{"id":"e-5ebb49cd3f3bda68","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-68250fd6ae5aea2b","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":"0e62a9eb390e1fa0766f14296a50bc1757fb5c270390b0956a6fd853ab57d93c","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":14876,"certificate_compressed_size":2863,"conclusion_name":"basis_map_A013611 of Expansion of 1/sqrt(1-4*x*y-4*x^2*y).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-eacb751f39dbd056","role":"sequence","name":"Expansion of 1/sqrt(1-4*x*y-4*x^2*y).","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-68250fd6ae5aea2b","claim":"real_rooted"},{"node_id":"n-68250fd6ae5aea2b","claim":"one_signed_coefficients"},{"node_id":"n-68250fd6ae5aea2b","claim":"hadamard_kernel"},{"node_id":"n-68250fd6ae5aea2b","claim":"interlacing"}]}