{"rank":3,"n":6,"seq":10,"label":"3.6.10","id":"r3_n6_0000************0***","beta_invariant":2,"birational_type":"rational","birational_type_components":"[{\"dim\":1,\"free_rank\":1,\"torus_rank\":1,\"core_dim\":0,\"qbar_components\":1,\"type\":\"rational\",\"reason\":\"free realization space\"}]","birational_type_method":"free_presentation","char_poly_splits":true,"char_set":"[0]","expected_dimension_over_Z":2,"free_realization_space":true,"girth":3,"good_basis":"1,2,5","good_basis_v2":"1,2,5","is_binary":false,"is_coloopless":true,"is_connected":true,"is_divisionally_free":true,"is_graphic":false,"is_identically_self_dual":false,"is_laminar":false,"is_loopless":true,"is_nested":false,"is_orientable":true,"is_paving":true,"is_quaternary":true,"is_realizable":true,"is_realizable_char0":true,"is_regular":false,"is_self_dual":false,"is_series_parallel":false,"is_simple":true,"is_simplicial_arrangement":false,"is_supersolvable":true,"is_ternary":true,"is_three_lines":false,"is_transversal":true,"is_uniform":null,"n_automorphisms":12,"n_bases":15,"n_circuits":8,"n_components":1,"n_connected_components":1,"n_cyclic_flats":4,"n_flats":16,"n_loops":0,"principal_ideal":true,"rs_characteristic_dimension_unexpected":false,"rs_characteristic_dimension_varies":false,"rs_characteristic_dimensions":"[{\"p\":0,\"d\":1}]","rs_characteristic_dimensions_method":"cofinite_strong_groebner_candidates_exact","rs_dim":1,"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":"three_lines_deletion","rs_regularity_witness":"1=>r3_n5_0*********","rs_scheme_simple_core_id":"r3_n6_0000************0***","rs_singular_fiber_characteristics":null,"rs_singular_fiber_characteristics_method":null,"rs_singular_fiber_primes":"[]","rs_singular_fiber_primes_method":"smooth_over_ZZ","rs_smoothness_method":"three_lines_deletion","rs_smoothness_witness":"1=>r3_n5_0*********","singular_primes":"[]","smooth_char_0":true,"status":"computed_realization_space","tutte_polynomial":"x_0^3 + 3*x_0^2 + x_0*x_1^2 + 3*x_0*x_1 + 2*x_0 + x_1^3 + 2*x_1^2 + 2*x_1","realization_space":{"vars":["x1"],"ideal":["0"],"inequations":["x1","x1 - 1"],"matrix":[["1","0","1","1","0","1"],["0","1","1","x1","0","0"],["0","0","0","0","1","1"]]}}