{"id":"e-9781ec1f8490e6f3","operation":{"map":"A013610","operation":"basis_map"},"operation_detail":"A013610","conclusion_id":"n-47a2e536b5967de9","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":"33eeddabf08da604c65d3a2afaf7d27d6e22ae84adead54ca657f37778a448d7","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":12230,"certificate_compressed_size":2258,"conclusion_name":"basis_map_A013610 of A Motzkin related triangle.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-de4284a2d5d7d0a6","role":"sequence","name":"A Motzkin related triangle.","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-47a2e536b5967de9","claim":"real_rooted"},{"node_id":"n-47a2e536b5967de9","claim":"one_signed_coefficients"},{"node_id":"n-47a2e536b5967de9","claim":"hadamard_kernel"}]}