{"id":"e-1a23c946b3a4bebe","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-a9307f854ca152e2","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":"eafe501b883ab93d75da7d8b3a6050a46cb513554104b412ec835130ab1838d7","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":14408,"certificate_compressed_size":2794,"conclusion_name":"basis_map_A007318 of Riordan array (1, 3+x).","claims":[{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":2,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-5d39164c4108e043","role":"sequence","name":"Riordan array (1, 3+x).","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-a9307f854ca152e2","claim":"real_rooted"},{"node_id":"n-a9307f854ca152e2","claim":"one_signed_coefficients"},{"node_id":"n-a9307f854ca152e2","claim":"hadamard_kernel"},{"node_id":"n-a9307f854ca152e2","claim":"interlacing"}]}