{"id":"e-a15a4571c9a83032","operation":{"map":"A013610","operation":"basis_map"},"operation_detail":"A013610","conclusion_id":"n-8409b69bc5d8591b","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":"e30375342a244f51cb8522aeca66931de40ac6540f49a5a8fb133b22738fa1a8","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":11708,"certificate_compressed_size":2209,"conclusion_name":"basis_map_A013610 of Exponential Riordan array (1, x(1+x/2)).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-f6268da8d9636534","role":"sequence","name":"Exponential Riordan array (1, x(1+x/2)).","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-8409b69bc5d8591b","claim":"real_rooted"},{"node_id":"n-8409b69bc5d8591b","claim":"one_signed_coefficients"},{"node_id":"n-8409b69bc5d8591b","claim":"hadamard_kernel"}]}