{"id":"e-b1566c9eddf7e689","operation":{"map":"A013610","operation":"basis_map"},"operation_detail":"A013610","conclusion_id":"n-c51d3e880faa56cc","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":"59f6f0e2b4700ceb43503f8703c39f0aa95bbd324e69f7b71668f6d6b283bf43","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":13881,"certificate_compressed_size":2657,"conclusion_name":"basis_map_A013610 of hadamard_factor parent of Triangle read by rows: t(n,m) = binomial(2*n,2*m) * binomial(n,m).","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-dbc23e13bb290987","role":"sequence","name":"hadamard_factor parent of Triangle read by rows: t(n,m) = binomial(2*n,2*m) * binomial(n,m).","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-c51d3e880faa56cc","claim":"real_rooted"},{"node_id":"n-c51d3e880faa56cc","claim":"one_signed_coefficients"},{"node_id":"n-c51d3e880faa56cc","claim":"hadamard_kernel"},{"node_id":"n-c51d3e880faa56cc","claim":"interlacing"}]}