{"id":"e-ea24c5115718581a","operation":{"operation":"obreschkoff_combination"},"operation_detail":null,"conclusion_id":"n-a8fee83659838741","premise_count":2,"theorem":"Hermite--Kakeya--Obreschkoff: real-rooted f, g with interlacing zeros give a zero or real-rooted a f + b g for all real a, b (Obreschkoff 1963; Fisk, Polynomials, roots, and interlacing, Thm 1.43)","lean_route":null,"lean_declarations":[],"certificate_hash":"13174c3f1acebf7dc307025f5c2b595ab43fff59b8102dd2a72f26340bae43a0","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"obreschkoff_combination","certificate_raw_size":8523,"certificate_compressed_size":2221,"conclusion_name":"obreschkoff_combination of Triangle whose (i,j)-th entry is binomial(i,j)*12^(i-j)*1^j.","claims":[{"claim":"real_rooted","from_index":0,"region":{}}],"premises":[{"position":0,"node_id":"n-81e6fb4f9f226d77","role":"sequence","name":"Triangle whose (i,j)-th entry is binomial(i,j)*12^(i-j)*1^j.","uses":{"claim":"real_rooted","from_index":0,"region":{}},"uses_text":"Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, +inf)"},{"position":1,"node_id":"n-81e6fb4f9f226d77","role":"sequence","name":"Triangle whose (i,j)-th entry is binomial(i,j)*12^(i-j)*1^j.","uses":{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"unordered"},"uses_text":"Rows P_(m-1), P_m interlace (weak, unordered) for every m >= 1"}],"cited_by":[{"node_id":"n-a8fee83659838741","claim":"real_rooted"}]}