{"id":"e-bf7e65720bb019eb","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-e9f99a7290620624","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":"f5e4f9696eb0e3271ed0b679117bf7b399a02fc53d522d3943f4e0cb8e3811de","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":6865,"certificate_compressed_size":1390,"conclusion_name":"basis_map_A013611 of 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-e1d1088f7d1ff894","role":"sequence","name":"Triangle read by rows whose (i,j)-th entry is binomial(i,j)*11^(i-j)*10^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-e9f99a7290620624","claim":"real_rooted"},{"node_id":"n-e9f99a7290620624","claim":"one_signed_coefficients"},{"node_id":"n-e9f99a7290620624","claim":"hadamard_kernel"}]}