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The Grothendieck ring of Chow motives admits two natural opposite$\lambda$-ring structures, one of which is a special structure allowing thedefinition of Adams operations on the ring. In this work I present algorithmswhich allow an effective simplification of expressions that involve both$\lambda$-ring structures, as well as Adams operations. In particular, thesealgorithms allow the symbolic simplification of algebraic expressions in thesub-$\lambda$-ring of motives generated by a finite set of curves intopolynomial 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 thesespaces.

Simplification of $\lambda$-ring expressions in the Grothendieck ring of Chow motives