{"id":"e-504998c35fa768f4","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-623b56c3e833abe6","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":"180a5a84a3648b9613e4d74f00bd1b523decf59eb86801c71e6ff6eb6170672c","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":6944,"certificate_compressed_size":1418,"conclusion_name":"shift_x_plus_one of basis_map_A013610 of Triangle of coefficients in expansion of (1+11x)^n.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-ea3be122f7c7526c","role":"sequence","name":"basis_map_A013610 of Triangle of coefficients in expansion of (1+11x)^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-623b56c3e833abe6","claim":"one_signed_coefficients"},{"node_id":"n-623b56c3e833abe6","claim":"hadamard_kernel"},{"node_id":"n-623b56c3e833abe6","claim":"real_rooted"}]}