Spracherkennung für: .include vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen]
gap> id := IdentityMat(8,GF(7));
< mutable compressed matrix 8x8 over GF(7) >
gap> form := BilinearFormByMatrix(id,GF(7));
< bilinear form >
gap> ps := PolarSpace(form);
<polar space in ProjectiveSpace(
7,GF(7)): x_1^2+x_2^2+x_3^2+x_4^2+x_5^2+x_6^2+x_7^2+x_8^2=0 >
gap> Rank(ps);
4
gap> ps;
Q+(7, 7): x_1^2+x_2^2+x_3^2+x_4^2+x_5^2+x_6^2+x_7^2+x_8^2=0
gap> mat := [[1,0,0,0,3,2,0,0],[0,1,0,0,0,0,3,2],[0,0,1,0,5,3,0,0]]*Z(7)^0;
[ [ Z(7)^0, 0*Z(7), 0*Z(7), 0*Z(7), Z(7), Z(7)^2, 0*Z(7), 0*Z(7) ],
[ 0*Z(7), Z(7)^0, 0*Z(7), 0*Z(7), 0*Z(7), 0*Z(7), Z(7), Z(7)^2 ],
[ 0*Z(7), 0*Z(7), Z(7)^0, 0*Z(7), Z(7)^5, Z(7), 0*Z(7), 0*Z(7) ] ]
gap> plane := VectorSpaceToElement(ps,mat);
<a plane in Q+(7, 7): x_1^2+x_2^2+x_3^2+x_4^2+x_5^2+x_6^2+x_7^2+x_8^2=0>
gap> time;
1
gap> shadow := ShadowOfElement(ps,plane,4);
<shadow solids in Q+(7, 7): x_1^2+x_2^2+x_3^2+x_4^2+x_5^2+x_6^2+x_7^2+x_8^2=0>
gap> List(shadow);
[ <a solid in Q+(7, 7): x_1^2+x_2^2+x_3^2+x_4^2+x_5^2+x_6^2+x_7^2+x_8^2=0>,
<a solid in Q+(7, 7): x_1^2+x_2^2+x_3^2+x_4^2+x_5^2+x_6^2+x_7^2+x_8^2=0> ]
gap> shadow := ShadowOfElement(ps,plane,2);
<shadow lines in Q+(7, 7): x_1^2+x_2^2+x_3^2+x_4^2+x_5^2+x_6^2+x_7^2+x_8^2=0>
