{"id":"e-22c9ba4d8e0c0a0e","operation":{"map":"A013610","operation":"basis_map"},"operation_detail":"A013610","conclusion_id":"n-f929f0b56bd73253","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":"6a307cc51bc668c26cdd8e15bb40e135d55214170db0ab5d02be4a226be83de3","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":10671,"certificate_compressed_size":2362,"conclusion_name":"basis_map_A013610 of Triangular array:  the fusion of polynomial sequences P and Q given by p(n,x)=(x+2)^n and q(n,x)=(x+2)^n.","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-cedb1276760d9bb1","role":"sequence","name":"Triangular array:  the fusion of polynomial sequences P and Q given by p(n,x)=(x+2)^n and q(n,x)=(x+2)^n.","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-f929f0b56bd73253","claim":"real_rooted"},{"node_id":"n-f929f0b56bd73253","claim":"one_signed_coefficients"},{"node_id":"n-f929f0b56bd73253","claim":"hadamard_kernel"},{"node_id":"n-f929f0b56bd73253","claim":"interlacing"}]}