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Multi-loop scattering amplitudes in N=4 Yang-Mills theory possess clusteralgebra structure. In order to develop a computational framework which exploitsthis connection, we show how to construct bases of Goncharov polylogarithmfunctions, at any weight, whose symbol alphabet consists of cluster coordinateson the $A_n$ cluster algebra. Using such a basis we present a new expressionfor the 2-loop 6-particle NMHV amplitude which makes some of its clusterstructure manifest.

Hedgehog Bases for A_n Cluster Polylogarithms and An Application to Six-Point Amplitudes