{"id":"e-7b1159fca4765fad","operation":{"map":"A013609","operation":"basis_map"},"operation_detail":"A013609","conclusion_id":"n-3992e0c998ec014d","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":"f3adee6828f89137985ea75bf9c051451bb67491e1e0c6719c7d789b9b3b3643","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":10264,"certificate_compressed_size":2303,"conclusion_name":"basis_map_A013609 of basis_map_A013610 of Triangle T(n,k) = n!*binomial(n-1, k-1) for 1 <= k <= n, read by rows.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-9c0ed28aed848f75","role":"sequence","name":"basis_map_A013610 of Triangle T(n,k) = n!*binomial(n-1, k-1) for 1 <= k <= n, read by rows.","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-3992e0c998ec014d","claim":"real_rooted"},{"node_id":"n-3992e0c998ec014d","claim":"one_signed_coefficients"},{"node_id":"n-3992e0c998ec014d","claim":"hadamard_kernel"},{"node_id":"n-3992e0c998ec014d","claim":"interlacing"}]}