{"id":"e-322a2e4c0bbd3231","operation":{"map":"A013609","operation":"basis_map"},"operation_detail":"A013609","conclusion_id":"n-53dc6d1eeb1907f4","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":"3c7ff80f81b420dafdb27ad0df0d0885ebbebfeca15d959318c84f090c43cffe","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":6929,"certificate_compressed_size":1419,"conclusion_name":"basis_map_A013609 of Triangle whose (i,j)-th entry is binomial(i,j)*11^(i-j)*7^j.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-7dcf11eddf2b9a8a","role":"sequence","name":"Triangle whose (i,j)-th entry is binomial(i,j)*11^(i-j)*7^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-53dc6d1eeb1907f4","claim":"real_rooted"},{"node_id":"n-53dc6d1eeb1907f4","claim":"one_signed_coefficients"},{"node_id":"n-53dc6d1eeb1907f4","claim":"hadamard_kernel"}]}