{"id":"e-cb34b4e535d79689","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-0fcd1eb4c6e3650a","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":"fdcaa7651e729da8c52dfa22ba17bdb3a3012dc9efcc0ef2520a7537c9912320","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":10652,"certificate_compressed_size":2350,"conclusion_name":"basis_map_A013611 of shift_x_plus_one of A127733 * A007318 as infinite lower triangular matrices.","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-63d7f3b1eb8cf1f2","role":"sequence","name":"shift_x_plus_one of A127733 * A007318 as infinite lower triangular matrices.","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-0fcd1eb4c6e3650a","claim":"real_rooted"},{"node_id":"n-0fcd1eb4c6e3650a","claim":"one_signed_coefficients"},{"node_id":"n-0fcd1eb4c6e3650a","claim":"hadamard_kernel"},{"node_id":"n-0fcd1eb4c6e3650a","claim":"interlacing"}]}