{"id":"e-9a59a0e45d5a02ef","operation":{"map":"A013609","operation":"basis_map"},"operation_detail":"A013609","conclusion_id":"n-9b955a7242764c97","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":"d47b773d294f5aa8b0100fb4e0c1cb932719d3b0fc67bbaac4386b8840df3e12","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":15738,"certificate_compressed_size":3165,"conclusion_name":"basis_map_A013609 of veronese_section_2_1 of Even-numbered rows of Pascal's 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-7a03fdbbc6f038d4","role":"sequence","name":"veronese_section_2_1 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-9b955a7242764c97","claim":"real_rooted"},{"node_id":"n-9b955a7242764c97","claim":"one_signed_coefficients"},{"node_id":"n-9b955a7242764c97","claim":"hadamard_kernel"},{"node_id":"n-9b955a7242764c97","claim":"interlacing"}]}