{"id":"e-3318c326dc0e9fdb","operation":{"map":"A013609","operation":"basis_map"},"operation_detail":"A013609","conclusion_id":"n-60d1035d9816e10d","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":"84077cba3c4f24f374ab20fb3166ac4434ba1026df2de511219852d69b556e39","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":6865,"certificate_compressed_size":1394,"conclusion_name":"basis_map_A013609 of basis_map_A013609 of basis-map coefficients of Riordan array (1+2x,x(1+x)). shifted by x -> -x + 0","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-cb064c72efa341c9","role":"sequence","name":"basis_map_A013609 of basis-map coefficients of Riordan array (1+2x,x(1+x)). shifted by x -> -x + 0","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-60d1035d9816e10d","claim":"real_rooted"},{"node_id":"n-60d1035d9816e10d","claim":"one_signed_coefficients"},{"node_id":"n-60d1035d9816e10d","claim":"hadamard_kernel"}]}