{"id":"e-2b30cfe0c65df0c9","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-1a9e5fc6991d4de9","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":"93ac43a2e04076a6f413b41e0e12dd961db055aa6eaadaa5967930f973a834aa","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":14155,"certificate_compressed_size":2662,"conclusion_name":"shift_x_plus_one of basis_map_A013611 of narayana","claims":[{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":2,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-3af50523900b3357","role":"sequence","name":"basis_map_A013611 of narayana","uses":{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}},"uses_text":"Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]"}],"cited_by":[{"node_id":"n-1a9e5fc6991d4de9","claim":"one_signed_coefficients"},{"node_id":"n-1a9e5fc6991d4de9","claim":"hadamard_kernel"},{"node_id":"n-1a9e5fc6991d4de9","claim":"interlacing"},{"node_id":"n-1a9e5fc6991d4de9","claim":"real_rooted"}]}