{"id":"e-a647198769a5a6c1","operation":{"map":"A013610","operation":"basis_map"},"operation_detail":"A013610","conclusion_id":"n-60114611aeb15c63","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":"dc1047ca650d94b51b811ce3534ce4954ff93c335fbdd098e80355e0e5f81b84","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":14730,"certificate_compressed_size":2902,"conclusion_name":"basis_map_A013610 of Triangle of coefficients of Legendre polynomials 2^n P_n (x).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-b2f14d9f44a39df2","role":"sequence","name":"Triangle of coefficients of Legendre polynomials 2^n P_n (x).","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-60114611aeb15c63","claim":"one_signed_coefficients"},{"node_id":"n-60114611aeb15c63","claim":"hadamard_kernel"},{"node_id":"n-60114611aeb15c63","claim":"interlacing"},{"node_id":"n-60114611aeb15c63","claim":"real_rooted"}]}