{"rank":3,"n":12,"seq":1825310,"label":"3.12.1825310","id":"r3_n12_0******0******0**********0********0*******0*********************0*****************0***********0**********************************************0************0****0********************************0***0******0*******0********","beta_invariant":29,"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":"4,5,9","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":true,"is_transversal":false,"is_uniform":null,"n_automorphisms":1,"n_bases":204,"n_circuits":367,"n_components":null,"n_connected_components":1,"n_cyclic_flats":18,"n_flats":48,"n_loops":0,"principal_ideal":false,"rs_characteristic_dimension_unexpected":false,"rs_characteristic_dimension_varies":false,"rs_characteristic_dimensions":"[{\"p\":0,\"d\":0}]","rs_characteristic_dimensions_method":"exact_flatness_and_exceptional_fibers","rs_dim":7,"rs_is_regular_scheme":null,"rs_is_smooth_over_QQ":true,"rs_is_smooth_over_ZZ":false,"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\":[\"331\"]}","rs_singular_fiber_characteristics_method":"reused_direct_equidimensional_jacobian_certificate","rs_singular_fiber_primes":null,"rs_singular_fiber_primes_method":null,"rs_smoothness_method":"direct_equidimensional_jacobian_certificate","rs_smoothness_witness":"331","singular_primes":null,"smooth_char_0":null,"status":"computed_realization_space","tutte_polynomial":"x_0^3 + 9*x_0^2 + 16*x_0*x_1 + 29*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 + 36*x_1^2 + 29*x_1","realization_space":{"vars":["x1","x2"],"ideal":["3*x1*x2 - 2*x1 - 2*x2^2 - 1","x1^2 + x1*x2 + 3*x1 - 3*x2^2 + 2*x2 - 3","x1*x2 - x1 + x2^3 - 4*x2^2 + 2*x2 - 2","x1*x2^2 - x1*x2 - 2*x2^2 + x2 - 1"],"inequations":["x1*x2 + x2^2 - x2 + 1","3*x1^2*x2^3 - 9*x1^2*x2^2 + 3*x1^2*x2 + x1^2 - 4*x1*x2^3 + 10*x1*x2^2 - 3*x1*x2 + x1 - x2^2 + x2 - 1","x1^2*x2^3 - 3*x1^2*x2^2 + x1^2*x2 - x1^2 + 10*x1*x2^5 - 40*x1*x2^4 + 49*x1*x2^3 - 39*x1*x2^2 + 10*x1*x2 - x1 - 7*x2^5 + 22*x2^4 - 28*x2^3 + 25*x2^2 - 10*x2 + 4","10*x1*x2^4 - 31*x1*x2^3 + 13*x1*x2^2 - 3*x1*x2 + x1 - 7*x2^4 + 16*x2^3 - 9*x2^2 + 6*x2 - 1","x1^2*x2^3 - 3*x1^2*x2^2 + x1^2*x2 - x1^2 - x1*x2^6 + 6*x1*x2^5 - 22*x1*x2^4 + 51*x1*x2^3 - 48*x1*x2^2 + 14*x1*x2 - 3*x1 + x2^6 - 6*x2^5 + 20*x2^4 - 37*x2^3 + 34*x2^2 - 16*x2 + 6","3*x1*x2^3 - 9*x1*x2^2 + 3*x1*x2 + x1 - 4*x2^3 + 10*x2^2 - 2*x2 + 1","3*x1^2*x2^3 - 9*x1^2*x2^2 + 3*x1^2*x2 + x1^2 - 3*x1*x2^6 + 18*x1*x2^5 - 36*x1*x2^4 + 28*x1*x2^3 - 11*x1*x2^2 + x1*x2 + 3*x1 + 4*x2^6 - 22*x2^5 + 41*x2^4 - 38*x2^3 + 29*x2^2 - 7*x2 + 1","x1*x2 - x2^4 + 3*x2^3 - 2*x2^2 + x2 + 1","x1^2*x2^3 - 3*x1^2*x2^2 + x1^2*x2 - x1^2 + 10*x1*x2^5 - 30*x1*x2^4 + 18*x1*x2^3 - 26*x1*x2^2 + 8*x1*x2 - 7*x2^5 + 15*x2^4 - 12*x2^3 + 17*x2^2 - 5*x2 + 4","x1*x2^6 + 4*x1*x2^5 - 18*x1*x2^4 - 2*x1*x2^3 + 10*x1*x2^2 - 4*x1*x2 + 2*x1 - x2^6 - 2*x2^5 + 6*x2^4 + 3*x2^3 - 2*x2^2 + 2*x2","30*x1^2*x2^6 - 180*x1^2*x2^5 + 330*x1^2*x2^4 - 