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motives: A SymPy Package for Lambda-Ring and Motivic Expression Manipulation
A Python package (motives) built on the SymPy symbolic framework that manipulates, simplifies, and compares arbitrary expressions in lambda-rings, in particular the Grothendieck ring of Chow motives, reducing them to polynomials in chosen motivic generators. It provides explicit tools for the motives of common moduli schemes and stacks of decorated bundles on curves, including plethystic operations. Applied to Mozgovoy's conjectural formula for the motive of the moduli space of twisted Higgs bundles, it verifies the conjecture in rank 2 and 3 for any curve of genus up to 18 and twisting bundles of small degree, extending prior ad-hoc MATLAB verification (genus up to 11).