{"id":"e-e333d81f779c4158","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-8548b8471ae89704","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":"6a62a3ac2610ae7f93c448710a7db3775e03c1ae9936ba9ad5cbad115b8c9c3a","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":14013,"certificate_compressed_size":2709,"conclusion_name":"basis_map_A013611 of Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.","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-eac80c2bf8e566f5","role":"sequence","name":"Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.","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-8548b8471ae89704","claim":"interlacing"},{"node_id":"n-8548b8471ae89704","claim":"real_rooted"},{"node_id":"n-8548b8471ae89704","claim":"one_signed_coefficients"},{"node_id":"n-8548b8471ae89704","claim":"hadamard_kernel"}]}