{"id":"e-33edb077f1832341","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-79d0a909b2a6e62d","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":"d6e34dc6a6b424c225efcdb7a9daddb39aa1c68f3589c2f5ecf0f7e9203d5a2d","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":13781,"certificate_compressed_size":2613,"conclusion_name":"shift_x_plus_one of veronese_section_2_0 of Even-numbered rows of Pascal's triangle.","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-a8ee0944a0199e83","role":"sequence","name":"veronese_section_2_0 of Even-numbered rows of Pascal's triangle.","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-79d0a909b2a6e62d","claim":"one_signed_coefficients"},{"node_id":"n-79d0a909b2a6e62d","claim":"hadamard_kernel"},{"node_id":"n-79d0a909b2a6e62d","claim":"interlacing"},{"node_id":"n-79d0a909b2a6e62d","claim":"real_rooted"}]}