{"rank":3,"n":12,"seq":16783418,"label":"3.12.16783418","id":"r3_n12_0000************0*********0***0***0*******0*********************0********************************0*********0**********0**********************0*******0**********0******************************0*0********0**********0******","beta_invariant":27,"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":"1,2,5","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":false,"is_transversal":false,"is_uniform":null,"n_automorphisms":1,"n_bases":200,"n_circuits":341,"n_components":null,"n_connected_components":1,"n_cyclic_flats":16,"n_flats":46,"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 + 16*x_0*x_1 + 27*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 + 27*x_1","realization_space":{"vars":["x1","x2","x3","x4","x5","x6","x7","x8","x9","x10","x11"],"ideal":["1"],"inequations":["x8*x11 - x9*x10","x9 - x11","x8*x11 - x9*x10 + x9 - x11","-x8 + x10","x8*x11 - x8 - x9*x10 + x10","-x2*x8 + x2*x10 + x8*x11 - x9*x10","-x3*x8 + x3*x10 + x9 - x11","x4*x9 - x4*x11 - x5*x8 + x5*x10 + x8*x11 - x9*x10","x6*x9 - x6*x11 - x7*x8 + x7*x10 + x8*x11 - x9*x10","x6*x11 - x7*x10","x6*x11 - x7*x10 + x7 - x11","x1*x7 - x1*x11 + x6*x11 - x7*x10","-x6 + x10","x6*x11 - x6 - x7*x10 + x10","-x2*x6 + x2*x10 + x6*x11 - x7*x10","-x3*x6 + x3*x10 + x7 - x11","x4*x7 - x4*x11 - x5*x6 + x5*x10 + x6*x11 - x7*x10","x5 - x11","x4*x11 - x5*x10 + x5 - x11","x1*x5 - x1*x11 + x4*x11 - x5*x10","-x4 + x10","x4*x11 - x4 - x5*x10 + x10","-x2*x4 + x2*x10 + x4*x11 - x5*x10","-x3*x4 + x3*x10 + x5 - x11","-x3*x10 + x11","x3","-x3*x10 + x3 + x11","x1*x3 - x3*x10 + x11","-x2 - x3*x10 + x11","-x2*x10","x2 - x11","-x2*x10 + x2 - x11","x1*x2 - x1*x11 - x2*x10","x10","-x2*x10 + x10","-x10","-x11 + 1","-x10 - x11 + 1","-x1*x11 + x1 - x10","x10","-x10","-x10 + 1","x1 - x10","x1*x11","-x11","x1*x11 - x11","x11","-x11","x11","x6*x9 - x7*x8","x7 - x9","x6*x9 - x7*x8 + x7 - x9","x1*x7 - x1*x9 + x6*x9 - x7*x8","x6*x9 - x6 - x7*x8 + x8","-x2*x6 + x2*x8 + x6*x9 - x7*x8","-x3*x6 + x3*x8 + x7 - x9","x4*x7 - x4*x9 - x5*x6 + x5*x8 + x6*x9 - x7*x8","x4*x9 - x5*x8","x4*x9 - x5*x8 + x5 - x9","x1*x5 - x1*x9 + x4*x9 - x5*x8","-x4 + x8","x4*x9 - x4 - x5*x8 + x8","-x2*x4 + x2*x8 + x4*x9 - x5*x8","-x3*x4 + x3*x8 + x5 - x9","x3","-x3*x8 + x3 + x9","x1*x3 - x3*x8 + x9","-x3*x8 + x9 - 1","-x2 - x3*x8 + x9","-x2*x8","x2 - x9","-x2*x8 + x2 - x9","x1*x2 - x1*x9 - x2*x8","x8","-x2*x8 + x8","-x8","-x9 + 1","-x8 - x9 + 1","-x1*x9 + x1 - x8","x8","-x8","-x8 + 1","x1 - x8","x1*x9","-x9","x1*x9 - x9","x9","-x9","x9","x4*x7 - x5*x6","x5 - x7","x4*x7 - x5*x6 + x5 - x7","x1*x5 - x1*x7 + x4*x7 - x5*x6","-x4 + x6","x4*x7 - x4 - x5*x6 + x6","-x3*x4 + x3*x6 + x5 - x7","-x3*x6 + x7","x3","x1*x3 - x3*x6 + x7","-x3*x6 + x7 - 1","-x2 - x3*x6 + x7","-x2*x6","x2 - x7","-x2*x6 + x2 - x7","x1*x2 - x1*x7 - x2*x6","x6","-x2*x6 + x6","-x6","-x7 + 1","-x6 - x7 + 1","x6","-x6","-x6 + 1","x1 - x6","x1*x7","-x7","x1*x7 - x7","x7","-x7","x7","-x3*x4 + x5","x3","-x3*x4 + x3 + x5","x1*x3 - x3*x4 + x5","-x3*x4 + x5 - 1","-x2 - x3*x4 + x5","-x2*x4","x2 - x5","-x2*x4 + x2 - x5","x1*x2 - x1*x5 - x2*x4","x4","-x2*x4 + x4","-x4","-x5 + 1","-x4 - x5 + 1","-x1*x5 + x1 - x4","x4","-x4","x1 - x4","x1*x5","-x5","x1*x5 - x5","x5","-x5","x5","-x2","-x3","-x2 - x3","-x1*x3 - x2","-x2 + 1","-x3","-x3 - 1","-x1*x3 - 1","x1*x3","-x3","x1*x3 - x3","x3","-x3","x3","-x2 + 1","-x2 + 1","-x1*x2 + x1","x1","x1*x2","-x2","x1*x2 - x2","x2","-x2","x2","x1","x1","x1 - 1","x1","x1 - 1"],"matrix":null}}