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The scale data structure

 

Description

Examples

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, _varx,a,expr means that the function occurs in an expansion in the variable x at the point a, and 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

withMultiSeries,multiseries:

scaleop1,multiseriesx,x=:

scalelist

_var1x

(1)

multiseriesexpx+expx,scale,3

ⅇx+O1

(2)

scalelist

_var1x,_var1ⅇx

(3)

See Also

MultiSeries