{"id":"e-c477fbeecbbc62a9","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-acacc82d3699f634","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":"7e413fb08a2c40d7c1c2489d6ea1368536a82f4b6f125cf85bceb72193897dcb","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":15127,"certificate_compressed_size":2809,"conclusion_name":"basis_map_A013611 of Triangle read by rows: The convolution triangle of 2^n, where the convolution triangle of a sequence is defined in A357368.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-ff74e25052457f18","role":"sequence","name":"Triangle read by rows: The convolution triangle of 2^n, where the convolution triangle of a sequence is defined in A357368.","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-acacc82d3699f634","claim":"real_rooted"},{"node_id":"n-acacc82d3699f634","claim":"one_signed_coefficients"},{"node_id":"n-acacc82d3699f634","claim":"hadamard_kernel"},{"node_id":"n-acacc82d3699f634","claim":"interlacing"}]}