{"id":"e-0b0545c4769e0ad6","operation":{"map":"A013610","operation":"basis_map"},"operation_detail":"A013610","conclusion_id":"n-8e47c78f771d4cfd","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":"79bb2268ede610144bfd92c1a993d40ce8d2240fc51ce9e276b5343c4e94379a","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":12292,"certificate_compressed_size":2338,"conclusion_name":"basis_map_A013610 of 3n + 1 preceded by n zeros.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-ccc86c3dcf2ac685","role":"sequence","name":"3n + 1 preceded by n zeros.","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-8e47c78f771d4cfd","claim":"real_rooted"},{"node_id":"n-8e47c78f771d4cfd","claim":"one_signed_coefficients"},{"node_id":"n-8e47c78f771d4cfd","claim":"hadamard_kernel"}]}