The Grothendieck ring of Chow motives admits two natural opposite λ-ring structures, one of which is a special structure allowing the definition of Adams operations on the ring. In this work I present algorithms which allow an effective simplification of expressions that involve both λ-ring structures, as well as Adams operations. In particular, these algorithms allow the symbolic simplification of algebraic expressions in the sub-λ-ring of motives generated by a finite set of curves into polynomial expressions in a small set of motivic generators. As a consequence, the explicit computation of motives of some moduli spaces is performed, allowing the computational verification of some conjectural formulas for these spaces.

Chow 动机的 Grothendieck 环承认两个自然相反的λ -环结构，其中一个是允许在环上定义 Adams 操作的特殊结构。在这项工作中，我提出了允许有效简化涉及λ环结构以及 Adams 运算的表达式的算法。特别是，这些算法允许将由有限曲线集生成的动机的子λ环中的代数表达式符号简化为一小组动机生成器中的多项式表达式。结果，执行了一些模空间的动机的显式计算，允许对这些空间的一些猜想公式进行计算验证。