{"rank":3,"n":12,"seq":14226209,"label":"3.12.14226209","id":"r3_n12_0000************0**********0****0**********0*********************0***********0*****************0***************0**************************0**********0********0******************************0********0**0******************","beta_invariant":28,"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":"1,2,9","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":202,"n_circuits":354,"n_components":null,"n_connected_components":1,"n_cyclic_flats":17,"n_flats":47,"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":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":"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 + x_0*x_1^2 + 16*x_0*x_1 + 28*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 + 35*x_1^2 + 28*x_1","realization_space":{"vars":["x1","x2","x3","x4","x5","x6","x7","x8","x9","x10","x11","x12"],"ideal":["1"],"inequations":["-x10*x11 + x12","x10","-x10*x11 + x10 + x12","x1*x10 - x10*x11 + x12","x2*x10 - x10*x11 + x12 - 1","x3*x10 - x5 - x10*x11 + x12","x4*x10 - x6 - x10*x11 + x12","-x7 - x10*x11 + x12","x8*x10 - x9 - x10*x11 + x12","x9 - x12","x8*x12 - x9*x11 + x9 - x12","x1*x9 - x1*x12 + x8*x12 - x9*x11","x2*x9 - x2*x12 + x8*x12 - x8 - x9*x11 + x11","x3*x9 - x3*x12 - x5*x8 + x5*x11 + x8*x12 - x9*x11","x4*x9 - x4*x12 - x6*x8 + x6*x11 + x8*x12 - x9*x11","-x7*x8 + x7*x11 + x8*x12 - x9*x11","-x8 + x11","-x11","-x11 + 1","x1 - x11","x2 - x11","x4 - x11","-x11","-x7*x11","x7 - x12","-x7*x11 + x7 - x12","x2*x7 - x2*x12 - x7*x11 + x11","x3*x7 - x3*x12 + x5*x11 - x7*x11","x4*x7 - x4*x12 + x6*x11 - x7*x11","x4*x12 - x6*x11","x6 - x12","x4*x12 - x6*x11 + x6 - x12","x1*x6 - x1*x12 + x4*x12 - x6*x11","x2*x6 - x2*x12 + x4*x12 - x4 - x6*x11 + x11","x3*x6 - x3*x12 - x4*x5 + x4*x12 + x5*x11 - x6*x11","x3*x12 - x5*x11","x5 - x12","x3*x12 - x5*x11 + x5 - x12","x1*x5 - x1*x12 + x3*x12 - x5*x11","x2*x5 - x2*x12 + x3*x12 - x3 - x5*x11 + x11","x2*x12 - x11","-x12 + 1","x2*x12 - x11 - x12 + 1","-x1*x12 + x1 + x2*x12 - x11","x1*x12","-x12","x1*x12 - x12","x12","-x12","x12","x8*x10 - x9","-x10","-x1*x10 + x8*x10 - x9","-x2*x10 + x8*x10 - x9 + 1","-x3*x10 + x5 + x8*x10 - x9","-x4*x10 + x6 + x8*x10 - x9","x7 + x8*x10 - x9","-x7","-x10","-x7 - x10","-x1*x10 - x7","-x2*x10 - x7 + 1","-x3*x10 + x5 - x7","-x4*x10 + x6 - x7","x4*x10 - x6","-x10","x4*x10 - x6 - x10","-x2*x10 + x4*x10 - x6 + 1","-x3*x10 + x4*x10 + x5 - x6","x3*x10 - x5","-x10","x3*x10 - x5 - x10","-x1*x10 + x3*x10 - x5","-x2*x10 + x3*x10 - x5 + 1","x2*x10 - 1","-x10","x2*x10 - x10 - 1","-x1*x10 + x2*x10 - 1","x1*x10","-x10","x1*x10 - x10","x10","-x10","x10","-x8","-x8 + 1","x1 - x8","x2 - x8","x3 - x8","x4 - x8","-x8","-x7*x8","x7 - x9","-x7*x8 + x7 - x9","x1*x7 - x1*x9 - x7*x8","x2*x7 - x2*x9 - x7*x8 + x8","x3*x7 - x3*x9 + x5*x8 - x7*x8","x4*x9 - x6*x8","x6 - x9","x4*x9 - x6*x8 + x6 - x9","x1*x6 - x1*x9 + x4*x9 - x6*x8","x2*x6 - x2*x9 + x4*x9 - x4 - x6*x8 + x8","x3*x6 - x3*x9 - x4*x5 + x4*x9 + x5*x8 - x6*x8","x3*x9 - x5*x8","x3*x9 - x5*x8 + x5 - x9","x1*x5 - x1*x9 + x3*x9 - x5*x8","x2*x5 - x2*x9 + x3*x9 - x3 - x5*x8 + x8","x2*x9 - x8","-x9 + 1","x2*x9 - x8 - x9 + 1","-x1*x9 + x1 + x2*x9 - x8","x1*x9","-x9","x1*x9 - x9","x9","-x9","x9","-x1","-x2","-x3","-x4","x4","x4 - 1","-x1 + x4","-x2 + x4","-x3 + x4","x3","x3 - 1","-x1 + x3","-x2 + x3","x2","x2 - 1","x1","x1 - 1","x4*x7","x6 - x7","x4*x7 + x6 - x7","x1*x6 - x1*x7 + x4*x7","x2*x6 - x2*x7 + x4*x7 - x4","x3*x6 - x3*x7 - x4*x5 + x4*x7","x3*x7","x5 - x7","x3*x7 + x5 - x7","x1*x5 - x1*x7 + x3*x7","x2*x5 - x2*x7 + x3*x7 - x3","x2*x7","-x7 + 1","-x1*x7 + x1 + x2*x7","x1*x7","-x7","x1*x7 - x7","x7","-x7","x7","x3*x6 - x4*x5","x5 - x6","x1*x5 - x1*x6 + x3*x6 - x4*x5","x2*x5 - x2*x6 + x3*x6 - x3 - x4*x5 + x4","x2*x6 - x4","x2*x6 - x4 - x6 + 1","-x1*x6 + x1 + x2*x6 - x4","x1*x6","-x6","x1*x6 - x6","x6","-x6","x6","-x5 + 1","x2*x5 - x3 - x5 + 1","-x1*x5 + x1 + x2*x5 - x3","x1*x5","-x5","x1*x5 - x5","x5","-x5","x5","x1","x1 - 1"],"matrix":null}}