{"rank":3,"n":10,"seq":6540,"label":"3.10.6540","id":"r3_n10_000000*0**00*0**00**00*0**0*0*0****00*0**0**00****0****000*0**0***0*0**0**0**00*****00*0**0***0****0*****0******0*******","beta_invariant":0,"birational_type":"rational over Q(a)/(a^2 - a + 1)","birational_type_components":"[{\"dim\":2,\"free_rank\":2,\"torus_rank\":2,\"core_dim\":0,\"qbar_components\":2,\"type\":\"rational over Q(a)/(a^2 - a + 1)\",\"field\":\"Q(a)/(a^2 - a + 1)\",\"minpoly\":\"T^2 - T + 1\",\"degree\":2,\"reason\":\"A^2 over the field of definition\",\"core_vars\":[\"x1\"],\"core_gens\":[\"x1^2 - x1 + 1\"]}]","birational_type_method":"point_field","char_poly_splits":false,"char_set":"[0]","expected_dimension_over_Z":3,"free_realization_space":false,"girth":1,"good_basis":null,"good_basis_v2":"2,3,7","is_binary":false,"is_coloopless":true,"is_connected":false,"is_divisionally_free":false,"is_graphic":false,"is_identically_self_dual":false,"is_laminar":false,"is_loopless":false,"is_nested":false,"is_orientable":false,"is_paving":false,"is_quaternary":false,"is_realizable":true,"is_realizable_char0":true,"is_regular":false,"is_self_dual":false,"is_series_parallel":false,"is_simple":false,"is_simplicial_arrangement":false,"is_supersolvable":false,"is_ternary":false,"is_three_lines":null,"is_transversal":false,"is_uniform":null,"n_automorphisms":48,"n_bases":76,"n_circuits":87,"n_components":2,"n_connected_components":2,"n_cyclic_flats":10,"n_flats":31,"n_loops":1,"principal_ideal":true,"rs_characteristic_dimension_unexpected":false,"rs_characteristic_dimension_varies":false,"rs_characteristic_dimensions":"[{\"p\":0,\"d\":2}]","rs_characteristic_dimensions_method":"simple_core","rs_dim":4,"rs_is_regular_scheme":true,"rs_is_smooth_over_QQ":null,"rs_is_smooth_over_ZZ":false,"rs_n_qbar_components":2,"rs_regularity_method":"simple_core","rs_regularity_witness":"r3_n9_0******0******0**********0********0*******0****0**0*********************************","rs_scheme_simple_core_id":"r3_n9_0******0******0**********0********0*******0****0**0*********************************","rs_singular_fiber_characteristics":null,"rs_singular_fiber_characteristics_method":null,"rs_singular_fiber_primes":"[3]","rs_singular_fiber_primes_method":"simple_core","rs_smoothness_method":"simple_core","rs_smoothness_witness":"r3_n9_0******0******0**********0********0*******0****0**0*********************************","singular_primes":null,"smooth_char_0":null,"status":"computed_realization_space","tutte_polynomial":"x_0^3*x_1 + 6*x_0^2*x_1 + 8*x_0*x_1^2 + 13*x_0*x_1 + x_1^7 + 3*x_1^6 + 6*x_1^5 + 10*x_1^4 + 15*x_1^3 + 13*x_1^2","realization_space":{"vars":["x1","x2","x3"],"ideal":["x1^2 - x1 + 1"],"inequations":["x1*x2 - x3","x1 - x3","x2 - 1","x1 + x2 - x3 - 1","x1^2 - x1*x3 - x1 - x2 + x3 + 1","x1*x2 - x1*x3 - x2","x1 - x3 - 1","x2 - x3 - 1","x1 - x2","x2","x2 - x3","x1*x2 - x1*x3 - x1 + x3","x3"],"matrix":[["0","1","0","1","0","1","0","1","1","1"],["0","0","1","1","1","x1","0","x1","1","x2"],["0","0","0","0","1","x1","1","x1 - 1","x1","x3"]]}}