{"id":"e-52e7f70645fda7c1","operation":{"map":"A013610","operation":"basis_map"},"operation_detail":"A013610","conclusion_id":"n-f52aae032f81ced6","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":"6959da3fc12d421d7430278fbd4ec99753005aa366f208b2b29806cf70608bf1","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":16298,"certificate_compressed_size":3319,"conclusion_name":"basis_map_A013610 of Exponential Riordan array [x*exp(x),x].","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-308cf60736924b4c","role":"sequence","name":"Exponential Riordan array [x*exp(x),x].","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-f52aae032f81ced6","claim":"real_rooted"},{"node_id":"n-f52aae032f81ced6","claim":"one_signed_coefficients"},{"node_id":"n-f52aae032f81ced6","claim":"hadamard_kernel"},{"node_id":"n-f52aae032f81ced6","claim":"interlacing"}]}