{"id":"e-bf1bcfa6d864a6cb","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-2779a75fc60be9a6","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":"6691f1059f9505224b2a7fce2286a3405365b9d674648e7c2d2868ab48253bc7","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":15035,"certificate_compressed_size":2795,"conclusion_name":"basis_map_A013611 of theta_plus_one_squared of basis-map coefficients of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals. shifted by x -> -x + 0","claims":[{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":2,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-38e0e1d209c2aec5","role":"sequence","name":"theta_plus_one_squared of basis-map coefficients of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals. shifted by x -> -x + 0","uses":{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}},"uses_text":"Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]"}],"cited_by":[{"node_id":"n-2779a75fc60be9a6","claim":"one_signed_coefficients"},{"node_id":"n-2779a75fc60be9a6","claim":"hadamard_kernel"},{"node_id":"n-2779a75fc60be9a6","claim":"interlacing"},{"node_id":"n-2779a75fc60be9a6","claim":"real_rooted"}]}