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gap> pg:=PG(5,3);
ProjectiveSpace(5, 3)
gap> planes:=Planes(pg);
<planes of ProjectiveSpace(5, 3)>
gap> gv:=GrassmannVariety(2,pg);
Grassmann Variety in ProjectiveSpace(19, 3)
gap> DefiningListOfPolynomials(gv);
[ x_13*x_20-x_15*x_19+x_16*x_18, x_12*x_20-x_14*x_19+x_16*x_17,
x_11*x_20-x_14*x_18+x_15*x_17, x_11*x_19-x_12*x_18+x_13*x_17,
x_7*x_20-x_9*x_19+x_10*x_18, x_6*x_20-x_8*x_19+x_10*x_17,
x_5*x_20-x_8*x_18+x_9*x_17, x_5*x_19-x_6*x_18+x_7*x_17,
x_4*x_20-x_9*x_16+x_10*x_15, x_4*x_19-x_7*x_16+x_10*x_13,
x_4*x_18-x_7*x_15+x_9*x_13, x_4*x_17+x_5*x_16-x_6*x_15+x_8*x_13,
x_3*x_20-x_8*x_16+x_10*x_14, x_3*x_19-x_6*x_16+x_10*x_12,
x_3*x_18-x_5*x_16-x_7*x_14+x_9*x_12, x_3*x_18-x_4*x_17-x_5*x_16+x_10*x_11,
x_3*x_17-x_6*x_14+x_8*x_12, x_2*x_20-x_8*x_15+x_9*x_14,
x_2*x_19-x_6*x_15+x_7*x_14+x_10*x_11, x_2*x_19+x_4*x_17-x_6*x_15+x_9*x_12,
x_2*x_19-x_3*x_18+x_7*x_14-x_8*x_13, x_2*x_18-x_5*x_15+x_9*x_11,
x_2*x_17-x_5*x_14+x_8*x_11, x_2*x_16-x_3*x_15+x_4*x_14,
x_1*x_20-x_8*x_13+x_9*x_12-x_10*x_11, x_1*x_20-x_4*x_17+x_7*x_14-x_8*x_13,
x_1*x_20+x_3*x_18-x_6*x_15+x_9*x_12, x_1*x_20-x_2*x_19+x_5*x_16-x_10*x_11,
x_1*x_19-x_6*x_13+x_7*x_12, x_1*x_18-x_5*x_13+x_7*x_11,
x_1*x_17-x_5*x_12+x_6*x_11, x_1*x_16-x_3*x_13+x_4*x_12,
x_1*x_15-x_2*x_13+x_4*x_11, x_1*x_14-x_2*x_12+x_3*x_11 ]
gap> Size(Points(gv));
33880
gap> gm:=GrassmannMap(gv);
Grassmann Map of <planes of ProjectiveSpace(5, 3)>
[ Dauer der Verarbeitung: 0.13 Sekunden
(vorverarbeitet)
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