{"id":"e-f2e5e2864fad238b","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-8c0973a753fcbe28","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":"0bc0aa8ce3636754b83585376f00d7e51f29b54c837951c10269a27882a485f5","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":6875,"certificate_compressed_size":1388,"conclusion_name":"basis_map_A007318 of Even-numbered rows of Pascal's triangle.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-08f49539099949d5","role":"sequence","name":"Even-numbered rows of Pascal's 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-8c0973a753fcbe28","claim":"real_rooted"},{"node_id":"n-8c0973a753fcbe28","claim":"one_signed_coefficients"},{"node_id":"n-8c0973a753fcbe28","claim":"hadamard_kernel"}]}