Spracherkennung für: .tst vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen]
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#W 4.1.14.tst GAP4 package IBNP Gareth Evans & Chris Wensley
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## Copyright (C) 2024: please refer to the COPYRIGHT file for details.
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gap> START_TEST( "4.1.14.tst" );
gap> ibnp_infolevel_saved := InfoLevel( InfoIBNP );;
gap> SetInfoLevel( InfoIBNP, 0 );;
gap> ## this implements Example 4.1.14 in the thesis,
gap> ## using four different orderings when finding a Grobner basis,
gap> ## and where GB3 = GB4 is the Grobner basis found there
gap> R := PolynomialRing( Rationals, [ "x", "y", "z" ] );;
gap> x := R.1;; y := R.2;; z := R.3;;
gap> U := [ x^5*y^2*z, x^4*y*z^2, x^2*y^2*z, x*y*z^3, x*z^3, y^2*z, z ];
[ x^5*y^2*z, x^4*y*z^2, x^2*y^2*z, x*y*z^3, x*z^3, y^2*z, z ]
gap> ord := MonomialLexOrdering( [x,y,z] );;
gap> PommaretDivision( R, U, ord );
[ [ 1 ], [ 1 ], [ 1 ], [ 1 ], [ 1 ], [ 1, 2 ], [ 1 .. 3 ] ]
gap> ThomasDivision( R, U, ord );
[ [ 1, 2 ], [ ], [ 2 ], [ 3 ], [ 3 ], [ 2 ], [ ] ]
gap> JanetDivision( R, U, ord );
[ [ 1, 2 ], [ 1, 2 ], [ 2 ], [ 1, 2, 3 ], [ 1, 3 ], [ 2 ], [ 1 ] ]
gap> ##
gap> ## get the same results using OverlapDivCP
gap> ##
gap> CommutativeDivision := "Thomas";
"Thomas"
gap> DivisionRecord( R, U, ord );
rec( div := "Thomas",
mvars := [ [ 1, 2 ], [ ], [ 2 ], [ 3 ], [ 3 ], [ 2 ], [ ] ],
polys := [ x^5*y^2*z, x^4*y*z^2, x^2*y^2*z, x*y*z^3, x*z^3, y^2*z, z ] )
gap> CommutativeDivision := "Janet";
"Janet"
gap> DivisionRecord( R, U, ord );
rec( div := "Janet",
mvars := [ [ 1, 2 ], [ 1, 2 ], [ 2 ], [ 1, 2, 3 ], [ 1, 3 ], [ 2 ], [ 1 ] ],
polys := [ x^5*y^2*z, x^4*y*z^2, x^2*y^2*z, x*y*z^3, x*z^3, y^2*z, z ] )
gap> CommutativeDivision := "Pommaret";
"Pommaret"
gap> DivisionRecord( R, U, ord );
rec( div := "Pommaret",
mvars := [ [ 1 ], [ 1 ], [ 1 ], [ 1 ], [ 1 ], [ 1, 2 ], [ 1 .. 3 ] ],
polys := [ x^5*y^2*z, x^4*y*z^2, x^2*y^2*z, x*y*z^3, x*z^3, y^2*z, z ] )
gap> SetInfoLevel( InfoIBNP, ibnp_infolevel_saved );;
gap> STOP_TEST( "4.1.14.tst", 10000 );
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#E 4.1.14.tst . . . . . . . . . . . . . . . . . . . . . . . . . . ends here
