The scale data structure is used to represent asymptotic scales (see MultiSeries for a definition).

A scale is represented as a table whose entries are:

The functions in the scale are represented using the global name _var with three arguments. Thus, $\mathrm{\_var}\left(x\,a\,\mathrm{expr}\right)$ means that the function occurs in an expansion in the variable $x$ at the point $a$, and $\mathrm{expr}$ is the expression of the function.

Scales being stored as tables, they can be extended during a computation.

Currently, only operations between multiseries expressed in the same scale are supported.

$\mathrm{with}\left(\mathrm{MultiSeries}\,\mathrm{multiseries}\right)\:$

$\mathrm{scale}≔\mathrm{op}\left(1\,\mathrm{multiseries}\left(x\,x\=\mathrm{\∞}\right)\right)\:$

${\mathrm{scale}}_{\mathrm{list}}$

$\left[{\mathrm{\_var}}_{\frac{1}{x}}\right]$

$\mathrm{multiseries}\left({\ⅇ}^{x\+{\ⅇ}^{-x}}\,\mathrm{scale}\,3\right)$

${\ⅇ}^x+\mathrm{O}\left(1\right)$

${\mathrm{scale}}_{\mathrm{list}}$

$\left[{\mathrm{\_var}}_{\frac{1}{x}}\,{\mathrm{\_var}}_{\frac{1}{{\ⅇ}^x}}\right]$