{"rank":3,"n":10,"seq":6252,"label":"3.10.6252","id":"r3_n10_00000****00****0****0****0********00****0***************0****0*******************0**0****0********************0*********","beta_invariant":12,"birational_type":"rational","birational_type_components":"[{\"dim\":5,\"free_rank\":5,\"torus_rank\":5,\"core_dim\":0,\"qbar_components\":1,\"type\":\"rational\",\"reason\":\"free after 1 linear eliminations\",\"n_linear_eliminations\":1}]","birational_type_method":"linear_elimination","char_poly_splits":false,"char_set":"[0]","expected_dimension_over_Z":6,"free_realization_space":false,"girth":2,"good_basis":null,"good_basis_v2":"1,3,5","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":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":101,"n_circuits":139,"n_components":1,"n_connected_components":1,"n_cyclic_flats":8,"n_flats":32,"n_loops":0,"principal_ideal":true,"rs_characteristic_dimension_unexpected":false,"rs_characteristic_dimension_varies":false,"rs_characteristic_dimensions":"[{\"p\":0,\"d\":5}]","rs_characteristic_dimensions_method":"simple_core","rs_dim":6,"rs_is_regular_scheme":true,"rs_is_smooth_over_QQ":null,"rs_is_smooth_over_ZZ":true,"rs_n_qbar_components":1,"rs_regularity_method":"simple_core","rs_regularity_witness":"r3_n8_0******0******0*****************************************","rs_scheme_simple_core_id":"r3_n8_0******0******0*****************************************","rs_singular_fiber_characteristics":null,"rs_singular_fiber_characteristics_method":null,"rs_singular_fiber_primes":"[]","rs_singular_fiber_primes_method":"simple_core","rs_smoothness_method":"simple_core","rs_smoothness_witness":"r3_n8_0******0******0*****************************************","singular_primes":null,"smooth_char_0":null,"status":"computed_realization_space","tutte_polynomial":"x_0^3 + 2*x_0^2*x_1 + 5*x_0^2 + x_0*x_1^2 + 13*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 + 20*x_1^2 + 12*x_1","realization_space":{"vars":["x1","x2","x3","x4","x5","x6"],"ideal":["x2*x5 - x2 - x3*x6 + x3 - x5 + x6"],"inequations":["x3*x6 - x4*x5","x4 - x6","x3 - x5","x3*x6 - x3 - x4*x5 + x4 + x5 - x6","x1*x3 - x1*x5 - x3*x6 + x4*x5 - x4 + x6","x2 - x4","x2*x5 - x3*x6","x2 - x6","x1*x3 - x1*x5 + x2*x5 - x2 - x3*x6 + x6","x1*x5 - x6","x1 - x6","x5 - 1","x1 - 1","x5 - x6","x6 - 1","x5","x6","x3","x3 - 1","x1*x3 - x4","x1 - x4","x3 - x4","x4 - 1","x4","x1*x3 - x2","x1 - x2","x2 - x3","x2 - 1","x2","x1"],"matrix":[["1","1","0","0","0","1","1","1","1","1"],["0","0","1","1","0","1","1","x3","x3","x5"],["0","0","0","0","1","1","x1","x2","x4","x6"]]}}