{"id":"e-c58678c575cc640f","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-714dab5edd34705c","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":"9ecc8824800599d48ed0e0231871c3a9cb8ca3565a294b71882a3d22261fd224","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":6945,"certificate_compressed_size":1391,"conclusion_name":"shift_x_plus_one of Triangle read by rows, A007318 rows repeated four times .","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-3f3dc597d31e7e01","role":"sequence","name":"Triangle read by rows, A007318 rows repeated four times .","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-714dab5edd34705c","claim":"one_signed_coefficients"},{"node_id":"n-714dab5edd34705c","claim":"hadamard_kernel"},{"node_id":"n-714dab5edd34705c","claim":"real_rooted"}]}