{"rank":3,"n":10,"seq":4834,"label":"3.10.4834","id":"r3_n10_0000************0*********0***0***0*******0****0*****0**********0****0**0********************0*0*****0*****************0","beta_invariant":12,"birational_type":"point over Q(a)/(a^2 - a + 1)","birational_type_components":"[{\"dim\":0,\"free_rank\":0,\"torus_rank\":0,\"core_dim\":0,\"qbar_components\":2,\"type\":\"point over Q(a)/(a^2 - a + 1)\",\"field\":\"Q(a)/(a^2 - a + 1)\",\"minpoly\":\"T^2 - T + 1\",\"degree\":2,\"core_vars\":[\"x1\"],\"core_gens\":[\"x1^2 - x1 + 1\"]}]","birational_type_method":"point_field","char_poly_splits":true,"char_set":"[0]","expected_dimension_over_Z":-1,"free_realization_space":false,"girth":3,"good_basis":"2,3,5","good_basis_v2":"1,2,5","is_binary":false,"is_coloopless":true,"is_connected":true,"is_divisionally_free":true,"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":true,"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":36,"n_bases":102,"n_circuits":108,"n_components":2,"n_connected_components":1,"n_cyclic_flats":14,"n_flats":27,"n_loops":0,"principal_ideal":true,"rs_characteristic_dimension_unexpected":true,"rs_characteristic_dimension_varies":false,"rs_characteristic_dimensions":"[{\"p\":0,\"d\":0}]","rs_characteristic_dimensions_method":"cofinite_strong_groebner_candidates_exact","rs_dim":2,"rs_is_regular_scheme":true,"rs_is_smooth_over_QQ":null,"rs_is_smooth_over_ZZ":true,"rs_n_qbar_components":2,"rs_regularity_method":"smooth","rs_regularity_witness":null,"rs_scheme_simple_core_id":"r3_n10_0000************0*********0***0***0*******0****0*****0**********0****0**0********************0*0*****0*****************0","rs_singular_fiber_characteristics":null,"rs_singular_fiber_characteristics_method":null,"rs_singular_fiber_primes":"[]","rs_singular_fiber_primes_method":"smooth_over_ZZ","rs_smoothness_method":"direct_integer_critical_certificate","rs_smoothness_witness":null,"singular_primes":"[]","smooth_char_0":true,"status":"computed_realization_space","tutte_polynomial":"x_0^3 + 7*x_0^2 + 2*x_0*x_1^2 + 14*x_0*x_1 + 12*x_0 + x_1^7 + 3*x_1^6 + 6*x_1^5 + 10*x_1^4 + 15*x_1^3 + 19*x_1^2 + 12*x_1","realization_space":{"vars":["x1"],"ideal":["x1^2 - x1 + 1"],"inequations":["x1 + 1"],"matrix":[["1","0","1","1","0","1","1","0","1","1"],["0","1","1","x1","0","0","0","1","1","x1"],["0","0","0","0","1","1","x1","-1","x1","1"]]}}