{"id":"e-d866df21d4355ff2","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-24b741eba413aeed","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":"e3246867dcc6cc0a6f038a79c26c0eaf536b43990d2a0d4b3a9fd8f122b2e95c","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":7647,"certificate_compressed_size":1703,"conclusion_name":"basis_map_A013611 of theta_plus_one of basis-map coefficients of Triangle of coefficients in expansion of x^n in terms of Laguerre polynomials L_n(x).","claims":[{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-0fadb6a502ab98be","role":"sequence","name":"theta_plus_one of basis-map coefficients of Triangle of coefficients in expansion of x^n in terms of Laguerre polynomials L_n(x).","uses":{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}},"uses_text":"Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]"}],"cited_by":[{"node_id":"n-24b741eba413aeed","claim":"real_rooted"},{"node_id":"n-24b741eba413aeed","claim":"one_signed_coefficients"},{"node_id":"n-24b741eba413aeed","claim":"hadamard_kernel"}]}