Quelle test_forms5.tst
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Quellsprache: Binärcode.tst aufgebrochen in jeweils 16 ZeichenUnknown {[0] [0] [0]}zum Wurzelverzeichnis wechseln
gap> START_TEST("Forms: test_forms5.tst");
gap> f := GF(9);
GF(3^2)
gap> gram := [[0,0,0,Z(9)^2],[0,0,1,0],[0,1,0,0],[-Z(9)^2,0,0,0]]*Z(9)^0;
[ [ 0*Z(3), 0*Z(3), 0*Z(3), Z(3^2)^2 ], [ 0*Z(3), 0*Z(3), Z(3)^0, 0*Z(3) ],
[ 0*Z(3), Z(3)^0, 0*Z(3), 0*Z(3) ], [ Z(3^2)^6, 0*Z(3), 0*Z(3), 0*Z(3) ] ]
gap> form := HermitianFormByMatrix(gram,f);
< hermitian form >
gap> TypeOfForm(form);
1/2
gap> BaseChangeToCanonical(form);
[ [ Z(3)^0, 0*Z(3), 0*Z(3), Z(3^2)^3 ], [ Z(3^2), 0*Z(3), 0*Z(3), Z(3^2)^2 ],
[ 0*Z(3), Z(3^2), Z(3)^0, 0*Z(3) ], [ 0*Z(3), Z(3^2)^2, Z(3^2)^3, 0*Z(3) ] ]
gap> iso := IsometricCanonicalForm(form);
< hermitian form >
gap> Display(form);
Hermitian form
Gram Matrix:
z = Z(9)
. . . z^2
. . 1 .
. 1 . .
z^6 . . .
Witt Index: 2
gap> Display(iso);
Hermitian form
Gram Matrix:
1 . . .
. 1 . .
. . 1 .
. . . 1
Witt Index: 2
gap> STOP_TEST("test_forms5.tst", 10000 );
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2026-03-28
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