{"id":"e-0f31cc897fc45a50","operation":{"map":"A013609","operation":"basis_map"},"operation_detail":"A013609","conclusion_id":"n-e1d1088f7d1ff894","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":"64ee37337478dfef978bd9e3f787e307252d9489551db15a30d6c2629c95b2ad","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":6859,"certificate_compressed_size":1392,"conclusion_name":"Triangle read by rows whose (i,j)-th entry is binomial(i,j)*11^(i-j)*10^j.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-e6ebe74518d42cbe","role":"sequence","name":"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-e1d1088f7d1ff894","claim":"one_signed_coefficients"},{"node_id":"n-e1d1088f7d1ff894","claim":"hadamard_kernel"},{"node_id":"n-e1d1088f7d1ff894","claim":"real_rooted"}]}