{"id":"e-1f4c98973d4afd88","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-718e8eb36d755083","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":"828e3c0616842168f9950a9709df778cb0027d56781fdc64c9d866b6bc53056d","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":6857,"certificate_compressed_size":1390,"conclusion_name":"basis_map_A013611 of basis_map_A013609 of Triangle of coefficients in expansion of (1+2*x)^n.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-026074a09c74735a","role":"sequence","name":"basis_map_A013609 of Triangle of coefficients in expansion of (1+2*x)^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-718e8eb36d755083","claim":"real_rooted"},{"node_id":"n-718e8eb36d755083","claim":"one_signed_coefficients"},{"node_id":"n-718e8eb36d755083","claim":"hadamard_kernel"}]}