{"id":"e-77bf2cb365051314","operation":{"map":"A013610","operation":"basis_map"},"operation_detail":"A013610","conclusion_id":"n-412b54b3d1f71393","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":"24fe69ae6d8aefca8f29b2d4f13f8b23b7b316dbc0fa45177db4debfafe21c81","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":7409,"certificate_compressed_size":1615,"conclusion_name":"basis_map_A013610 of Triangle read by rows: row n consists of n zeros followed by n!.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-fbb4b9430d9de872","role":"sequence","name":"Triangle read by rows: row n consists of n zeros followed by 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-412b54b3d1f71393","claim":"real_rooted"},{"node_id":"n-412b54b3d1f71393","claim":"one_signed_coefficients"},{"node_id":"n-412b54b3d1f71393","claim":"hadamard_kernel"}]}