{"id":"e-0db30c1d149f8e9a","operation":{"map":"A027467","operation":"basis_map"},"operation_detail":"A027467","conclusion_id":"n-ba196dcd01800741","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":"785c38337254a7c91729a552a4390a6b9436b55707a5cb2f30bbfe742b6eb516","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":11703,"certificate_compressed_size":2203,"conclusion_name":"A Jacobsthal triangle.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-eb460955a5ddb26b","role":"sequence","name":"basis-map coefficients of A Jacobsthal triangle.","uses":{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"15"}}},"uses_text":"Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 15]"}],"cited_by":[{"node_id":"n-ba196dcd01800741","claim":"real_rooted"},{"node_id":"n-ba196dcd01800741","claim":"one_signed_coefficients"},{"node_id":"n-ba196dcd01800741","claim":"hadamard_kernel"}]}