Constructions of free commutative integro-differential algebras
  In this survey, we outline two recent constructions of free commutative integro-differential algebras. They are based on the construction of free commutative Rota-Baxter algebras by mixable shuffles. The first is by evaluations. The second is by the method of Gr\"obner-Shirshov bases. 
Xing Gao, Li Guo
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