{"id":"e-0e13ca82ccc1a33c","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-408f7506d6594551","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":"ae86af9c5af7be8b5ec9d16e7ddd47548ba8bba983a1e5a1c1fd858e8776d149","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":6855,"certificate_compressed_size":1389,"conclusion_name":"basis_map_A013611 of Triangle whose (i,j)-th entry is 5^(i-j)*binomial(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-408f7506d6594551","claim":"real_rooted"},{"node_id":"n-408f7506d6594551","claim":"one_signed_coefficients"},{"node_id":"n-408f7506d6594551","claim":"hadamard_kernel"}]}