{"id":"e-e8b665303e1ab844","operation":{"map":"A013609","operation":"basis_map"},"operation_detail":"A013609","conclusion_id":"n-523988d0c7c28a88","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":"91ef2cc8ee804cc00affe5dec498ed3b594f5fae522155f70ba46bd2b11f5ca7","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":17443,"certificate_compressed_size":3457,"conclusion_name":"basis_map_A013609 of derivative of Exponential Riordan array [x*exp(x),x].","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":3,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-4330f616ae0ed2bc","role":"sequence","name":"derivative of Exponential Riordan array [x*exp(x),x].","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-523988d0c7c28a88","claim":"real_rooted"},{"node_id":"n-523988d0c7c28a88","claim":"one_signed_coefficients"},{"node_id":"n-523988d0c7c28a88","claim":"hadamard_kernel"},{"node_id":"n-523988d0c7c28a88","claim":"interlacing"}]}