In the paper, (5.28) on page 35 is a formula which translate cluster A-coordinates to cluster X-coordinates: \begin{align} x_i = \prod_{i \to j} a_j. \end{align}\begin{align} x_i = \prod_{i \to j} a_j. \end{align}
Is there a formula which translate cluster X-coordinates to cluster A-coordinates? Thank you very much.
Edit: as David Speyer pointed out, the correction formula to translate cluster A-coordinates to cluster X-coordinates is \begin{align} x_i = \prod_{i \to j} a_j/\prod_{j \to i} a_j = \prod_{j} a_j^{Q_{ij}}. \end{align}