatrices( M6 );
[ [ [ [ 1, 2 ], [ 3, 4 ], [ 5, 6 ] ], [ [ 9 ] ], [ [ 1, 2, 3 ], [ 4, 5, 6 ] ]
] ]
gap> M4 := [ [0,3,0,0], [0,0,0,0], [0,0,0,0], [0,0,4,0] ];;
gap> Display( M4 );
[ [ 0, 3, 0, 0 ],
[ 0, 0, 0, 0 ],
[ 0, 0, 0, 0 ],
[ 0, 0, 4, 0 ] ]
gap> L4 := DirectSumDecompositionMatrices( M4 );
[ [ [ [ 0, 3 ] ], [ [ 0, 0 ], [ 0, 0 ], [ 4, 0 ] ] ],
[ [ [ 0, 3 ], [ 0, 0 ] ], [ [ 0, 0 ], [ 4, 0 ] ] ],
[ [ [ 0, 3 ], [ 0, 0 ], [ 0, 0 ] ], [ [ 4, 0 ] ] ] ]
gap> for L in L4 do
> A := DirectSumMat( L );;
> if ( A = M4 ) then Print( "yes, A = M4\n" ); fi;
> od;
yes, A = M4
yes, A = M4
yes, A = M4
gap> M8 := DirectSumMat( M4, M4 );;
gap> Display( M8 );
[ [ 0, 3, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 4, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 3, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 4, 0 ] ]
gap> L8 := DirectSumDecompositionMatrices( M8 );;
gap> Length( L8 );
16
gap> M3 := [ [0,0,0,7,0,0,0], [0,0,0,0,8,0,0], [0,0,0,0,0,9,0] ];;
gap> Display( M3 );
[ [ 0, 0, 0, 7, 0, 0, 0 ],
[ 0, 0, 0, 0, 8, 0, 0 ],
[ 0, 0, 0, 0, 0, 9, 0 ] ]
gap> L3 := DirectSumDecompositionMatrices( M3 );
[ [ [ [ 0, 0, 0, 7 ] ], [ [ 8 ] ], [ [ 9, 0 ] ] ] ]
gap> M5 := [ [1,2,0,0,0], [3,4,0,0,0], [0,0,0,0,0],
> [0,0,0,6,7], [0,0,0,8,9] ];;
gap> Display(M5);
[ [ 1, 2, 0, 0, 0 ],
[ 3, 4, 0, 0, 0 ],
[ 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 6, 7 ],
[ 0, 0, 0, 8, 9 ] ]
gap> L5 := DirectSumDecompositionMatrices( M5 );
[ [ [ [ 1, 2 ], [ 3, 4 ] ], [ [ 0 ] ], [ [ 6, 7 ], [ 8, 9 ] ] ] ]
#############################################################################
##
#E matrix.tst . . . . . . . . . . . . . . . . . . . . . . . . . . ends here
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