{"id":"e-c76f073fb8f8b4f4","operation":{"map":"A027466","operation":"basis_map"},"operation_detail":"A027466","conclusion_id":"n-c27b11147fce8bfa","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":"d551e069afb798796d36117409067e314e3892ec64eec8d86902fe71816361a5","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":14338,"certificate_compressed_size":2758,"conclusion_name":"Riordan array (1+2x,x(1+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-2ae85de8aa2f7a20","role":"sequence","name":"basis-map coefficients of Riordan array (1+2x,x(1+x)).","uses":{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"7"}}},"uses_text":"Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 7]"}],"cited_by":[{"node_id":"n-c27b11147fce8bfa","claim":"interlacing"},{"node_id":"n-c27b11147fce8bfa","claim":"one_signed_coefficients"},{"node_id":"n-c27b11147fce8bfa","claim":"hadamard_kernel"},{"node_id":"n-c27b11147fce8bfa","claim":"real_rooted"}]}