{"id":"e-b4660546a5e77fa6","operation":{"map":"A013609","operation":"basis_map"},"operation_detail":"A013609","conclusion_id":"n-393cac5827041b9e","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":"7e87555fc07ee280a064397613bb96909e70a605ccce69c93fdabd2bdc590359","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":13663,"certificate_compressed_size":2603,"conclusion_name":"basis_map_A013609 of Triangle: row #n has n+1 terms. T(n,m) = 4^m (2n+1)! / ( (2n-2m)! (2m+1)! ).","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-9aec4822212db1dc","role":"sequence","name":"Triangle: row #n has n+1 terms. T(n,m) = 4^m (2n+1)! / ( (2n-2m)! (2m+1)! ).","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-393cac5827041b9e","claim":"real_rooted"},{"node_id":"n-393cac5827041b9e","claim":"one_signed_coefficients"},{"node_id":"n-393cac5827041b9e","claim":"hadamard_kernel"},{"node_id":"n-393cac5827041b9e","claim":"interlacing"}]}