{"id":"e-f615883c5fdfd7df","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-ce5b0c4643351ea7","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":"449d61578e5322b97ca823d2f06a76b1c5295b8e36f8674ac16e37bfb9923548","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":13923,"certificate_compressed_size":2662,"conclusion_name":"basis_map_A013611 of derivative of Triangle read by rows: n-th row is n^2 preceded by (n-1) zeros.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-a23fdacbe8c6317d","role":"sequence","name":"derivative of Triangle read by rows: n-th row is n^2 preceded by (n-1) zeros.","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-ce5b0c4643351ea7","claim":"real_rooted"},{"node_id":"n-ce5b0c4643351ea7","claim":"one_signed_coefficients"},{"node_id":"n-ce5b0c4643351ea7","claim":"hadamard_kernel"}]}