{"id":"e-fd1e0e214e835b97","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-3b0e9ba368b8ed81","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":"fc3e5cc21fefb0a3a7962d83bb5881742ffb89a5f9ba383ae2fd92a2c34d8548","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":15611,"certificate_compressed_size":3023,"conclusion_name":"basis_map_A007318 of Riordan array (1, x/(1-x)^2).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":2,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-83d230649c15eed8","role":"sequence","name":"Riordan array (1, x/(1-x)^2).","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-3b0e9ba368b8ed81","claim":"real_rooted"},{"node_id":"n-3b0e9ba368b8ed81","claim":"one_signed_coefficients"},{"node_id":"n-3b0e9ba368b8ed81","claim":"hadamard_kernel"},{"node_id":"n-3b0e9ba368b8ed81","claim":"interlacing"}]}