{"id":"e-40b86dba603ec538","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-ce43d728e75b3d82","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":"36430d10a56bfc082e8bdbb5da1da006ba06694d756c1c62bcb4be7a1aef84dd","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":15163,"certificate_compressed_size":2805,"conclusion_name":"basis_map_A007318 of Triangle read by rows. A130713 in the columns.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":3,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-b442c9393792f928","role":"sequence","name":"Triangle read by rows. A130713 in the columns.","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-ce43d728e75b3d82","claim":"real_rooted"},{"node_id":"n-ce43d728e75b3d82","claim":"one_signed_coefficients"},{"node_id":"n-ce43d728e75b3d82","claim":"hadamard_kernel"},{"node_id":"n-ce43d728e75b3d82","claim":"interlacing"}]}