{"id":"e-7e466a04f17f31a0","operation":{"map":"A013609","operation":"basis_map"},"operation_detail":"A013609","conclusion_id":"n-b0b9f0e48753af20","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":"310991b71e471553681d88611398675c57082b6d3f1074f33774f69839fa8c7d","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":13620,"certificate_compressed_size":2516,"conclusion_name":"basis_map_A013609 of theta_plus_one 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-eb8640ed213f9508","role":"sequence","name":"theta_plus_one 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-b0b9f0e48753af20","claim":"real_rooted"},{"node_id":"n-b0b9f0e48753af20","claim":"one_signed_coefficients"},{"node_id":"n-b0b9f0e48753af20","claim":"hadamard_kernel"}]}