{"id":"e-c418c95a7e1e218e","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-f8abeed5fe1a08b5","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":"00e8c16b7a1a3f556b961c7a53af246d0a93230607485032292bdf1d52062f55","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":6865,"certificate_compressed_size":1388,"conclusion_name":"shift_x_plus_one of basis_map_A013610 of Triangle whose (i,j)-th entry is binomial(i,j)*6^(i-j)*5^j.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-f562ab3e3b669a1b","role":"sequence","name":"basis_map_A013610 of Triangle whose (i,j)-th entry is binomial(i,j)*6^(i-j)*5^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-f8abeed5fe1a08b5","claim":"hadamard_kernel"},{"node_id":"n-f8abeed5fe1a08b5","claim":"real_rooted"},{"node_id":"n-f8abeed5fe1a08b5","claim":"one_signed_coefficients"}]}