{"id":"e-f89207c37b53647e","operation":{"map":"A013609","operation":"basis_map"},"operation_detail":"A013609","conclusion_id":"n-4d4af5f206880e6d","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":"95c80fef03e8470ad863d0ea8d7af25a8574782640a10bf334d9a81651270d36","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":6895,"certificate_compressed_size":1404,"conclusion_name":"basis_map_A013609 of shift_x_plus_one of basis-map coefficients of A scaled Hermite triangle.","claims":[{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-dd649f176537f8e7","role":"sequence","name":"shift_x_plus_one of basis-map coefficients of A scaled Hermite triangle.","uses":{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}},"uses_text":"Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]"}],"cited_by":[{"node_id":"n-4d4af5f206880e6d","claim":"real_rooted"},{"node_id":"n-4d4af5f206880e6d","claim":"one_signed_coefficients"},{"node_id":"n-4d4af5f206880e6d","claim":"hadamard_kernel"}]}