{"rank":3,"n":12,"seq":23246771,"label":"3.12.23246771","id":"r3_n12_0000************0*********0***0***0*******0****0****************0*********0******************0***********************0*************0************0*****************0***************0*************0********0************0*****","beta_invariant":26,"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":"4,5,6","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":199,"n_circuits":333,"n_components":null,"n_connected_components":1,"n_cyclic_flats":17,"n_flats":44,"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 + 2*x_0*x_1^2 + 17*x_0*x_1 + 26*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 + 34*x_1^2 + 26*x_1","realization_space":{"vars":["x1","x2","x3","x4","x5","x6","x7","x8","x9","x10","x11","x12"],"ideal":["1"],"inequations":["-x10 + x11 - x12","-x2*x10 + x10*x12 + x11 - x12","x1*x11 - x1*x12 - x3*x10 + x10*x12","x10*x12","-x10","-x4*x10 + x11 - x12","x5*x11 - x5*x12 - x6*x10 + x10*x12","x7*x11 - x7*x12 - x8*x10 + x10*x12","x9*x11 - x9*x12 + x10*x12","-x2*x9 + x9*x12 - x12","-x1*x12 - x3*x9 + x9*x12","x9*x12","-x12","-x9","-x4*x9 - x12","-x5*x12 - x6*x9 + x9*x12","-x7*x12 - x8*x9 + x9*x12","-x7 + x8 - x12","-x2*x7 + x7*x12 + x8 - x12","x1*x8 - x1*x12 - x3*x7 + x7*x12","x7*x12","x8 - x12","-x7","-x4*x7 + x8 - x12","x5*x8 - x5*x12 - x6*x7 + x7*x12","-x5 + x6 - x12","-x2*x5 + x5*x12 + x6 - x12","x1*x6 - x1*x12 - x3*x5 + x5*x12","x5*x12","x6 - x12","-x5","x4 - 1","-x2 + x4 + x12","x1*x4 - x3 + x12","x12","x4","x1","-x2 + x12","-x3 + x12","x12","-x12","-x12","-x1*x12","-x1 + x3 - x12","-x1*x2 + x1*x12 + x3 - x12","x2 - x12 - 1","-x9 + x10 - x11","-x2*x9 + x2*x10 + x9*x11 - x11","-x1*x11 - x3*x9 + x3*x10 + x9*x11","x9*x11","-x11","-x9 + x10","-x5*x11 - x6*x9 + x6*x10 + x9*x11","-x7*x11 - x8*x9 + x8*x10 + x9*x11","-x7 + x8 + x10 - x11","-x2*x7 + x2*x10 + x7*x11 - x8*x10 + x8 - x11","x1*x8 - x1*x11 - x3*x7 + x3*x10 + x7*x11 - x8*x10","x7*x11 - x8*x10","x8 - x11","-x7 + x10","-x4*x7 + x4*x10 + x8 - x11","x5*x8 - x5*x11 - x6*x7 + x6*x10 + x7*x11 - x8*x10","-x5 + x6 + x10 - x11","-x2*x5 + x2*x10 + x5*x11 - x6*x10 + x6 - x11","x1*x6 - x1*x11 - x3*x5 + x3*x10 + x5*x11 - x6*x10","x6 - x11","-x5 + x10","-x4*x5 + x4*x10 + x6 - x11","x4 - 1","-x2 - x4*x10 + x4 + x11","x1*x4 - x3 - x4*x10 + x11","-x4*x10 + x11","x4","x1 - x10","-x10","-x2 + x11","-x3 + x11","x11","x10 - x11","x2*x10 - x11","-x1*x11 + x3*x10","-x1 + x3 + x10 - x11","-x1*x2 + x1*x11 + x2*x10 - x3*x10 + x3 - x11","x2 + x10 - x11 - 1","-x7 + x8 + x9","-x2*x7 + x2*x9 - x8*x9 + x8","x1*x8 - x3*x7 + x3*x9 - x8*x9","-x8*x9","x8","-x4*x7 + x4*x9 + x8","x5*x8 - x6*x7 + x6*x9 - x8*x9","-x5 + x6 + x9","-x2*x5 + x2*x9 - x6*x9 + x6","x1*x6 - x3*x5 + x3*x9 - x6*x9","-x6*x9","x6","-x5 + x9","-x4*x5 + x4*x9 + x6","x4 - 1","-x2 - x4*x9 + x4","x1*x4 - x3 - x4*x9","-x4*x9","x4","-x9 + 1","x1 - x9","-x9","-x2","-x3","x9","x2*x9","x3*x9","-x1 + x3 + x9","-x1*x2 + x2*x9 - x3*x9 + x3","x2 + x9 - 1","-x5 + x6 + x7 - x8","-x2*x5 + x2*x7 + x5*x8 - x6*x7 + x6 - x8","x1*x6 - x1*x8 - x3*x5 + x3*x7 + x5*x8 - x6*x7","x5*x8 - x6*x7","x6 - x8","-x5 + x7","-x4*x5 + x4*x7 + x6 - x8","x4 - 1","-x2 - x4*x7 + x4 + x8","x1*x4 - x3 - x4*x7 + x8","x4","-x7 + 1","x1 - x7","-x7","-x2 + x8","x8","x7 - x8","x2*x7 - x8","-x1*x8 + x3*x7","-x1 + x3 + x7 - x8","-x1*x2 + x1*x8 + x2*x7 - x3*x7 + x3 - x8","x2 + x7 - x8 - 1","x4 - 1","-x2 - x4*x5 + x4 + x6","x1*x4 - x3 - x4*x5 + x6","-x4*x5 + x6","x4","-x5 + 1","-x5","-x3 + x6","x6","x5 - x6","x2*x5 - x6","-x1*x6 + x3*x5","-x1 + x3 + x5 - x6","-x1*x2 + x1*x6 + x2*x5 - x3*x5 + x3 - x6","x2 + x5 - x6 - 1","x4","x4","x4","-x4 + 1","x2 - x4","-x1*x4 + x3","-x4 + 1","x1*x4 + x2 - x3 - x4","-x4 + 1","-x1","x1 - 1","x2","x3","x2 - x3"],"matrix":null}}