173*x1^2*x2^3 + 9*x1^2*x2^2 + 7*x1^2*x2 - x1^2 - 61*x1*x2^6 + 328*x1*x2^5 - 544*x1*x2^4 + 309*x1*x2^3 - 112*x1*x2^2 + 20*x1*x2 + 2*x1 + 28*x2^6 - 130*x2^5 + 195*x2^4 - 129*x2^3 + 75*x2^2 - 19*x2 + 4","x1*x2^3 - 3*x1*x2^2 + x1*x2 - x1 - x2^3 + 2*x2^2 - x2","11*x1*x2^6 - 56*x1*x2^5 + 91*x1*x2^4 - 59*x1*x2^3 + 19*x1*x2^2 - 3*x1*x2 + x1 - 8*x2^6 + 34*x2^5 - 51*x2^4 + 37*x2^3 - 17*x2^2 + 5*x2","10*x1*x2^3 - 30*x1*x2^2 + 10*x1*x2 - x1 - 7*x2^3 + 15*x2^2 - 6*x2 + 4","x1*x2^6 + 4*x1*x2^5 - 19*x1*x2^4 + 2*x1*x2^3 + 6*x1*x2^2 - 2*x1*x2 + x1 - x2^6 - 2*x2^5 + 7*x2^4 + x2^2 + x2","x1 - 1","x1*x2^3 - 2*x1*x2^2 + x1*x2 - x2^5 + 3*x2^4 - 3*x2^3 + 6*x2^2 - 2*x2 + 1","3*x1*x2^6 - 18*x1*x2^5 + 33*x1*x2^4 - 20*x1*x2^3 + 9*x1*x2^2 - 2*x1*x2 - x1 - 4*x2^6 + 22*x2^5 - 37*x2^4 + 23*x2^3 - 14*x2^2 + 3*x2 - 1","x2^2 + 1","3*x1^2*x2^3 - 9*x1^2*x2^2 + 3*x1^2*x2 + x1^2 - 7*x1*x2^3 + 19*x1*x2^2 - 6*x1*x2 + 4*x2^3 - 11*x2^2 + 3*x2 - 2","3*x1*x2^6 - 18*x1*x2^5 + 36*x1*x2^4 - 32*x1*x2^3 + 21*x1*x2^2 - 4*x1*x2 - 2*x1 - 4*x2^6 + 22*x2^5 - 41*x2^4 + 38*x2^3 - 30*x2^2 + 8*x2 - 2","x1*x2^2 - x2^5 + 3*x2^4 - 3*x2^3 + 4*x2^2 - 2*x2 + 2","10*x1*x2^3 - 30*x1*x2^2 + 10*x1*x2 - 2*x1 - 7*x2^3 + 15*x2^2 - 6*x2 + 5","10*x1*x2^3 - 30*x1*x2^2 + 10*x1*x2 - x1 - 8*x2^3 + 18*x2^2 - 8*x2 + 6","x1^2*x2^3 - 3*x1^2*x2^2 + x1^2*x2 - x1^2 - x1*x2^6 + 6*x1*x2^5 - 11*x1*x2^4 + 16*x1*x2^3 - 31*x1*x2^2 + 10*x1*x2 - x1 + x2^6 - 6*x2^5 + 11*x2^4 - 14*x2^3 + 19*x2^2 - 7*x2 + 5","x1*x2^3 - 3*x1*x2^2 + x1*x2 - x1 - x2^3 + 3*x2^2 - x2","x1^2 - 10*x1*x2^3 + 30*x1*x2^2 - 10*x1*x2 + 7*x2^3 - 15*x2^2 + 6*x2 - 4","9*x1*x2^6 - 54*x1*x2^5 + 98*x1*x2^4 - 49*x1*x2^3 + 2*x1*x2^2 + 3*x1*x2 - 2*x1 - 7*x2^6 + 36*x2^5 - 58*x2^4 + 37*x2^3 - 18*x2^2 + 4*x2","30*x1^2*x2^6 - 180*x1^2*x2^5 + 330*x1^2*x2^4 - 176*x1^2*x2^3 + 18*x1^2*x2^2 + 4*x1^2*x2 - 2*x1^2 - 61*x1*x2^6 + 328*x1*x2^5 - 544*x1*x2^4 + 316*x1*x2^3 - 131*x1*x2^2 + 26*x1*x2 + 2*x1 + 28*x2^6 - 130*x2^5 + 195*x2^4 - 133*x2^3 + 86*x2^2 - 22*x2 + 6","30*x1^2*x2^6 - 180*x1^2*x2^5 + 330*x1^2*x2^4 - 173*x1^2*x2^3 + 9*x1^2*x2^2 + 7*x1^2*x2 - x1^2 - 64*x1*x2^6 + 346*x1*x2^5 - 580*x1*x2^4 + 341*x1*x2^3 - 133*x1*x2^2 + 24*x1*x2 + 4*x1 + 32*x2^6 - 152*x2^5 + 236*x2^4 - 167*x2^3 + 105*x2^2 - 27*x2 + 6","x1^2*x2^3 - 3*x1^2*x2^2 + x1^2*x2 - x1^2 - x1*x2^6 + 6*x1*x2^5 - 12*x1*x2^4 + 20*x1*x2^3 - 35*x1*x2^2 + 12*x1*x2 - 2*x1 + x2^6 - 6*x2^5 + 12*x2^4 - 18*x2^3 + 23*x2^2 - 9*x2 + 6"],"matrix":[["1","1","0","1","0","1","1","1","0","1","1","1"],["1","2*x2^3 - 7*x2^2 + 4*x2 - 3","1","0","1","2*x2^3 - 7*x2^2 + 5*x2 - 4","x1","2*x2^3 - 7*x2^2 + 5*x2 - 4","0","-10*x1^2 + 2*x1*x2^3 - x1*x2^2 - 33*x1 + 12*x2^4 - 52*x2^3 + 69*x2^2 - 55*x2 + 35","x1","0"],["0","1","3*x1^2 + 2*x1*x2^2 - 2*x1*x2 + 10*x1 - 4*x2^4 + 18*x2^3 - 34*x2^2 + 26*x2 - 20","0","0","-x1 + 2*x2^3 - 7*x2^2 + 5*x2 - 4","-x1 + 2*x2^3 - 7*x2^2 + 5*x2 - 4","1","1","x1^2 - 2*x1*x2^3 + x1*x2^2 - x1*x2 + 3*x1 + 6*x2^3 - 7*x2^2 + 7*x2 - 4","x2^2 + 1","x2"]]}}