{"rank":4,"n":8,"seq":303,"label":"4.8.303","id":"r4_n8_00***0******0**0*******0******0****0********0*************************","beta_invariant":12,"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":"[3]","expected_dimension_over_Z":null,"free_realization_space":true,"girth":3,"good_basis":null,"good_basis_v2":"1,3,4,5","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":true,"is_paving":false,"is_quaternary":false,"is_realizable":true,"is_realizable_char0":false,"is_regular":false,"is_self_dual":false,"is_series_parallel":false,"is_simple":true,"is_simplicial_arrangement":false,"is_supersolvable":false,"is_ternary":false,"is_three_lines":null,"is_transversal":false,"is_uniform":null,"n_automorphisms":2,"n_bases":61,"n_circuits":35,"n_components":1,"n_connected_components":1,"n_cyclic_flats":7,"n_flats":69,"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":-1,"rs_is_regular_scheme":null,"rs_is_smooth_over_QQ":null,"rs_is_smooth_over_ZZ":null,"rs_n_qbar_components":1,"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 + 4*x_0^3 + x_0^2*x_1 + 9*x_0^2 + 7*x_0*x_1 + 12*x_0 + x_1^4 + 4*x_1^3 + 10*x_1^2 + 12*x_1","realization_space":{"vars":["x1","x2","x3"],"ideal":["0"],"inequations":["x1 - x2 + x3 - 1","x1*x3 + x1 - x2 - 1","x1 - 1","x3","x1 - x2 - 1","x1 - x2","x1","x2","x3 - 1","x1*x3 - x2","x2 + 1","x3 + 1","x2 - x3"],"matrix":[["1","1","0","0","0","1","1","0"],["0","1","1","0","0","0","1","1"],["0","0","0","1","0","1","x1","x2"],["0","0","0","0","1","1","1","x3"]]}}