{"id":"e-35c130c218183b03","operation":{"map":"A013609","operation":"basis_map"},"operation_detail":"A013609","conclusion_id":"n-856b6394d4d7e682","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":"a4bbcb769b51adc8fd677d00b0d5e1c6c327638cde2c696085386d129c329cc0","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":10664,"certificate_compressed_size":2348,"conclusion_name":"basis_map_A013609 of (10,1) Pascal triangle.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":2,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-28582b6d055a713a","role":"sequence","name":"(10,1) Pascal triangle.","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-856b6394d4d7e682","claim":"real_rooted"},{"node_id":"n-856b6394d4d7e682","claim":"one_signed_coefficients"},{"node_id":"n-856b6394d4d7e682","claim":"hadamard_kernel"},{"node_id":"n-856b6394d4d7e682","claim":"interlacing"}]}