{"rank":4,"n":9,"seq":189480,"label":"4.9.189480","id":"r4_n9_00000000000000000000000000000000000000000*0**00*0**0***00*0**0***0****000000*0**00*0**0***00*0**0***0****000000000000000000000","beta_invariant":0,"birational_type":"rational","birational_type_components":"[{\"dim\":3,\"free_rank\":3,\"torus_rank\":3,\"core_dim\":0,\"qbar_components\":1,\"type\":\"rational\",\"reason\":\"free realization space\"}]","birational_type_method":"free_presentation","char_poly_splits":false,"char_set":"[0]","expected_dimension_over_Z":null,"free_realization_space":true,"girth":1,"good_basis":null,"good_basis_v2":"2,3,5,8","is_binary":false,"is_coloopless":true,"is_connected":false,"is_divisionally_free":false,"is_graphic":false,"is_identically_self_dual":false,"is_laminar":true,"is_loopless":false,"is_nested":false,"is_orientable":true,"is_paving":false,"is_quaternary":false,"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":true,"is_uniform":null,"n_automorphisms":72,"n_bases":38,"n_circuits":15,"n_components":null,"n_connected_components":3,"n_cyclic_flats":6,"n_flats":42,"n_loops":1,"principal_ideal":true,"rs_characteristic_dimension_unexpected":null,"rs_characteristic_dimension_varies":null,"rs_characteristic_dimensions":null,"rs_characteristic_dimensions_method":null,"rs_dim":1,"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_1 + x_0^3*x_1^2 + 3*x_0^3*x_1 + 4*x_0^2*x_1^2 + 5*x_0^2*x_1 + x_0*x_1^4 + 4*x_0*x_1^3 + 10*x_0*x_1^2 + x_1^5 + 3*x_1^4 + 5*x_1^3","realization_space":{"vars":["x1","x2","x3"],"ideal":["0"],"inequations":["x1*x3 - x2","x3 - 1","x1*x3 - x2 - x3 + 1","x1 - x2","x2","x2 - 1","x3","x1","x1 - 1"],"matrix":[["0","1","0","1","0","1","1","0","0"],["0","0","1","1","0","x1","x2","0","0"],["0","0","0","0","1","1","x3","0","0"],["0","0","0","0","0","0","0","1","1"]]}}