{"id":"e-b33bc3eaffd61d75","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-b7a274e8348d5af4","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":"84442d4b156c35f305dd769d0f26f762ddb0252d03befe6a799736ad3db8b2ff","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":6899,"certificate_compressed_size":1404,"conclusion_name":"shift_x_plus_one of basis_map_A013610 of basis-map coefficients of A scaled Hermite triangle.","claims":[{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-b8d8f9de0e27e805","role":"sequence","name":"basis_map_A013610 of basis-map coefficients of A scaled Hermite triangle.","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-b7a274e8348d5af4","claim":"hadamard_kernel"},{"node_id":"n-b7a274e8348d5af4","claim":"real_rooted"},{"node_id":"n-b7a274e8348d5af4","claim":"one_signed_coefficients"}]}