Gr3(R^(10,1))

The AutoKron can't determine the cohomology of $\text{Gr}_3(\mathbb{R}^{10,1})$.

There are 4 possibilities.
Here are their Poincaré polynomials: $$x^{21} y^{3} + x^{20} y^{3} + 2 x^{19} y^{3} + 3 x^{18} y^{3} + 4 x^{17} y^{3} + 4 x^{16} y^{3} + x^{16} y^{2} + 5 x^{15} y^{3} + 2 x^{15} y^{2} + 4 x^{14} y^{3} + 4 x^{14} y^{2} + 4 x^{13} y^{3} + 5 x^{13} y^{2} + 3 x^{12} y^{3} + 7 x^{12} y^{2} + 2 x^{11} y^{3} + 8 x^{11} y^{2} + x^{10} y^{3} + 9 x^{10} y^{2} + x^{9} y^{3} + 8 x^{9} y^{2} + x^{9} y + 7 x^{8} y^{2} + 2 x^{8} y + 5 x^{7} y^{2} + 3 x^{7} y + 4 x^{6} y^{2} + 3 x^{6} y + 2 x^{5} y^{2} + 3 x^{5} y + x^{4} y^{2} + 3 x^{4} y + 3 x^{3} y + 2 x^{2} y + x y + 1$$ $$x^{21} y^{3} + x^{20} y^{3} + 2 x^{19} y^{3} + 3 x^{18} y^{3} + 4 x^{17} y^{3} + 4 x^{16} y^{3} + x^{16} y^{2} + 5 x^{15} y^{3} + 2 x^{15} y^{2} + 4 x^{14} y^{3} + 4 x^{14} y^{2} + 4 x^{13} y^{3} + 5 x^{13} y^{2} + 3 x^{12} y^{3} + 7 x^{12} y^{2} + 2 x^{11} y^{3} + 8 x^{11} y^{2} + 10 x^{10} y^{2} + x^{9} y^{3} + 9 x^{9} y^{2} + 7 x^{8} y^{2} + 2 x^{8} y + 5 x^{7} y^{2} + 3 x^{7} y + 4 x^{6} y^{2} + 3 x^{6} y + 2 x^{5} y^{2} + 3 x^{5} y + x^{4} y^{2} + 3 x^{4} y + 3 x^{3} y + 2 x^{2} y + x y + 1$$ $$x^{21} y^{3} + x^{20} y^{3} + 2 x^{19} y^{3} + 3 x^{18} y^{3} + 4 x^{17} y^{3} + 4 x^{16} y^{3} + x^{16} y^{2} + 5 x^{15} y^{3} + 2 x^{15} y^{2} + 4 x^{14} y^{3} + 4 x^{14} y^{2} + 4 x^{13} y^{3} + 5 x^{13} y^{2} + 3 x^{12} y^{3} + 7 x^{12} y^{2} + 2 x^{11} y^{3} + 8 x^{11} y^{2} + x^{10} y^{3} + 9 x^{10} y^{2} + 9 x^{9} y^{2} + x^{9} y + 8 x^{8} y^{2} + x^{8} y + 5 x^{7} y^{2} + 3 x^{7} y + 4 x^{6} y^{2} + 3 x^{6} y + 2 x^{5} y^{2} + 3 x^{5} y + x^{4} y^{2} + 3 x^{4} y + 3 x^{3} y + 2 x^{2} y + x y + 1$$ $$x^{21} y^{3} + x^{20} y^{3} + 2 x^{19} y^{3} + 3 x^{18} y^{3} + 4 x^{17} y^{3} + 4 x^{16} y^{3} + x^{16} y^{2} + 5 x^{15} y^{3} + 2 x^{15} y^{2} + 4 x^{14} y^{3} + 4 x^{14} y^{2} + 4 x^{13} y^{3} + 5 x^{13} y^{2} + 3 x^{12} y^{3} + 7 x^{12} y^{2} + 2 x^{11} y^{3} + 8 x^{11} y^{2} + 10 x^{10} y^{2} + 10 x^{9} y^{2} + 8 x^{8} y^{2} + x^{8} y + 5 x^{7} y^{2} + 3 x^{7} y + 4 x^{6} y^{2} + 3 x^{6} y + 2 x^{5} y^{2} + 3 x^{5} y + x^{4} y^{2} + 3 x^{4} y + 3 x^{3} y + 2 x^{2} y + x y + 1$$ Here are the corresponding generator grids to these 4 possibilities: