{"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":"327718c8-3fba-5242-bcad-f9fcccd8114a","task_key":"train--Challenge~5f65~5fmain","task_revision_id":"1","upstream_id":"Challenge_65_main","short_description":"Consider a fermion field $\\psi$ that is in the adjoint representations of a…","config":"","split":"train","body":"{\"code_template\":\"import sympy as sp\\n\\npsi = sp.symbols('psi')\\ntr = sp.Function('tr')\\n\\ndef answer(psi, tr):\\n    r\\\"\\\"\\\"\\n    Return expressions of the indecomposable gauge invariant operators in Sympy format.\\n\\n    Inputs\\n    ----------\\n    psi: sympy.Symbol, the fermion field, $\\\\psi$\\n    tr: sympy.Function, the trace function, $\\\\text{tr}$\\n\\n    Outputs\\n    ----------\\n    operators: set[sympy.Expr], a set of all the indecomposable gauge invariant operators with charge smaller or equal to 5 in the rank 2 theory.\\n    \\\"\\\"\\\"\\n\\n    # ------------------ FILL IN YOUR RESULTS BELOW ------------------\\n    operators = ... # a SymPy expression of inputs\\n    # ---------------------------------------------------------------\\n\\n    return operators\",\"problem_description\":\"# Problem setup:\\nConsider a fermion field $\\\\psi$ that is in the adjoint representations of a $U(N)$ gauge group and carries a global $U(1)$ charge 1. Please use the following notation: denote the fermion field by $\\\\psi$ and the trace of the gauge group representation by $\\\\text{tr}$. So, for example, a charge $1$ single trace field should be written as $\\\\text{tr} (\\\\psi)$. If two orderings of field define the same operator up to a sign, always write smaller charge fields on the left whenever possible.\\n\\n# Main problem:\\nIn the rank 2 theory, write down all the indecomposable gauge-invariant operators with charge smaller or equal to 5.\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://critpt.com/","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}