| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/fining/examples/include/ (Algebra von RWTH Aachen Version 4.15.1©) Datei vom 27.6.2023 mit Größe 2 kB |
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SSL morphisms_isopolar.include
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rahmenlose Ansicht.include DruckansichtUnknown {[0] [0] [0]}Entwicklung gap> mat1 := IdentityMat(6,GF(5)); < mutable compressed matrix 6x6 over GF(5) > gap> form1 := BilinearFormByMatrix(mat1,GF(5)); < bilinear form > gap> ps1 := PolarSpace(form1); <polar space in ProjectiveSpace( 5,GF(5)): x_1^2+x_2^2+x_3^2+x_4^2+x_5^2+x_6^2=0 > gap> mat2 := [[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0], > [0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]]*Z(5)^0; [ [ 0*Z(5), 0*Z(5), 0*Z(5), 0*Z(5), 0*Z(5), Z(5)^0 ], [ 0*Z(5), 0*Z(5), 0*Z(5), 0*Z(5), Z(5)^0, 0*Z(5) ], [ 0*Z(5), 0*Z(5), 0*Z(5), Z(5)^0, 0*Z(5), 0*Z(5) ], [ 0*Z(5), 0*Z(5), 0*Z(5), 0*Z(5), 0*Z(5), 0*Z(5) ], [ 0*Z(5), 0*Z(5), 0*Z(5), 0*Z(5), 0*Z(5), 0*Z(5) ], [ 0*Z(5), 0*Z(5), 0*Z(5), 0*Z(5), 0*Z(5), 0*Z(5) ] ] gap> form2 := QuadraticFormByMatrix(mat2,GF(5)); < quadratic form > gap> ps2 := PolarSpace(form2); <polar space in ProjectiveSpace(5,GF(5)): x_1*x_6+x_2*x_5+x_3*x_4=0 > gap> iso := IsomorphismPolarSpaces(ps1,ps2,true); #I No intertwiner computed. One of the polar spaces must have a collineation group computed <geometry morphism from <Elements of Q+(5, 5): x_1^2+x_2^2+x_3^2+x_4^2+x_5^2+x_6^2=0> to <Elements of Q+(5, 5): x_1*x_6+x_2*x_5+x_3*x_4=0>> gap> CollineationGroup(ps1); #I Computing collineation group of canonical polar space... <projective collineation group of size 58032000000 with 4 generators> gap> CollineationGroup(ps2); #I Computing collineation group of canonical polar space... <projective collineation group of size 58032000000 with 4 generators> gap> iso := IsomorphismPolarSpaces(ps1,ps2,true); <geometry morphism from <Elements of Q+(5, 5): x_1^2+x_2^2+x_3^2+x_4^2+x_5^2+x_6^2=0> to <Elements of Q+(5, 5): x_1*x_6+x_2*x_5+x_3*x_4=0>> gap> hom := Intertwiner( iso ); MappingByFunction( <projective collineation group of size 58032000000 with 4 generators>, <projective collineation group of size 58032000000 with 4 generators>, function( y ) ... end, function( x ) ... end ) gap> ps1 := ParabolicQuadric(6,8); Q(6, 8) gap> ps2 := SymplecticSpace(5,8); W(5, 8) gap> em := IsomorphismPolarSpaces(ps1,ps2); #I Have 36171 points. #I Have 37381 points in new orbit. #I Have 36171 points. #I Have 37388 points in new orbit. <geometry morphism from <Elements of Q(6, 8)> to <Elements of W(5, 8)>> gap> hom := Intertwiner(em); MappingByFunction( PGammaO(7,8), <projective collineation group of size 27231016821530296320 with 3 generators>, function( el ) ... end, function( el ) ... end ) [ Verzeichnis aufwärts0.66unsichere Verbindung ] |
2026-03-28