{"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":"b3d77d3e-865b-56e0-a256-6fdc4d63929c","task_key":"train--Challenge~5f66~5fmain","task_revision_id":"1","upstream_id":"Challenge_66_main","short_description":"Consider fermion fields that are adjoint representations of a $U(N)$ gauge…","config":"","split":"train","body":"{\"code_template\":\"import sympy as sp\\n\\nq = sp.symbols('q')\\n\\ndef answer(q):\\n    r\\\"\\\"\\\"\\n    Return the expression of the generating function in SymPy format.\\n\\n    Inputs\\n    ----------\\n    q: sympy.Symbol, Fugacity for the U(1) R-charge, $q$\\n\\n    Outputs\\n    ----------\\n    generating_func: sympy.Expr, the generating function of the index of trace relations to up charge 15 in a free $U(2)$ gauge theory\\n    \\\"\\\"\\\"\\n\\n    # ------------------ FILL IN YOUR RESULTS BELOW ------------------\\n    generating_func = ...   # a SymPy expression of inputs\\n    # ---------------------------------------------------------------\\n\\n    return generating_func\",\"problem_description\":\"# Problem setup:\\nConsider fermion fields that are adjoint representations of a $U(N)$ gauge group. Suppose fields carry a $U(1)$ R-charge whose fugacity is $q$. A generating function of the Witten index, for example, could be $I_N(q)=1-q+q^2+...$, which means the index at charge 1 is -1 and the index at charge 2 is 1.\\n\\n# Main problem:\\nCompute the generating function of the index of trace relations up to charge 15 in a free $U(2)$ gauge theory that contains only two adjoint fields: a charge 1 fermion $\\\\psi$, and its derivative field $\\\\partial\\\\psi$ with charge 2.\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://critpt.com/","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}