{"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":"62893a15-0670-5328-9b13-4987f555b24e","task_key":"dev--49c68bb1-a088-53d9-a366-0885b5d1b63b--70~2e3","task_revision_id":"2","upstream_id":"70.3","short_description":"Write a function to compute the expansion coefficients $h_k$ of the three…","config":"","split":"dev","body":"{\"step_background\":\"Background\\nThe eight Gell-Mann matrices are:\\n$$\\n\\\\begin{array}{ll}\\n\\\\lambda_{1} & =\\\\left(\\\\begin{array}{lll}\\n0 & 1 & 0 \\\\\\\\\\n1 & 0 & 0 \\\\\\\\\\n0 & 0 & 0\\n\\\\end{array}\\\\right), \\\\lambda_{2} =\\\\left(\\\\begin{array}{ccc}\\n0 & -i & 0 \\\\\\\\\\ni & 0 & 0 \\\\\\\\\\n0 & 0 & 0\\n\\\\end{array}\\\\right) \\\\\\\\\\n\\\\lambda_{3} & =\\\\left(\\\\begin{array}{ccc}\\n1 & 0 & 0 \\\\\\\\\\n0 & -1 & 0 \\\\\\\\\\n0 & 0 & 0\\n\\\\end{array}\\\\right), \\\\lambda_{4}=\\\\left(\\\\begin{array}{lll}\\n0 & 0 & 1 \\\\\\\\\\n0 & 0 & 0 \\\\\\\\\\n1 & 0 & 0\\n\\\\end{array}\\\\right) \\\\\\\\\\n\\\\lambda_{5} & =\\\\left(\\\\begin{array}{ccc}\\n0 & 0 & -i \\\\\\\\\\n0 & 0 & 0 \\\\\\\\\\ni & 0 & 0\\n\\\\end{array}\\\\right), \\\\lambda_{6}=\\\\left(\\\\begin{array}{lll}\\n0 & 0 & 0 \\\\\\\\\\n0 & 0 & 1 \\\\\\\\\\n0 & 1 & 0\\n\\\\end{array}\\\\right) \\\\\\\\\\n\\\\lambda_{7} & =\\\\left(\\\\begin{array}{ccc}\\n0 & 0 & 0 \\\\\\\\\\n0 & 0 & -i \\\\\\\\\\n0 & i & 0\\n\\\\end{array}\\\\right), \\\\lambda_{8}=\\\\frac{1}{\\\\sqrt{3}}\\\\left(\\\\begin{array}{ccc}\\n1 & 0 & 0 \\\\\\\\\\n0 & 1 & 0 \\\\\\\\\\n0 & 0 & -2\\n\\\\end{array}\\\\right)\\n\\\\end{array}\\n$$\\n\\nEach of the coefficient can be computed as the following:\\n\\n$$\\n\\\\begin{array}{c|l}\\nh_{1} & \\\\operatorname{Re}\\\\left[\\\\left(\\\\mathrm{H}\\\\right)_{12}\\\\right] \\\\\\\\\\nh_{2} & -\\\\operatorname{Im}\\\\left[\\\\left(\\\\mathrm{H}\\\\right)_{12}\\\\right] \\\\\\\\\\nh_{3} & \\\\frac{1}{2}\\\\left[\\\\left(\\\\mathrm{H}\\\\right)_{11}-\\\\left(\\\\mathrm{H}\\\\right)_{22}\\\\right] \\\\\\\\\\nh_{4} & \\\\operatorname{Re}\\\\left[\\\\left(\\\\mathrm{H}\\\\right)_{13}\\\\right] \\\\\\\\\\nh_{5} & -\\\\operatorname{Im}\\\\left[\\\\left(\\\\mathrm{H}\\\\right)_{13}\\\\right] \\\\\\\\\\nh_{6} & \\\\operatorname{Re}\\\\left[\\\\left(\\\\mathrm{H}\\\\right)_{23}\\\\right] \\\\\\\\\\nh_{7} & -\\\\operatorname{Im}\\\\left[\\\\left(\\\\mathrm{H}\\\\right)_{23}\\\\right] \\\\\\\\\\nh_{8} & \\\\frac{\\\\sqrt{3}}{6}\\\\left[\\\\left(\\\\mathrm{H}\\\\right)_{11}+\\\\left(\\\\mathrm{H}\\\\right)_{22}-2\\\\left(\\\\mathrm{H}\\\\right)_{33}\\\\right] \\\\\\\\\\n\\\\end{array}\\n$$\\n\\nAs an example, the first coefficient $h_1$ is the real part of the number in the first row and the second column of the $3 \\\\times 3$ Hamiltonian.\",\"step_description_prompt\":\"Write a function to compute the expansion coefficients $h_k$ of the three neutrino oscillation Hamiltonian as defined in the previous prompt () if we expand the Hamiltonian in SU(3) using the expression $\\\\mathbb{H}=h_{0} \\\\mathbb{1}+h_{k} \\\\lambda^{k}$, where $\\\\mathbb{1}$ is the identity matrix, $h_k$ is the expansion coefficient, and $\\\\lambda^{k}$ is the kth Gell-Mann matrix. Consider all the terms from $k=1$ to $k=8$.\"}","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":[]}