{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"scicode","formal_name":"SciCode","introduction":"科学研究の問題をコードで解く能力を評価するベンチマークです。親問題を複数の小問題に分けており、今回のdev取得では15親問題と50小問題の関係を保持します。\n\nSciCode evaluates the ability to solve scientific research problems through code. Problems are decomposed into subproblems; this dev import preserves the relationships between 15 parent problems and 50 subproblems.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/SciCode1/SciCode","indexing_mode":"noindex"},"task_id":"b6d21d4a-3ffa-5df7-8647-f593157f1cc8","task_key":"dev--49c68bb1-a088-53d9-a366-0885b5d1b63b--70~2e8","task_revision_id":"2","upstream_id":"70.8","short_description":"Write a function to compute the $3 \\times 3$ evolution operator as defined in…","config":"","split":"dev","body":"{\"step_background\":\"Background\\n\\nThe evolution operator is $\\\\mathbb{U}_{3}(L)=e^{-i H_{3} L}=$ $e^{-i h_{0} \\\\mathbb{1} L} e^{-i h_{k} \\\\lambda^{k} L}$. If we discard the global phase, we are left with $\\\\mathbb{U}_{3}(L)=e^{-i h_{k} \\\\lambda^{k} L}$.\",\"step_description_prompt\":\"Write a function to compute the $3 \\\\times 3$ evolution operator as defined in the previous prompt (). Then compute the oscillation probabilities of the three neutrino oscillation problem using the expression $P_{\\\\nu_{\\\\alpha} \\\\rightarrow \\\\nu_{\\\\beta}}(L)=\\\\left|\\\\nu_{\\\\beta}^{\\\\dagger} U_{3}(L) \\\\nu_{\\\\alpha}\\\\right|^{2}$, where $\\\\nu$ is one of electron neutrino ($e$), muon neutrino ($\\\\mu$) or tau neutrino ($\\\\tau$). Use $\\\\nu_{e}=\\\\left(\\\\begin{array}{lll}1 & 0 & 0\\\\end{array}\\\\right)^{\\\\mathrm{T}}, \\\\nu_{\\\\mu}=\\\\left(\\\\begin{array}{lll}0 & 1 & 0\\\\end{array}\\\\right)^{\\\\mathrm{T}}$, and $\\\\nu_{\\\\tau}=\\\\left(\\\\begin{array}{lll}0 & 0 & 1\\\\end{array}\\\\right)^{\\\\mathrm{T}}$. Return the probabilities in a list in the following order : $e \\\\to e/\\\\mu/\\\\tau$, $\\\\mu \\\\to e/\\\\mu/\\\\tau$, and $\\\\tau \\\\to e/\\\\mu/\\\\tau$.\"}","display_format":"scicode-step","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/SciCode1/SciCode","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}