# Explicit chain homotopy for the Alexander-Whitney, Eilenberg-Zilber pair

Let $$A$$ and $$B$$ be simplicial abelian groups, and let $$N_\ast(-)$$ denote the normalized chain complex functor. Let $$AW_{A,B}\colon N_\ast(A\otimes B) \longrightarrow N_\ast(A)\otimes N_\ast(B)$$ and $$EZ_{A,B}\colon N_\ast(A)\otimes N_\ast(B) \longrightarrow N_\ast(A\otimes B)$$ denote the Alexander-Whitney map and the Eilenberg-Zilber map respectively. Does anyone know of an explicit chain homotopy realizing $$EZ_{A,B}\circ AW_{A,B}\sim Id_{N_\ast(A\otimes B)}.$$

Motivation for its existence can be found in the comments of this question.