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We prove that $\\pi_n\\hom(A,B^\\Delta)$ is the set of homotopy classes of morphisms from $A$ to $B^{S_n}$, where $B^{S_n}$ is the ind-algebra of polynomials on the $n$-dimensional cube with coefficients in $B$ vanishing at the boundary of the cube. 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To every pair of $\\ell$-algebras $A$ and $B$ one can associate a simplicial set $\\hom(A,B^\\Delta)$ so that $\\pi_0\\hom(A,B^\\Delta)$ equals the set of polynomial homotopy classes of morphisms from $A$ to $B$. We prove that $\\pi_n\\hom(A,B^\\Delta)$ is the set of homotopy classes of morphisms from $A$ to $B^{S_n}$, where $B^{S_n}$ is the ind-algebra of polynomials on the $n$-dimensional cube with coefficients in $B$ vanishing at the boundary of the cube. 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