Definition 11.1 . [030G]

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Definition 11.1.

A ray or line in $M_{\mathbb{R}}$ is a pair $(\mathfrak{d},f_{\mathfrak{d}})$ for some $\mathfrak{d}=\mathbb{R}_{\leq 0}m$ if $\mathfrak{d}$ is a ray and $\mathfrak{d}=\mathbb{R}m$ if $\mathfrak{d}$ is a line, where $m\in M\setminus\{0\}$ . Furthermore,

f_{\mathfrak{d}}=1+tz^{m}\cdot g(z^{m},t)\in R,\quad g(z,t)\in\mathbb{C}[z]\mbox{{[}}t\mbox{{]}},

A scattering diagram $\mathfrak{D}$ is a collection of rays and lines $\{(\mathfrak{d},f_{\mathfrak{d}})\}$ with the property that for any $k>0$ , $f_{\mathfrak{d}}\equiv 1\mod t^{k}$ for all but a finite number of elements of $\mathfrak{D}$ .