{"id":"e-b045b4757da86ee8","operation":{"map":"A013609","operation":"basis_map"},"operation_detail":"A013609","conclusion_id":"n-2f46ab61d8cae267","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":"077ac631128b0c6c4241e6eb784ef6e52fd1ed9836d5d8dca39f8ce0f2bed59b","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":6904,"certificate_compressed_size":1414,"conclusion_name":"basis_map_A013609 of basis_map_A013611 of Riordan array (1-x,x/(1-x)).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-84c761192e0db3c0","role":"sequence","name":"basis_map_A013611 of Riordan array (1-x,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-2f46ab61d8cae267","claim":"real_rooted"},{"node_id":"n-2f46ab61d8cae267","claim":"one_signed_coefficients"},{"node_id":"n-2f46ab61d8cae267","claim":"hadamard_kernel"}]}