{"id":"e-c1595f6e5718e258","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-b85d9f7216f04287","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":"5b035c6655fb83e1f8faf35b3a24fd28a262fd7f360b312d41aa1f59d22c1d76","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":13586,"certificate_compressed_size":2589,"conclusion_name":"basis_map_A013611 of Triangle of coefficients of polynomials u(n,x) jointly generated with A207607; see the Formula section.","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-dfab35176bd08e72","role":"sequence","name":"Triangle of coefficients of polynomials u(n,x) jointly generated with A207607; see the Formula section.","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-b85d9f7216f04287","claim":"real_rooted"},{"node_id":"n-b85d9f7216f04287","claim":"one_signed_coefficients"},{"node_id":"n-b85d9f7216f04287","claim":"hadamard_kernel"},{"node_id":"n-b85d9f7216f04287","claim":"interlacing"}]}