{"id":"e-a670c1df7257747a","operation":{"map":"A013610","operation":"basis_map"},"operation_detail":"A013610","conclusion_id":"n-9e472291b944d56e","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":"aff162d9da9ae152a80966980ccaf5c58b0d231ca1d1531b0ba25728854504cc","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":6859,"certificate_compressed_size":1392,"conclusion_name":"Triangle whose (i,j)-th entry is binomial(i,j)*11^(i-j)*12^j.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-ade19c5257c8a726","role":"sequence","name":"basis_map_A013611 of Triangle whose (i,j)-th entry is binomial(i,j)*6^(i-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-9e472291b944d56e","claim":"one_signed_coefficients"},{"node_id":"n-9e472291b944d56e","claim":"hadamard_kernel"},{"node_id":"n-9e472291b944d56e","claim":"real_rooted"}]}