{"id":"e-3252cc2fe5229b3d","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-1f0d56c568ab8221","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":"8cd348c48039a1500ac8b258630eb8ecae4dea3bdd82a73bc36099e44bf42d25","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":11661,"certificate_compressed_size":2188,"conclusion_name":"basis_map_A007318 of Riordan array (1, 3+3x).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-016d7724d51f6416","role":"sequence","name":"Riordan array (1, 3+3x).","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-1f0d56c568ab8221","claim":"real_rooted"},{"node_id":"n-1f0d56c568ab8221","claim":"one_signed_coefficients"},{"node_id":"n-1f0d56c568ab8221","claim":"hadamard_kernel"}]}