{"id":"e-9fbcf9ea58f2c005","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-ea69de4dd6061116","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":"f968653d0dd7c1dbce31cd8fa30583075ee01c1966cf4d58d556fa7334ed6863","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":14966,"certificate_compressed_size":2915,"conclusion_name":"shift_x_plus_one of A triangle of numbers related to triangle A030528; array a(n,m), read by rows (1 <= m <= n).","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-47e3a1a59edf16da","role":"sequence","name":"A triangle of numbers related to triangle A030528; array a(n,m), read by rows (1 <= m <= 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-ea69de4dd6061116","claim":"one_signed_coefficients"},{"node_id":"n-ea69de4dd6061116","claim":"hadamard_kernel"},{"node_id":"n-ea69de4dd6061116","claim":"real_rooted"},{"node_id":"n-ea69de4dd6061116","claim":"interlacing"}]}