{"id":"e-4d9b574196438af5","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-268fc412659cc990","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":"bcbc849c7322b87c8ef87beb588d9eff0767044d83e9f0689671e0172c791e54","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":15585,"certificate_compressed_size":3117,"conclusion_name":"basis_map_A013611 of basis_map_A013609 of Coefficients of a special case of Poisson-Charlier polynomials.","claims":[{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":2,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-95c4930a6d47b128","role":"sequence","name":"basis_map_A013609 of Coefficients of a special case of Poisson-Charlier polynomials.","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-268fc412659cc990","claim":"real_rooted"},{"node_id":"n-268fc412659cc990","claim":"one_signed_coefficients"},{"node_id":"n-268fc412659cc990","claim":"hadamard_kernel"},{"node_id":"n-268fc412659cc990","claim":"interlacing"}]}