{"rank":3,"n":11,"seq":29094,"label":"3.11.29094","id":"r3_n11_0******0******0**********0********0*******0****0****************0*****************************0****************0*0**********************0****0*****************0*****","beta_invariant":22,"birational_type":"point over Q(a)/(a^2 + 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 + 1)\",\"field\":\"Q(a)/(a^2 + 1)\",\"minpoly\":\"T^2 + 1\",\"degree\":2,\"core_vars\":[\"x1\"],\"core_gens\":[\"x1^2 + 2*x1 + 2\"]}]","birational_type_method":"point_field","char_poly_splits":false,"char_set":"[0,2,3,5]","expected_dimension_over_Z":1,"free_realization_space":false,"girth":3,"good_basis":"1,2,4","good_basis_v2":"2,3,7","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":151,"n_circuits":232,"n_components":null,"n_connected_components":1,"n_cyclic_flats":16,"n_flats":40,"n_loops":0,"principal_ideal":true,"rs_characteristic_dimension_unexpected":false,"rs_characteristic_dimension_varies":false,"rs_characteristic_dimensions":"[{\"p\":0,\"d\":0}]","rs_characteristic_dimensions_method":"cofinite_strong_groebner_candidates_exact","rs_dim":0,"rs_is_regular_scheme":true,"rs_is_smooth_over_QQ":null,"rs_is_smooth_over_ZZ":true,"rs_n_qbar_components":null,"rs_regularity_method":"three_lines_deletion","rs_regularity_witness":"9=>r3_n10_0******0******0**********0********0*******0****0******************0****************0***************0********0****0******","rs_scheme_simple_core_id":"r3_n11_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":"three_lines_deletion","rs_smoothness_witness":"9=>r3_n10_0******0******0**********0********0*******0****0******************0****************0***************0********0****0******","singular_primes":"[]","smooth_char_0":true,"status":"computed_realization_space","tutte_polynomial":"x_0^3 + 8*x_0^2 + 14*x_0*x_1 + 22*x_0 + x_1^8 + 3*x_1^7 + 6*x_1^6 + 10*x_1^5 + 15*x_1^4 + 21*x_1^3 + 28*x_1^2 + 22*x_1","realization_space":{"vars":["x1"],"ideal":["x1^2 + 2*x1 + 2"],"inequations":["x1 + 2","x1","x1 - 1","x1^2 + 4*x1 + 1","2*x1 + 1","2","3","2*x1 - 1","2*x1^2 + 3*x1 + 2","x1^3 + 2*x1^2 + 1","x1^2 + x1 - 1","x1 + 3"],"matrix":[["1","1","0","0","1","1","0","1","1","1","1"],["1","0","1","1","-x1","-x1","0","2","-x1 - 2","2","0"],["0","0","0","1","-x1 - 1","-x1","1","-x1","-x1 - 1","x1 + 2","x1"]]}}