{"rank":3,"n":12,"seq":2209030,"label":"3.12.2209030","id":"r3_n12_0******0******0**********0********0*******0****0****************0*0********************************0********0**************************************0*********0******************************************0**0**********0*****","beta_invariant":29,"birational_type":null,"birational_type_components":null,"birational_type_method":null,"char_poly_splits":false,"char_set":"[0]","expected_dimension_over_Z":1,"free_realization_space":false,"girth":3,"good_basis":null,"good_basis_v2":"2,3,8","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":true,"is_transversal":false,"is_uniform":null,"n_automorphisms":1,"n_bases":204,"n_circuits":367,"n_components":null,"n_connected_components":1,"n_cyclic_flats":18,"n_flats":48,"n_loops":0,"principal_ideal":true,"rs_characteristic_dimension_unexpected":false,"rs_characteristic_dimension_varies":false,"rs_characteristic_dimensions":"[{\"p\":0,\"d\":0}]","rs_characteristic_dimensions_method":"primitive_hypersurface_flat","rs_dim":9,"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":"univariate_resultant_and_localized_gcd","rs_smoothness_witness":"","singular_primes":null,"smooth_char_0":null,"status":"computed_realization_space","tutte_polynomial":"x_0^3 + 9*x_0^2 + 16*x_0*x_1 + 29*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 + 29*x_1","realization_space":{"vars":["x1"],"ideal":["2*x1^3 - 6*x1^2 + 4*x1 + 1"],"inequations":["2*x1^3 - 5*x1^2 + x1 + 4","4*x1^2 - 11*x1 + 8","4*x1^5 - 22*x1^4 + 42*x1^3 - 33*x1^2 + 10*x1 - 2","8*x1^3 - 26*x1^2 + 26*x1 - 7","4*x1^5 - 20*x1^4 + 31*x1^3 - 13*x1^2 - 2*x1 - 2","8*x1^5 - 50*x1^4 + 115*x1^3 - 106*x1^2 + 14*x1 + 22","4*x1^4 - 22*x1^3 + 51*x1^2 - 59*x1 + 28","4*x1^4 - 22*x1^3 + 49*x1^2 - 52*x1 + 22","4*x1^5 - 16*x1^4 + 15*x1^3 + 11*x1^2 - 16*x1 - 2","12*x1^5 - 74*x1^4 + 171*x1^3 - 173*x1^2 + 60*x1 + 6","4*x1^5 - 24*x1^4 + 54*x1^3 - 53*x1^2 + 18*x1 + 2","x1 - 3","2*x1^4 - 11*x1^3 + 19*x1^2 - 10*x1 - 2","8*x1^5 - 48*x1^4 + 107*x1^3 - 102*x1^2 + 30*x1 + 6","4*x1^4 - 20*x1^3 + 36*x1^2 - 25*x1 + 4"],"matrix":[["1","1","0","x1 - 2","1","0","1","0","1","x1 - 2","x1 - 2","x1 - 2"],["1","0","1","-x1 + 1","0","1","x1","0","2*x1^2 - 3*x1","-x1 + 1","x1^2 - 2*x1","-x1^2 + 2*x1 - 1"],["0","0","0","x1 - 2","2*x1^2 - 3*x1","-2*x1^2 + 4*x1 - 1","1","1","2*x1^2 - 3*x1","-2*x1^2 + 4*x1 - 2","-1","-2*x1^2 + 4*x1 - 2"]]}}