{"id":"e-3536b8525dc3d550","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-3e182303707cc129","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":"3532ed761a01adcb3191b0e55ee97eecc20ded39102de300bccefa601b96e50c","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":15012,"certificate_compressed_size":3006,"conclusion_name":"shift_x_plus_one of veronese_section_2_1 of Triangle whose (i,j)-th entry is binomial(i,j)*2^(i-j).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":2,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-4e34a7abc01c81bb","role":"sequence","name":"veronese_section_2_1 of Triangle whose (i,j)-th entry is binomial(i,j)*2^(i-j).","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-3e182303707cc129","claim":"one_signed_coefficients"},{"node_id":"n-3e182303707cc129","claim":"hadamard_kernel"},{"node_id":"n-3e182303707cc129","claim":"real_rooted"},{"node_id":"n-3e182303707cc129","claim":"interlacing"}]}