{"id":"e-2c0e83fb0e1d16d7","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-3eb516a297f686ad","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":"ff8b1c38d8dbe7ef8f322d4df159b282798fd8a31ba9d22879c2f12956709faa","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":6930,"certificate_compressed_size":1413,"conclusion_name":"basis_map_A013611 of shift_x_plus_one of Riordan array ((1+x)^3,x).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-9aa9e3dd2403bca2","role":"sequence","name":"shift_x_plus_one of Riordan array ((1+x)^3,x).","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-3eb516a297f686ad","claim":"real_rooted"},{"node_id":"n-3eb516a297f686ad","claim":"one_signed_coefficients"},{"node_id":"n-3eb516a297f686ad","claim":"hadamard_kernel"}]}