{"id":"e-1c2a2704f938fd35","operation":{"map":"A013609","operation":"basis_map"},"operation_detail":"A013609","conclusion_id":"n-20d13d43b8d2496f","premise_count":1,"theorem":"geometric family P_k = g(t) (a + d t)^k: T(p) = g(t) p(a + d t), so the roots of T(p) are those of g and the points (r - a)/d for the roots r of p (elementary)","lean_route":null,"lean_declarations":[],"certificate_hash":"f0c9d3bf6f5572bc25516f03e2817e34e0c4c2f9bbe1a9dbe988d56b6d11c303","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":6931,"certificate_compressed_size":1415,"conclusion_name":"basis_map_A013609 of basis_map_A013609 of Triangle read by rows: triangle of repeated stepped binomial coefficients.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-e42a65125928b4c5","role":"sequence","name":"basis_map_A013609 of Triangle read by rows: triangle of repeated stepped binomial coefficients.","uses":{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},"uses_text":"Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]"}],"cited_by":[{"node_id":"n-20d13d43b8d2496f","claim":"real_rooted"},{"node_id":"n-20d13d43b8d2496f","claim":"one_signed_coefficients"},{"node_id":"n-20d13d43b8d2496f","claim":"hadamard_kernel"}]}