{"id":"e-9c46cccbde3c10ab","operation":{"map":"A013609","operation":"basis_map"},"operation_detail":"A013609","conclusion_id":"n-6d827197f1b1dfa7","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":"d32ea4aea2a0c4e574ee7e8e442e1facde8b0ce0381604097170baca57dfb90f","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":15245,"certificate_compressed_size":2813,"conclusion_name":"basis_map_A013609 of derivative of Triangle whose (i,j)-th entry is binomial(i,j)*2^i.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":2,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-2494c903d5dafb67","role":"sequence","name":"derivative of Triangle whose (i,j)-th entry is binomial(i,j)*2^i.","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-6d827197f1b1dfa7","claim":"real_rooted"},{"node_id":"n-6d827197f1b1dfa7","claim":"one_signed_coefficients"},{"node_id":"n-6d827197f1b1dfa7","claim":"hadamard_kernel"},{"node_id":"n-6d827197f1b1dfa7","claim":"interlacing"}]}