{"id":"e-a328da612d1a3acb","operation":{"map":"A013610","operation":"basis_map"},"operation_detail":"A013610","conclusion_id":"n-8f6d2c8dc196f9ed","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":"0865700d0197ea040236a56f38a79e5edf1dc18c6d85166725eab1f65fb4e6d0","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":14325,"certificate_compressed_size":2820,"conclusion_name":"basis_map_A013610 of Array of coefficients of denominator polynomials of the n-th approximation of the continued fraction x/(1+x/(2+x/(3+..., related to Laguerre polynomial coefficients.","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-8b17fbdec05b5547","role":"sequence","name":"Array of coefficients of denominator polynomials of the n-th approximation of the continued fraction x/(1+x/(2+x/(3+..., related to Laguerre polynomial 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-8f6d2c8dc196f9ed","claim":"real_rooted"},{"node_id":"n-8f6d2c8dc196f9ed","claim":"one_signed_coefficients"},{"node_id":"n-8f6d2c8dc196f9ed","claim":"hadamard_kernel"},{"node_id":"n-8f6d2c8dc196f9ed","claim":"interlacing"}]}