{"id":"e-b3cf2c801874c157","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-0cc3f39711d63ef9","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":"430aa0f1cb4afce13ba5617c997af4d05d5cc53a3cd7a6b2bf54e953be7636b3","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":15435,"certificate_compressed_size":2862,"conclusion_name":"basis_map_A013611 of derivative of Triangle read by rows: row n consists of n zeros followed by n!.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":2,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-900a36a3001cf31d","role":"sequence","name":"derivative of Triangle read by rows: row n consists of n zeros followed by n!.","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-0cc3f39711d63ef9","claim":"real_rooted"},{"node_id":"n-0cc3f39711d63ef9","claim":"one_signed_coefficients"},{"node_id":"n-0cc3f39711d63ef9","claim":"hadamard_kernel"},{"node_id":"n-0cc3f39711d63ef9","claim":"interlacing"}]}