{"id":"e-47adeea10c1f7991","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-57c367574a30fd7b","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":"f42a51ffe8a9b52486648b543ac75c43b70464aebf04fbb0feb45baa2ac8eb01","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":13970,"certificate_compressed_size":2608,"conclusion_name":"basis_map_A007318 of Square the entries of Pascal's triangle.","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-b13531ad79e7c629","role":"sequence","name":"Square the entries of Pascal's triangle.","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-57c367574a30fd7b","claim":"real_rooted"},{"node_id":"n-57c367574a30fd7b","claim":"one_signed_coefficients"},{"node_id":"n-57c367574a30fd7b","claim":"hadamard_kernel"},{"node_id":"n-57c367574a30fd7b","claim":"interlacing"}]}