{"id":"e-36015c56c1237184","operation":{"map":"A013610","operation":"basis_map"},"operation_detail":"A013610","conclusion_id":"n-0d23d1c7119dd8ef","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":"2cab8e8391f1df5fe878b4d775bd0fd1c5e433e8cbedab7af9a961f71c2bf173","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":7453,"certificate_compressed_size":1637,"conclusion_name":"basis_map_A013610 of Unsigned 2-Stirling numbers of the first kind.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-c237629cf5fdbb07","role":"sequence","name":"Unsigned 2-Stirling numbers of the first kind.","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-0d23d1c7119dd8ef","claim":"real_rooted"},{"node_id":"n-0d23d1c7119dd8ef","claim":"one_signed_coefficients"},{"node_id":"n-0d23d1c7119dd8ef","claim":"hadamard_kernel"}]}