{"id":"e-5008d121973b1f69","operation":{"map":"A013610","operation":"basis_map"},"operation_detail":"A013610","conclusion_id":"n-3ce4733084222518","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":"81da6c6aff9d86e7fbdee95c4a58e3e0c4845b792dfe04d7230adb031749af6b","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":15593,"certificate_compressed_size":3006,"conclusion_name":"basis_map_A013610 of A127733 * A007318 as infinite lower triangular matrices.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-375ba152c4aebf61","role":"sequence","name":"A127733 * A007318 as infinite lower triangular matrices.","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-3ce4733084222518","claim":"real_rooted"},{"node_id":"n-3ce4733084222518","claim":"one_signed_coefficients"},{"node_id":"n-3ce4733084222518","claim":"hadamard_kernel"}]}