{"id":"e-0767c9a9bed43370","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-233801744e594f7f","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":"1e0fc053346004d95ae1a4dd4f03325dda520c02969a02776aaea8903619523f","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":15048,"certificate_compressed_size":2927,"conclusion_name":"shift_x_plus_one of Another version of Fibonacci-Pascal triangle A037027.","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-e7c079f81f452bf3","role":"sequence","name":"Another version of Fibonacci-Pascal triangle A037027.","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-233801744e594f7f","claim":"one_signed_coefficients"},{"node_id":"n-233801744e594f7f","claim":"hadamard_kernel"},{"node_id":"n-233801744e594f7f","claim":"real_rooted"},{"node_id":"n-233801744e594f7f","claim":"interlacing"}]}