{"id":"e-3771d6044a0ef815","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-2a476baf987bc613","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":"ad61121c591232fa532480cf481dd94aa275d76d165dfda5ba7ceafecb2a58ee","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":14052,"certificate_compressed_size":2695,"conclusion_name":"basis_map_A013611 of Riordan array ((1+x)/(1-2x),x(1+x)/(1-2x)).","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-d6b7687ba0ff59dd","role":"sequence","name":"Riordan array ((1+x)/(1-2x),x(1+x)/(1-2x)).","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-2a476baf987bc613","claim":"one_signed_coefficients"},{"node_id":"n-2a476baf987bc613","claim":"hadamard_kernel"},{"node_id":"n-2a476baf987bc613","claim":"interlacing"},{"node_id":"n-2a476baf987bc613","claim":"real_rooted"}]}