{"rank":3,"n":6,"seq":25,"label":"3.6.25","id":"r3_n6_0000000000**********","beta_invariant":0,"birational_type":"rational","birational_type_components":"[{\"dim\":2,\"free_rank\":2,\"torus_rank\":2,\"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":3,"free_realization_space":true,"girth":3,"good_basis":null,"good_basis_v2":"1,2,6","is_binary":false,"is_coloopless":false,"is_connected":false,"is_divisionally_free":true,"is_graphic":false,"is_identically_self_dual":false,"is_laminar":true,"is_loopless":true,"is_nested":true,"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":true,"is_supersolvable":true,"is_ternary":false,"is_three_lines":null,"is_transversal":true,"is_uniform":null,"n_automorphisms":120,"n_bases":10,"n_circuits":10,"n_components":1,"n_connected_components":2,"n_cyclic_flats":2,"n_flats":14,"n_loops":0,"principal_ideal":true,"rs_characteristic_dimension_unexpected":false,"rs_characteristic_dimension_varies":false,"rs_characteristic_dimensions":"[{\"p\":0,\"d\":2}]","rs_characteristic_dimensions_method":"cofinite_smooth_equidimensional","rs_dim":0,"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_disconnected_open_affine","rs_regularity_witness":null,"rs_scheme_simple_core_id":"r3_n6_0000000000**********","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":"simple_disconnected_open_affine","rs_smoothness_witness":null,"singular_primes":null,"smooth_char_0":null,"status":"computed_realization_space","tutte_polynomial":"x_0^3 + 3*x_0^2 + x_0*x_1^3 + 2*x_0*x_1^2 + 3*x_0*x_1","realization_space":{"vars":["x1","x2"],"ideal":["0"],"inequations":["x2","x2 - 1","x1 - x2","x1","x1 - 1"],"matrix":[["1","0","1","1","1","0"],["0","1","1","x1","x2","0"],["0","0","0","0","0","1"]]}}