{"id":"e-1fe5b61acc156f66","operation":{"map":"A013609","operation":"basis_map"},"operation_detail":"A013609","conclusion_id":"n-1cb9c12ec3656f95","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":"9a608a81e71442185230b2d384bd09ac394570051be3369efc87dc8da3b5f8b1","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":6915,"certificate_compressed_size":1398,"conclusion_name":"basis_map_A013609 of Triangle read by rows, A007318 rows repeated three times.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-99e5bf113a0a46cd","role":"sequence","name":"Triangle read by rows, A007318 rows repeated three times.","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-1cb9c12ec3656f95","claim":"real_rooted"},{"node_id":"n-1cb9c12ec3656f95","claim":"one_signed_coefficients"},{"node_id":"n-1cb9c12ec3656f95","claim":"hadamard_kernel"}]}