{"id":"e-9c08db68889738c4","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-21b46279e9abe0a4","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":"0304737e43fddbcbaf85d7d2853417b5bf90739017476db7c80a0157a8fa5501","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":6860,"certificate_compressed_size":1389,"conclusion_name":"basis_map_A013611 of Triangle whose (n,k)-th entry is 15^(n-k)*binomial(n,k).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-ff0214c333bfdcca","role":"sequence","name":"Triangle whose (n,k)-th entry is 15^(n-k)*binomial(n,k).","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-21b46279e9abe0a4","claim":"real_rooted"},{"node_id":"n-21b46279e9abe0a4","claim":"one_signed_coefficients"},{"node_id":"n-21b46279e9abe0a4","claim":"hadamard_kernel"}]}