{"rank":3,"n":9,"seq":919,"label":"3.9.919","id":"r3_n9_000000000000000000000**************0****************0***0*****************0*********","beta_invariant":7,"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":4,"free_realization_space":true,"girth":2,"good_basis":null,"good_basis_v2":"1,3,7","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":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":false,"is_uniform":null,"n_automorphisms":8,"n_bases":59,"n_circuits":55,"n_components":1,"n_connected_components":1,"n_cyclic_flats":6,"n_flats":25,"n_loops":0,"principal_ideal":true,"rs_characteristic_dimension_unexpected":false,"rs_characteristic_dimension_varies":false,"rs_characteristic_dimensions":"[{\"p\":0,\"d\":3}]","rs_characteristic_dimensions_method":"simple_core","rs_dim":3,"rs_is_regular_scheme":true,"rs_is_smooth_over_QQ":null,"rs_is_smooth_over_ZZ":true,"rs_n_qbar_components":1,"rs_regularity_method":"simple_core","rs_regularity_witness":"r3_n8_0000000000********************0***************0*********","rs_scheme_simple_core_id":"r3_n8_0000000000********************0***************0*********","rs_singular_fiber_characteristics":null,"rs_singular_fiber_characteristics_method":null,"rs_singular_fiber_primes":"[]","rs_singular_fiber_primes_method":"simple_core","rs_smoothness_method":"simple_core","rs_smoothness_witness":"r3_n8_0000000000********************0***************0*********","singular_primes":null,"smooth_char_0":null,"status":"computed_realization_space","tutte_polynomial":"x_0^3 + x_0^2*x_1 + 5*x_0^2 + x_0*x_1^4 + 2*x_0*x_1^3 + 3*x_0*x_1^2 + 7*x_0*x_1 + 7*x_0 + x_1^6 + 3*x_1^5 + 5*x_1^4 + 7*x_1^3 + 9*x_1^2 + 7*x_1","realization_space":{"vars":["x1","x2","x3"],"ideal":["0"],"inequations":["x3 - 1","x3","x1 + x3 - 1","x2 + x3 - 1","x1 - 1","x2 - 1","x2","x1 - x2","x1"],"matrix":[["1","1","0","1","1","1","0","0","1"],["0","0","1","1","x1","x2","0","1","1"],["0","0","0","0","0","0","1","1","x3"]]}}