{"id":"e-1d7f8f614531604f","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-6bdb5d7e28f56300","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":"0d64732a6aa3bfa078322db279b41622c4dc238bdf2e5c36e54feb814a2156dc","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":13345,"certificate_compressed_size":2517,"conclusion_name":"basis_map_A007318 of Triangular array formed by the Mersenne numbers.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-9b5c7e97e5191da6","role":"sequence","name":"Triangular array formed by the Mersenne numbers.","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-6bdb5d7e28f56300","claim":"real_rooted"},{"node_id":"n-6bdb5d7e28f56300","claim":"one_signed_coefficients"},{"node_id":"n-6bdb5d7e28f56300","claim":"hadamard_kernel"},{"node_id":"n-6bdb5d7e28f56300","claim":"interlacing"}]}