{"id":"e-efe1634c04c9236a","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-22693abd431a71f2","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":"a42620a3038512229792bdd9c81ce7e1f734bf9bf6ba78421af3cb096ae9c652","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":6855,"certificate_compressed_size":1385,"conclusion_name":"Triangle whose (i,j)-th entry is binomial(i,j)*6^(i-j).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-7b91a7a037fb3513","role":"sequence","name":"Triangle whose (i,j)-th entry is 5^(i-j)*binomial(i,j).","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-22693abd431a71f2","claim":"one_signed_coefficients"},{"node_id":"n-22693abd431a71f2","claim":"hadamard_kernel"},{"node_id":"n-22693abd431a71f2","claim":"real_rooted"}]}