{"id":"e-91082a28c5d8ee02","operation":{"operation":"obreschkoff_combination"},"operation_detail":null,"conclusion_id":"n-75126c0548fd070f","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":"bf088405304c717a8bd93ad6a013dba7585692476a9a6272d4c60cf902b142d3","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"obreschkoff_combination","certificate_raw_size":13244,"certificate_compressed_size":2981,"conclusion_name":"obreschkoff_combination of The convolution matrix of the double factorial of odd numbers (A001147).","claims":[{"claim":"real_rooted","from_index":0,"region":{}}],"premises":[{"position":0,"node_id":"n-ca41bee2bc8fcdbe","role":"sequence","name":"The convolution matrix of the double factorial of odd numbers (A001147).","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-ca41bee2bc8fcdbe","role":"sequence","name":"The convolution matrix of the double factorial of odd numbers (A001147).","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-75126c0548fd070f","claim":"real_rooted"}]}