{"rank":3,"n":12,"seq":26878413,"label":"3.12.26878413","id":"r3_n12_0000************0*********0***0***0*******0****0*****0*********0**************0**0**********0*******0***********0****************0*0****************0*******0*******0******************************0************0*******0***","beta_invariant":24,"birational_type":null,"birational_type_components":null,"birational_type_method":null,"char_poly_splits":false,"char_set":"[0]","expected_dimension_over_Z":0,"free_realization_space":false,"girth":3,"good_basis":null,"good_basis_v2":"1,5,9","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":195,"n_circuits":307,"n_components":null,"n_connected_components":1,"n_cyclic_flats":15,"n_flats":42,"n_loops":0,"principal_ideal":true,"rs_characteristic_dimension_unexpected":false,"rs_characteristic_dimension_varies":false,"rs_characteristic_dimensions":"[]","rs_characteristic_dimensions_method":"empty","rs_dim":8,"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":"empty","rs_smoothness_witness":null,"singular_primes":null,"smooth_char_0":null,"status":"computed_realization_space","tutte_polynomial":"x_0^3 + 9*x_0^2 + 4*x_0*x_1^2 + 17*x_0*x_1 + 24*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 + 32*x_1^2 + 24*x_1","realization_space":{"vars":["x1","x2","x3","x4","x5","x6","x7","x8","x9","x10"],"ideal":["1"],"inequations":["-x8*x9","x8 + x9 - x10","x4*x9 - x8*x9 + x8 - x10","x1*x8 - x1*x10 + x5*x9 - x8*x9","x8 - x10","x2*x8 - x2*x10 - x8*x9","x6*x9 + x8 - x10","x9","x7*x9 - x8*x9","-x7*x9","x7 + x9 - x10","x4*x9 - x7*x9 + x7 - x10","x1*x7 - x1*x10 + x5*x9 - x7*x9","x7 - x10","x2*x7 - x2*x10 - x7*x9","x3*x7 - x3*x10 - x7*x9","x9","-x9","x1 - x9","x2 - x9","x3 - x9","-x6*x9 + x10","x6 - 1","-x4 - x6*x9 + x6 + x10","x1*x6 - x5 - x6*x9 + x10","x6","x2*x6 - x6*x9 + x10","x3*x6 - x6*x9 + x10","x3*x10","-x3 + x9 - x10","-x3*x4 + x3*x10 + x4*x9 - x10","-x1*x10 - x3*x5 + x3*x10 + x5*x9","-x10","-x2*x10 + x3*x10","x2*x10","-x2 + x9 - x10","-x2*x4 + x2*x10 + x4*x9 - x10","-x1*x10 - x2*x5 + x2*x10 + x5*x9","-x10","x10","-x4 + x10","-x5 + x10","x1*x10 - x5*x9","-x1 + x5 + x9 - x10","-x1*x4 + x1*x10 + x4*x9 - x5*x9 + x5 - x10","-x4*x9 + x10","x4 + x9 - x10 - 1","-x9 + x10","x7 - x8","x7 - x8","x1*x7 - x1*x8","x7 - x8","x2*x7 - x2*x8","x3*x7 - x3*x8","x7 - x8","x1","x2","x3","x8","x6 - 1","-x4 + x6 + x8","x1*x6 - x5 + x8","x6","x2*x6 + x8","x3*x6 + x8","x3*x8","-x3 - x8","-x3*x4 + x3*x8 - x8","-x1*x8 - x3*x5 + x3*x8","-x8","-x2*x8 + x3*x8","x2*x8","-x2*x4 + x2*x8 - x8","-x1*x8 - x2*x5 + x2*x8","-x8","x8","-x4 + x8","x1*x8","-x1 + x5 - x8","-x1*x4 + x1*x8 + x5 - x8","x8","x4 - x8 - 1","x8","x1","x2","x3","x7","x6 - 1","-x4 + x6 + x7","x1*x6 - x5 + x7","x6","x2*x6 + x7","x3*x6 + x7","x3*x7","-x3*x4 + x3*x7 - x7","-x1*x7 - x3*x5 + x3*x7","-x7","-x2*x7 + x3*x7","x2*x7","-x2 - x7","-x2*x4 + x2*x7 - x7","-x1*x7 - x2*x5 + x2*x7","-x7","x7","-x5 + x7","x1*x7","-x1 + x5 - x7","-x1*x4 + x1*x7 + x5 - x7","x7","x4 - x7 - 1","x7","x3","x3 - 1","-x1 + x3","-x2 + x3","x2","x2 - 1","-x1 + x2","x1","x1 - 1","x3*x6","-x6 + 1","x3*x6 + x4 - x6","-x6","-x2*x6 + x3*x6","x2*x6","-x6 + 1","-x1*x6 + x2*x6 + x5","-x6","x6","x6","x6","x1*x6 - x5","-x6 + 1","x1*x6 + x4 - x5 - x6","-x4 + x6","-x6 + 1","x6 - 1","-x2 + x3","-x2*x4 + x3*x4","-x2*x5 + x3*x5","-x4","-x5","-x3*x5","-x1 + x3 + x5","-x1*x4 + x3*x4 - x3*x5 + x5","-x3*x4","x3 + x4 - 1","-x3","-x4","-x5","-x2*x5","-x1 + x2 + x5","-x1*x4 + x2*x4 - x2*x5 + x5","-x2*x4","x2 + x4 - 1","-x2","-x5","x4 - x5","-x4"],"matrix":null}}