Summary:
We present a new Python package called "motives", a symbolic manipulation package based on SymPy capable of handling and simplifying motivic expressions in the Grothendieck ring of Chow motives and other types of λ-rings. The package is able to manipulate and compare arbitrary expressions in λ-rings and, in particular, it contains explicit tools for manipulating motives of several types of commonly used moduli schemes and moduli stacks of decorated bundles on curves. We have applied this new tool to advance in the verification of Mozgovoy's conjectural formula for the motive of the moduli space of twisted Higgs bundles, proving that it holds in rank 2 and 3 for any curve of genus up to 18 and any twisting bundle of small degree.
Spanish layman's summary:
Presentamos un nuevo paquete de Python llamado “motives” para simplificar y comparar fórmulas motívicas y expresiones en λ-anillos, y que contiene herramientas para manipular motivos de moduli comúnmente usados. Se ha aplicado al estudio de la conjetura de Mozgovoy sobre el moduli de Higgs twistado.
English layman's summary:
We present a new Python package called “motives” for simplifying and comparing motivic formulas and λ-rings expressions. It contains tools for manipulating motives of commonly used moduli schemes and stacks and we have applied it to study Mozgovoy’s conjecture on the moduli of twisted Higgs bundles.
Keywords: lambda-rings, symbolic computations of motives, Chow motives, moduli spaces, Higgs bundles moduli space
JCR Impact Factor and WoS quartile: 1,000 - Q1 (2023)
DOI reference:
https://doi.org/10.3934/era.2025093
Published on paper: 2025.
Published on-line: April 2025.
Citation:
D. Sánchez Sánchez, D. Alfaya, J. Pizarroso, Motives meet SymPy: studying -ring expressions in Python. Electronic Research Archive. Vol. 33, nº. 4, pp. 2118 - 2147, 2025. [Online: April 2025]
Download this paper