{"id":"e-7f2842f65b20a0e7","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-52d1ca8a36603b73","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":"55e0c30ecf77339cd7e8c26e98b80ea2c1e8f324e6d284763ba21bd6b2e7b785","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":6915,"certificate_compressed_size":1393,"conclusion_name":"shift_x_plus_one of shift_x_plus_one of Triangle read by rows, A007318 rows repeated three times.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-a5bdea4e5eb1caa8","role":"sequence","name":"shift_x_plus_one of Triangle read by rows, A007318 rows repeated three 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-52d1ca8a36603b73","claim":"one_signed_coefficients"},{"node_id":"n-52d1ca8a36603b73","claim":"hadamard_kernel"},{"node_id":"n-52d1ca8a36603b73","claim":"real_rooted"}]}