{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"scicode","formal_name":"SciCode","introduction":"SciCode 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","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"adbd390d-1702-57e7-bd92-c77e8ca00a02","task_key":"dev--49c68bb1-a088-53d9-a366-0885b5d1b63b--70~2e1","task_revision_id":"2","upstream_id":"70.1","short_description":"Write a function to compute the PMNS matrix of the three neutrino oscillation…","config":"","split":"dev","body":"{\"step_background\":\"Background\\nThe flavour mixing matrix for the three neutrino families is\\n\\n\\n$$\\n\\\\begin{pmatrix}\\n   \\\\nu_{e} \\\\\\\\\\n   \\\\nu_{\\\\mu}  \\\\\\\\\\n   \\\\nu_{\\\\tau}\\n\\\\end{pmatrix}\\n=\\n\\\\begin{pmatrix}\\n   U_{e1} & U_{e2} & U_{e3} \\\\\\\\\\n   U_{\\\\mu1} & U_{\\\\mu2} & U_{\\\\mu3} \\\\\\\\\\n   U_{\\\\tau1} & U_{\\\\tau2} & U_{\\\\tau3}\\n\\\\end{pmatrix}\\n\\\\cdot\\n\\\\begin{pmatrix}\\n   \\\\nu_{1} \\\\\\\\\\n   \\\\nu_{2}  \\\\\\\\\\n   \\\\nu_{3}\\n\\\\end{pmatrix}\\n$$\\n\\nThe PMNS matrix $U$ can be expressed as:\\n$$\\nU = \\\\begin{pmatrix}\\nc_{12}c_{13} & s_{12}c_{13} & s_{13}e^{-i\\\\delta_{CP}} \\\\\\\\\\n-s_{12}c_{23} - c_{12}s_{23}s_{13}e^{i\\\\delta_{CP}} & c_{12}c_{23} - s_{12}s_{23}s_{13}e^{i\\\\delta_{CP}} & s_{23}c_{13} \\\\\\\\\\ns_{12}s_{23} - c_{12}c_{23}s_{13}e^{i\\\\delta_{CP}} & -c_{12}s_{23} - s_{12}c_{23}s_{13}e^{i\\\\delta_{CP}} & c_{23}c_{13}\\n\\\\end{pmatrix}\\n$$\\n\\nwhere $s_{ij}$ and $c_{ij}$ are the sine and cosine of the corresponding mixing angles, and $\\\\delta_{cp}$ is the CP-violating phase (in radians).\",\"step_description_prompt\":\"Write a function to compute the PMNS matrix of the three neutrino oscillation problem. Express all values as complex numbers.\"}","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":[]}