{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"critpt","formal_name":"CritPt","introduction":"研究水準の物理問題で、科学的理解と多段階の推論・計算を評価するベンチマークです。公開データには70の課題があり、問題文とコード雛形を組み合わせて解答を構成します。\n\nCritPt evaluates scientific understanding and multi-step reasoning and computation on research-level physics problems. Its public dataset contains 70 challenges with problem descriptions and code templates.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://critpt.com/","indexing_mode":"noindex"},"task_id":"0a033e35-140a-5604-84a6-d78e8af0e7a1","task_key":"train--Challenge~5f5~5fmain","task_revision_id":"1","upstream_id":"Challenge_5_main","short_description":"Let $\\alpha \\in [0, 1]$ be a real parameter. Define the function $f(n, \\alpha)$…","config":"","split":"train","body":"{\"code_template\":\"import sympy as sp\\n\\nalpha = sp.symbols('alpha', real=True)\\n\\ndef answer(alpha):\\n    r\\\"\\\"\\\"\\n    Return the expression of the derivative $g(\\\\alpha)$ in Sympy format\\n\\n    Inputs\\n    ----------\\n    alpha: sympy.Symbol, real parameter, $\\\\alpha \\\\in [0, 1]$\\n\\n    Outputs\\n    ----------\\n    g_alpha:  sympy.Expr, $g(\\\\alpha)$ for $\\\\alpha \\\\in [0, 1]$.\\n    \\\"\\\"\\\"\\n\\n    # ------------------ FILL IN YOUR RESULTS BELOW ------------------\\n    g_alpha = ...\\n    # ---------------------------------------------------------------\\n\\n    return g_alpha\",\"problem_description\":\"# Problem setup:\\nLet $\\\\alpha \\\\in [0, 1]$ be a real parameter. Define the function $f(n, \\\\alpha)$ for complex $n$ by\\n\\\\begin{equation}\\nf(n, \\\\alpha) = (1 + \\\\alpha)^{n - 1} \\\\, {}_2F_1\\\\left( \\\\frac{1 - n}{2}, 1 - \\\\frac{n}{2}; 2; \\\\left( \\\\frac{2\\\\sqrt{\\\\alpha}}{1 + \\\\alpha} \\\\right)^2 \\\\right),\\n\\\\end{equation}\\nwhere ${}_2F_1(a, b; c; z)$ denotes the Gaussian hypergeometric function.\\n\\n# Main problem:\\n\\nEvaluate the derivative\\n\\\\begin{equation}\\ng(\\\\alpha) = \\\\left. \\\\frac{\\\\partial}{\\\\partial n} f(n, \\\\alpha) \\\\right|_{n = 0}\\n\\\\end{equation}\\nfor $\\\\alpha \\\\in [0, 1]$.\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://critpt.com/","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}