{"id":"e-0527b2f699cf5083","operation":{"index_shift":0,"modulus":2,"operation":"veronese_section","residue":0},"operation_detail":"r=2, j=0, shift 0","conclusion_id":"n-69fa7016edbdbb09","premise_count":1,"theorem":"Veronese sections of Polya frequency sequences (Aissen--Schoenberg--Whitney--Edrei): if P is real-rooted with coefficients of one sign, equivalently nonzero with all roots in (-inf, 0], every section V_(r,j)(P) is zero or real-rooted with roots in (-inf, 0]","lean_route":null,"lean_declarations":[],"certificate_hash":"ce60751ebdb78d20961c4caee57122e358f5e72fe84ee57515ef3e633173cc78","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"veronese_section","certificate_raw_size":7352,"certificate_compressed_size":2071,"conclusion_name":"veronese_section_2_0 of Triangular array read by rows: row n gives the coefficients of the polynomial p(n,x) defined in Comments.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-ac04e52510a48bb5","role":"sequence","name":"Triangular array read by rows: row n gives the coefficients of the polynomial p(n,x) defined in Comments.","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-69fa7016edbdbb09","claim":"real_rooted"},{"node_id":"n-69fa7016edbdbb09","claim":"one_signed_coefficients"},{"node_id":"n-69fa7016edbdbb09","claim":"hadamard_kernel"}]}