{"id":"e-8e7f1943c60a0009","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-ccd84167c908ea61","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":"e5e07fe1e6dad1d878a213e542415d601b2f364ff071ca9360520957a4ea9bd1","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":14011,"certificate_compressed_size":2703,"conclusion_name":"basis_map_A013611 of Square array of Delannoy numbers D(i,j) (i >= 0, j >= 0) read by antidiagonals.","claims":[{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":2,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-811c78acf96cbc19","role":"sequence","name":"Square array of Delannoy numbers D(i,j) (i >= 0, j >= 0) read by antidiagonals.","uses":{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}},"uses_text":"Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]"}],"cited_by":[{"node_id":"n-ccd84167c908ea61","claim":"real_rooted"},{"node_id":"n-ccd84167c908ea61","claim":"one_signed_coefficients"},{"node_id":"n-ccd84167c908ea61","claim":"hadamard_kernel"},{"node_id":"n-ccd84167c908ea61","claim":"interlacing"}]}