{"id":"e-58f0eb5265d39366","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-baf5264cc15878a7","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":"6c1fefef72daa67b60fa6bd87804d7979ebad660df19567c042cfecfa1d4449d","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":11711,"certificate_compressed_size":2125,"conclusion_name":"basis_map_A013611 of derivative 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-f1591709bf5cf41b","role":"sequence","name":"derivative of 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-baf5264cc15878a7","claim":"real_rooted"},{"node_id":"n-baf5264cc15878a7","claim":"one_signed_coefficients"},{"node_id":"n-baf5264cc15878a7","claim":"hadamard_kernel"}]}