{"id":"e-f92254fe3f61e8aa","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-24757ab977a41ca8","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":"2ad3085142660e21e9d22ab45c6ddb5bf94a8bc142c352d19a975d833db67406","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":14969,"certificate_compressed_size":2908,"conclusion_name":"shift_x_plus_one of basis_map_A007318 of Pascal-(1,5,1) array.","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-4f8c7533ab8b37bb","role":"sequence","name":"basis_map_A007318 of Pascal-(1,5,1) array.","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-24757ab977a41ca8","claim":"one_signed_coefficients"},{"node_id":"n-24757ab977a41ca8","claim":"hadamard_kernel"},{"node_id":"n-24757ab977a41ca8","claim":"real_rooted"},{"node_id":"n-24757ab977a41ca8","claim":"interlacing"}]}