{"id":"e-fdb502be056045be","operation":{"map":"A013609","operation":"basis_map"},"operation_detail":"A013609","conclusion_id":"n-37f06382db0098d8","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":"e7cf6caca6c7821ee6f3358c1ff9fa85d0a40241d9cf2097aebbdb6e62199437","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":15612,"certificate_compressed_size":3125,"conclusion_name":"basis_map_A013609 of A triangular array related to A077028 and distributing the values of A007582.","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-cf9f646a76b9c283","role":"sequence","name":"A triangular array related to A077028 and distributing the values of A007582.","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-37f06382db0098d8","claim":"real_rooted"},{"node_id":"n-37f06382db0098d8","claim":"one_signed_coefficients"},{"node_id":"n-37f06382db0098d8","claim":"hadamard_kernel"},{"node_id":"n-37f06382db0098d8","claim":"interlacing"}]}