{"id":"e-a134cf740a72d883","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-aa4f19523cc05a57","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":"f2f04cbf46b195153f3aab3ac1b3a03172dde7b33f9f4d94762f069be6562184","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":10789,"certificate_compressed_size":2372,"conclusion_name":"basis_map_A007318 of Triangle, read by rows, where T(n,k) = n!/(k!*(n-4*k)!*4^k) for n>=4*k>=0.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-fa138429dacf7586","role":"sequence","name":"Triangle, read by rows, where T(n,k) = n!/(k!*(n-4*k)!*4^k) for n>=4*k>=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-aa4f19523cc05a57","claim":"real_rooted"},{"node_id":"n-aa4f19523cc05a57","claim":"one_signed_coefficients"},{"node_id":"n-aa4f19523cc05a57","claim":"hadamard_kernel"},{"node_id":"n-aa4f19523cc05a57","claim":"interlacing"}]}