{"id":"e-fca1808ca715ed77","operation":{"map":"A013609","operation":"basis_map"},"operation_detail":"A013609","conclusion_id":"n-bf2f08bd0370af8d","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":"d26334e964aa2d76d0251dbd645de408e01b5d9d859f61e406d4dc8224986cae","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":14146,"certificate_compressed_size":2740,"conclusion_name":"basis_map_A013609 of Pascal-(1,4,1) 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-ed9434bfd889c409","role":"sequence","name":"Pascal-(1,4,1) 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-bf2f08bd0370af8d","claim":"real_rooted"},{"node_id":"n-bf2f08bd0370af8d","claim":"one_signed_coefficients"},{"node_id":"n-bf2f08bd0370af8d","claim":"hadamard_kernel"},{"node_id":"n-bf2f08bd0370af8d","claim":"interlacing"}]}