{"id":"e-de35ff8f60015c8a","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-a75ac50997f70dee","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":"aedc247b5e5f393fa79b163779e60ea97ddf56024e6aab777743cbacb6277465","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":7413,"certificate_compressed_size":1621,"conclusion_name":"basis_map_A007318 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-cf1765de6ac2bd4b","role":"sequence","name":"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-a75ac50997f70dee","claim":"real_rooted"},{"node_id":"n-a75ac50997f70dee","claim":"one_signed_coefficients"},{"node_id":"n-a75ac50997f70dee","claim":"hadamard_kernel"}]}