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The scale data structure

Description

 • 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:

 'list' The ordered list of functions in the scale; 'variable' the name of the first function having entered the scale; 'varname' the name of the variable given by the user; 'back' the expression of this variable in terms of 'variable'; 'log' a table of the logarithms of the functions in the scale.

 • 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.

Examples

 > with(MultiSeries,multiseries):
 > scale := op(1,multiseries(x,x=infinity)):
 > scale[list];
 $\left[{{\mathrm{_var}}}_{\frac{{1}}{{x}}}\right]$ (1)
 > multiseries(exp(x+exp(-x)),scale,3);
 ${{ⅇ}}^{{x}}{+}{\mathrm{O}}{}\left({1}\right)$ (2)
 > scale[list];
 $\left[{{\mathrm{_var}}}_{\frac{{1}}{{x}}}{,}{{\mathrm{_var}}}_{\frac{{1}}{{{ⅇ}}^{{x}}}}\right]$ (3)