{"rank":3,"n":12,"seq":14205257,"label":"3.12.14205257","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":"1,5,11","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":false,"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":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":10,"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":["-x11 + x12","-x11 + x12","-x11 + x12","-x11 + x12","-x11 + x12","-x11 + x12","-x11 + x12","-x11 + x12","x5*x12 - x10","x5*x12 - x10 - x12 + 1","-x1*x12 + x5*x12 + x6 - x10","-x2*x12 + x5*x12 + x7 - x10","-x12","-x3*x12 + x5*x12 - x10","-x4*x12 + x5*x12 + x9 - x10","x4*x12 - x9","x4*x12 - x9 - x12 + 1","-x1*x12 + x4*x12 + x6 - x9","-x2*x12 + x4*x12 + x7 - x9","-x12","x4*x12 + x8 - x9","-x8","-x8 - x12 + 1","-x1*x12 + x6 - x8","-x2*x12 + x7 - x8","-x12","-x3*x12 - x8","x3*x12","x3*x12 - x12 + 1","-x1*x12 + x3*x12 + x6","-x2*x12 + x3*x12 + x7","-x12","x12","x12","x12","x12","x2*x12 - x7","x2*x12 - x7 - x12 + 1","-x1*x12 + x2*x12 + x6 - x7","x1*x12 - x6","x1*x12 - x6 - x12 + 1","x12 - 1","x5","x5 - 1","-x1 + x5","-x2 + x5","x5","-x4 + x5","x4","-x1 + x4","-x2 + x4","-x3 + x4","x4","-x1","-x2","-x3","x3","x3 - 1","-x1 + x3","-x2 + x3","x2","x2 - 1","-x1 + x2","x1","x1 - 1","x5*x11 - x10","x5*x11 - x10 - x11 + 1","-x2*x11 + x5*x11 + x7 - x10","-x11","-x3*x11 + x5*x11 - x10","x5*x11 + x8 - x10","-x4*x11 + x5*x11 + x9 - x10","x4*x11 - x9","x4*x11 - x9 - x11 + 1","-x1*x11 + x4*x11 + x6 - x9","-x2*x11 + x4*x11 + x7 - x9","-x11","-x3*x11 + x4*x11 - x9","x4*x11 + x8 - x9","-x8","-x8 - x11 + 1","-x1*x11 + x6 - x8","-x2*x11 + x7 - x8","-x11","-x3*x11 - x8","x3*x11","-x1*x11 + x3*x11 + x6","-x2*x11 + x3*x11 + x7","-x11","x11","x11","x11","x11","x2*x11 - x7","x2*x11 - x7 - x11 + 1","-x1*x11 + x2*x11 + x6 - x7","x1*x11 - x6","x1*x11 - x6 - x11 + 1","x11 - 1","x4*x10 - x4 - x5*x9 + x5 + x9 - x10","x1*x9 - x1*x10 - x4*x6 + x4*x10 + x5*x6 - x5*x9","x2*x9 - x2*x10 - x4*x7 + x4*x10 + x5*x7 - x5*x9","x9 - x10","x3*x9 - x3*x10 + x4*x10 - x5*x9","-x4*x8 + x4*x10 + x5*x8 - x5*x9","-x5*x8","-x5*x8 + x5 + x8 - x10","x1*x8 - x1*x10 + x5*x6 - x5*x8","x2*x8 - x2*x10 + x5*x7 - x5*x8","x8 - x10","x3*x8 - x3*x10 - x5*x8","x3*x10","x3*x10 - x3 + x5 - x10","-x1*x10 - x3*x6 + x3*x10 + x5*x6","-x2*x10 - x3*x7 + x3*x10 + x5*x7","-x10","x10","x10 - 1","-x6 + x10","x2*x10 - x5*x7","x2*x10 - x2 - x5*x7 + x5 + x7 - x10","x1*x7 - x1*x10 - x2*x6 + x2*x10 + x5*x6 - x5*x7","x1*x10 - x5*x6","x1*x10 - x1 - x5*x6 + x5 + x6 - x10","-x5 + x10","-x4*x8","-x4*x8 + x4 + x8 - x9","x1*x8 - x1*x9 + x4*x6 - x4*x8","x2*x8 - x2*x9 + x4*x7 - x4*x8","x8 - x9","x3*x8 - x3*x9 - x4*x8","x3*x9","x3*x9 - x3 + x4 - x9","-x1*x9 - x3*x6 + x3*x9 + x4*x6","-x2*x9 - x3*x7 + x3*x9 + x4*x7","-x9","x9","x9 - 1","-x7 + x9","x2*x9 - x4*x7","x2*x9 - x2 - x4*x7 + x4 + x7 - x9","x1*x7 - x1*x9 - x2*x6 + x2*x9 + x4*x6 - x4*x7","x1*x9 - x4*x6","x1*x9 - x1 - x4*x6 + x4 + x6 - x9","-x4 + x9","x3*x8","x3*x8 - x3 - x8","-x2*x8 - x3*x7 + x3*x8","-x8","x8","-x6 + x8","-x7 + x8","x2*x8","x2*x8 - x2 + x7 - x8","x1*x7 - x1*x8 - x2*x6 + x2*x8","x1*x8","x1*x8 - x1 + x6 - x8","x8","-x6","-x7","-x3*x7","-x2 - x3*x7 + x3 + x7","x1*x7 - x2*x6 + x3*x6 - x3*x7","-x3*x6","-x1 - x3*x6 + x3 + x6","-x3","-x7","-x7 + 1","x6 - x7","-x6","-x6 + 1"],"matrix":null}}