{"id":"e-93ddd9dff3a50248","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-234411cdfee41c66","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":"8da655c8577a203d5a44a6cbf8d6b322b98992a747f634043756a03a642f596a","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":14870,"certificate_compressed_size":2854,"conclusion_name":"shift_x_plus_one of Expansion of 1/sqrt(1-4*x*y-4*x^2*y).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-eacb751f39dbd056","role":"sequence","name":"Expansion of 1/sqrt(1-4*x*y-4*x^2*y).","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-234411cdfee41c66","claim":"interlacing"},{"node_id":"n-234411cdfee41c66","claim":"one_signed_coefficients"},{"node_id":"n-234411cdfee41c66","claim":"hadamard_kernel"},{"node_id":"n-234411cdfee41c66","claim":"real_rooted"}]}