{"id":"e-01d2a4c51ed4f80c","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-b4a66ef190cb2745","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":"6534b169b306d43b2252a01e19b9fe090aa049ad9f5b270522fbf3f0d4b2820f","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":6925,"certificate_compressed_size":1402,"conclusion_name":"shift_x_plus_one of Triangle read by rows: triangle of repeated stepped binomial coefficients.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-35bd700768cac55f","role":"sequence","name":"Triangle read by rows: triangle of repeated stepped binomial coefficients.","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-b4a66ef190cb2745","claim":"one_signed_coefficients"},{"node_id":"n-b4a66ef190cb2745","claim":"hadamard_kernel"},{"node_id":"n-b4a66ef190cb2745","claim":"real_rooted"}]}