{"id":"e-f9e5e2bc826d3dc0","operation":{"map":"A027465","operation":"basis_map"},"operation_detail":"A027465","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":"03d65c3b36ef224ccbffc98231f7410c4d8529acc804fef86c5653a689f11bfa","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":11591,"certificate_compressed_size":2162,"conclusion_name":"Riordan array (1+2x,x(1+x)).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-87e7c3f73bb81aac","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":"3"}}},"uses_text":"Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 3]"}],"cited_by":[{"node_id":"n-c27b11147fce8bfa","claim":"one_signed_coefficients"},{"node_id":"n-c27b11147fce8bfa","claim":"hadamard_kernel"},{"node_id":"n-c27b11147fce8bfa","claim":"real_rooted"}]}