{"id":"e-39d66391a6d06c77","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-1d9325b8d0810008","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":"409ba04e62d339798955f1678468450531dd61bf6c75eff9041371ece7c93fb0","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":6929,"certificate_compressed_size":1412,"conclusion_name":"shift_x_plus_one of basis_map_A013610 of Triangle of coefficients in expansion of (1+5x)^n.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-31eaa59be7a07b63","role":"sequence","name":"basis_map_A013610 of Triangle of coefficients in expansion of (1+5x)^n.","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-1d9325b8d0810008","claim":"one_signed_coefficients"},{"node_id":"n-1d9325b8d0810008","claim":"hadamard_kernel"},{"node_id":"n-1d9325b8d0810008","claim":"real_rooted"}]}