{"id":"e-bfabd72dd723d866","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-38c87f97096dd293","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":"7b39ee6dac331b01e546a3952e851f0712f44dc60198d0bc71985c4e442d881f","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":10659,"certificate_compressed_size":2348,"conclusion_name":"basis_map_A013611 of (4,1) Pascal triangle.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":2,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-dc83b48b191d08a9","role":"sequence","name":"(4,1) Pascal 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-38c87f97096dd293","claim":"real_rooted"},{"node_id":"n-38c87f97096dd293","claim":"one_signed_coefficients"},{"node_id":"n-38c87f97096dd293","claim":"hadamard_kernel"},{"node_id":"n-38c87f97096dd293","claim":"interlacing"}]}