{"id":"e-9d334fdae2e1b425","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-fe336889ad341afa","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":"a070915a6396c0ab3f001f10dc761e25dfc545371debbacea52e21086e3df07d","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":15682,"certificate_compressed_size":3145,"conclusion_name":"basis_map_A013611 of Exponential Riordan array [x*exp(x),x].","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-7b5887f058255aa1","role":"sequence","name":"Triangle of denominators in Leibniz's Harmonic Triangle a(n,k), n >= 1, 1 <= k <= n.","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-fe336889ad341afa","claim":"interlacing"},{"node_id":"n-fe336889ad341afa","claim":"real_rooted"},{"node_id":"n-fe336889ad341afa","claim":"one_signed_coefficients"},{"node_id":"n-fe336889ad341afa","claim":"hadamard_kernel"}]}