{"id":"e-a6ba51f5436e1d18","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-e9184df34abecf6a","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":"e445fbd17796f02c2138bcd6e4954ed1e0b0dbc6f11c724e4932b7b2cec4c78a","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":10256,"certificate_compressed_size":2287,"conclusion_name":"shift_x_plus_one of basis_map_A007318 of Triangle read by rows: coefficients of 1; 1(X+2); 1(X+2)(X+3); 1(X+2)(X+3)(X+4); ....","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-b8883330fe0b24f8","role":"sequence","name":"basis_map_A007318 of Triangle read by rows: coefficients of 1; 1(X+2); 1(X+2)(X+3); 1(X+2)(X+3)(X+4); ....","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-e9184df34abecf6a","claim":"one_signed_coefficients"},{"node_id":"n-e9184df34abecf6a","claim":"hadamard_kernel"},{"node_id":"n-e9184df34abecf6a","claim":"interlacing"},{"node_id":"n-e9184df34abecf6a","claim":"real_rooted"}]}