{"id":"e-6fd9639eef78df97","operation":{"map":"A013610","operation":"basis_map"},"operation_detail":"A013610","conclusion_id":"n-5b0c1f0fe75b55a7","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":"c23cb6a47d6d40f542554fbccdd7a4a1f625f7f987cef602f15dde9cac7f2c54","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":6919,"certificate_compressed_size":1413,"conclusion_name":"basis_map_A013610 of basis_map_A007318 of Triangle whose (i,j)-th entry is binomial(i,j)*12^(i-j)*3^j.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-8447c9ce68adee7a","role":"sequence","name":"basis_map_A007318 of Triangle whose (i,j)-th entry is binomial(i,j)*12^(i-j)*3^j.","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-5b0c1f0fe75b55a7","claim":"real_rooted"},{"node_id":"n-5b0c1f0fe75b55a7","claim":"one_signed_coefficients"},{"node_id":"n-5b0c1f0fe75b55a7","claim":"hadamard_kernel"}]}