{"rank":3,"n":12,"seq":1230,"label":"3.12.1230","id":"r3_n12_0******0******0*************0*************************************************0******************************0******************************************0*************************************************0*****************","beta_invariant":37,"birational_type":null,"birational_type_components":null,"birational_type_method":null,"char_poly_splits":false,"char_set":"[0]","expected_dimension_over_Z":9,"free_realization_space":true,"girth":3,"good_basis":null,"good_basis_v2":"1,2,5","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":true,"is_quaternary":false,"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":false,"is_ternary":false,"is_three_lines":false,"is_transversal":false,"is_uniform":null,"n_automorphisms":4,"n_bases":212,"n_circuits":431,"n_components":null,"n_connected_components":1,"n_cyclic_flats":10,"n_flats":64,"n_loops":0,"principal_ideal":true,"rs_characteristic_dimension_unexpected":false,"rs_characteristic_dimension_varies":false,"rs_characteristic_dimensions":"[{\"p\":0,\"d\":8}]","rs_characteristic_dimensions_method":"audited_free_chart","rs_dim":11,"rs_is_regular_scheme":null,"rs_is_smooth_over_QQ":true,"rs_is_smooth_over_ZZ":true,"rs_n_qbar_components":null,"rs_regularity_method":null,"rs_regularity_witness":null,"rs_scheme_simple_core_id":null,"rs_singular_fiber_characteristics":"{\"kind\":\"finite\",\"primes\":[]}","rs_singular_fiber_characteristics_method":"smooth_over_ZZ","rs_singular_fiber_primes":null,"rs_singular_fiber_primes_method":null,"rs_smoothness_method":"audited_free_chart","rs_smoothness_witness":null,"singular_primes":null,"smooth_char_0":null,"status":"computed_realization_space","tutte_polynomial":"x_0^3 + 9*x_0^2 + 8*x_0*x_1 + 37*x_0 + x_1^9 + 3*x_1^8 + 6*x_1^7 + 10*x_1^6 + 15*x_1^5 + 21*x_1^4 + 28*x_1^3 + 36*x_1^2 + 37*x_1","realization_space":{"vars":["x1","x2","x3","x4","x5","x6","x7","x8"],"ideal":["0"],"inequations":["x5*x8 - x6*x7","x6 - x8","x5*x8 - x6*x7 + x6 - x8","x5*x8 - x5 - x6*x7 + x7","x5 - x7","x1*x6 - x1*x8 + x5*x8 - x5 - x6*x7 + x7","x2*x5 - x2*x7 - x5*x8 + x6*x7 - x6 + x8","x3*x5 - x3*x7 - x4*x6 + x4*x8 - x5*x8 + x6*x7","x3 - x6","x4 - x7","x8","x8 - 1","x2 - x8","x3 - x8","x3*x7 - x5*x8","x3*x7 - x3 - x5*x8 + x8","x3*x7 - x5*x8 + x5 - x7","x1*x3 - x1*x8 - x3*x7 + x5*x8 - x5 + x7","x2*x5 - x2*x7 + x3*x7 - x3 - x5*x8 + x8","x4 - x5","x3*x7 - x4*x8","x3*x7 - x3 - x4*x8 + x8","x3*x7 - x4*x8 + x4 - x7","x1*x3 - x1*x8 - x3*x7 + x4*x8 - x4 + x7","x2*x4 - x2*x7 + x3*x7 - x3 - x4*x8 + x8","x2*x7 - x8","x2","x7 - 1","x2*x7 - x7 - x8 + 1","x1*x2 - x1*x8 - x2*x7 + x7 + x8 - 1","x1*x8 - x7","x1*x8 - x7 - x8 + 1","x1","x1 - x7","x7","x7 + x8 - 1","x4*x6 - x5*x8","x4*x6 - x5*x8 - x6 + x8","x4*x6 - x4 - x5*x8 + x5","x1*x6 - x1*x8 - x4*x6 + x4 + x5*x8 - x5","x2*x4 - x2*x5 - x4*x6 + x5*x8 + x6 - x8","x5","x5 - 1","x1 - x5","x3*x5 - x4*x6","x3*x5 - x3 - x4*x6 + x6","x3*x5 - x4*x6 + x4 - x5","x1*x3 - x1*x6 - x3*x5 + x4*x6 - x4 + x5","x2*x4 - x2*x5 + x3*x5 - x3 - x4*x6 + x6","x2*x5 - x6","x2 - x6","x2*x5 - x5 - x6 + 1","x1*x2 - x1*x6 - x2*x5 + x5 + x6 - 1","x1*x6 - x5","x6 - 1","x1*x6 - x5 - x6 + 1","x5 + x6 - 1","x6","x3*x4 - x5*x8","x3*x4 - x3 - x5*x8 + x8","x3*x4 - x4 - x5*x8 + x5","x1*x3 - x1*x8 - x3*x4 + x4 + x5*x8 - x5","x2*x4 - x2*x5 - x3*x4 + x3 + x5*x8 - x8","x4","x4 - 1","x1 - x4","x2*x4 - x8","x2*x4 - x4 - x8 + 1","x1*x2 - x1*x8 - x2*x4 + x4 + x8 - 1","x1*x8 - x4","x1*x8 - x4 - x8 + 1","x4 + x8 - 1","x3","x3 - 1","x2 - x3","x2*x5 - x3","x2*x5 - x3 - x5 + 1","x1*x2 - x1*x3 - x2*x5 + x3 + x5 - 1","x1*x3 - x5","x1*x3 - x3 - x5 + 1","x3 + x5 - 1","x2*x4 - x3","x2*x4 - x3 - x4 + 1","x1*x2 - x1*x3 - x2*x4 + x3 + x4 - 1","x1*x3 - x4","x1*x3 - x3 - x4 + 1","x3 + x4 - 1","x1*x2 - 1","x2 - 1","x1 - 1"],"matrix":[["1","0","1","1","0","1","1","1","1","1","1","1"],["0","1","1","0","0","x1","1","x4","x5","x4","x5","x7"],["0","0","0","1","1","1","x2","x3","x3","x8","x6","x8"]]}}