{"id":"e-189a8da608edbb49","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-3deb3ea1ada5b4a1","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":"e7aa26ade5471ecc01c912d54f9257d101f9c314413eed4e8157ca49056453d9","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":6857,"certificate_compressed_size":1384,"conclusion_name":"basis_map_A013611 of Triangle of coefficients in expansion of (1+4x)^n.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-2e0409c0014ec240","role":"sequence","name":"Triangle of coefficients in expansion of (1+4x)^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-3deb3ea1ada5b4a1","claim":"real_rooted"},{"node_id":"n-3deb3ea1ada5b4a1","claim":"one_signed_coefficients"},{"node_id":"n-3deb3ea1ada5b4a1","claim":"hadamard_kernel"}]}