{"id":"e-ba56344dd1f68fd7","operation":{"map":"A013609","operation":"basis_map"},"operation_detail":"A013609","conclusion_id":"n-30551c14ec291558","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":"c4e4c3c7a68f2ead4a91bab8aa47044c00e73e8dc2c16b208378f52cb30faf13","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":11582,"certificate_compressed_size":2152,"conclusion_name":"basis_map_A013609 of 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-c27b11147fce8bfa","role":"sequence","name":"Riordan array (1+2x,x(1+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-30551c14ec291558","claim":"real_rooted"},{"node_id":"n-30551c14ec291558","claim":"one_signed_coefficients"},{"node_id":"n-30551c14ec291558","claim":"hadamard_kernel"}]}