{ "arithmetic": "rational LDL^T; integer comparisons and exact integer-square-root branch bounds", "best_history": [ { "nodes": 0, "normalized_value": "67240000/172075351", "polynomial": [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 ] } ], "canonical_tie_count": 1, "canonical_ties": [ [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 ] ], "decomposition_seconds": 0.4980138140017516, "degree_bound": 80, "elapsed_seconds": 1.9306741729997157, "improvements": 0, "initial_bound": "67240000/172075351", "initial_candidate_kind": "Dirichlet product", "initial_dirichlet_lengths": [ 40, 41 ], "integral_over_2pi_display": 4.245588222748232, "lambda": "5/2", "leaves": 1, "node_limit": 10000000, "nodes": 149987, "normalized_best": "67240000/172075351", "normalized_minimum": "67240000/172075351", "normalized_objective": "integral / (2*pi*c0(lambda))", "polynomial": [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 ], "polynomial_degree": 79, "python_version": "3.12.14", "real_relaxation_minimum": "133499189745056880149688856635597007162669032647290798121690100488888732861290034376435130433536/1345240737773187029898893229364826393732433451070121469883926999900870372480076274596709520025325", "script_sha256": "586c569e25f769cd87db7bc558942e622576af6f764910f8616523abaed41885", "search_denominator_bits": 447, "status": "complete" }