{"rank":4,"n":9,"seq":187579,"label":"4.9.187579","id":"r4_n9_00000000000000000**0*****0*********00**0*****0*********000******0*****00**0*****0*********0**00***0******0****000************0","beta_invariant":9,"birational_type":"empty","birational_type_components":"[]","birational_type_method":"empty_char0","char_poly_splits":false,"char_set":"[0]","expected_dimension_over_Z":null,"free_realization_space":false,"girth":2,"good_basis":null,"good_basis_v2":"1,3,4,7","is_binary":false,"is_coloopless":true,"is_connected":true,"is_divisionally_free":false,"is_graphic":false,"is_identically_self_dual":false,"is_laminar":false,"is_loopless":true,"is_nested":false,"is_orientable":false,"is_paving":false,"is_quaternary":true,"is_realizable":true,"is_realizable_char0":true,"is_regular":false,"is_self_dual":false,"is_series_parallel":false,"is_simple":false,"is_simplicial_arrangement":false,"is_supersolvable":false,"is_ternary":false,"is_three_lines":null,"is_transversal":false,"is_uniform":null,"n_automorphisms":12,"n_bases":86,"n_circuits":38,"n_components":null,"n_connected_components":1,"n_cyclic_flats":11,"n_flats":64,"n_loops":0,"principal_ideal":true,"rs_characteristic_dimension_unexpected":null,"rs_characteristic_dimension_varies":null,"rs_characteristic_dimensions":null,"rs_characteristic_dimensions_method":null,"rs_dim":2,"rs_is_regular_scheme":null,"rs_is_smooth_over_QQ":null,"rs_is_smooth_over_ZZ":null,"rs_n_qbar_components":null,"rs_regularity_method":null,"rs_regularity_witness":null,"rs_scheme_simple_core_id":null,"rs_singular_fiber_characteristics":null,"rs_singular_fiber_characteristics_method":null,"rs_singular_fiber_primes":null,"rs_singular_fiber_primes_method":null,"rs_smoothness_method":null,"rs_smoothness_witness":null,"singular_primes":"[]","smooth_char_0":true,"status":"computed_realization_space","tutte_polynomial":"x_0^4 + x_0^3*x_1 + 4*x_0^3 + 4*x_0^2*x_1 + 10*x_0^2 + x_0*x_1^3 + 6*x_0*x_1^2 + 14*x_0*x_1 + 9*x_0 + x_1^5 + 4*x_1^4 + 9*x_1^3 + 13*x_1^2 + 9*x_1","realization_space":{"vars":["x1"],"ideal":["2"],"inequations":["x1 - 1","x1"],"matrix":[["1","1","0","0","1","1","0","1","1"],["0","0","1","0","1","-x1 + 1","0","1","0"],["0","0","0","1","1","x1","0","0","1"],["0","0","0","0","0","0","1","1","1"]]}}