Dimension in the Atlas package

In the Atlas package the working dimension can be integer or symbolic. The corresponding variable is automatically assigned by Coframe procedure.
If the dimension is not an integer then all calculations are performed in terms of Sum operator (see examples below).

Examples:

Functions[f1f1[x1,x2,...,xn],f2f2[y1,y2,...,ym],...,
fkfk[z1,z2,...,zj]]
fk=fk[z1, z2, ..., zj] - rules where fk-function identifier and zj - variables
Vectors[v1,v2,...,vi,...,vn]vi - vector identivier
Forms[f1n,f2k,...,fip]fip - rules where fi - form identifier and p is a variable or an integer - the s degree
Coframe[idj,{j,1,n}]id - identifier for indexed variable - the coframe 1-forms n - dimension of working manifold (a variable or integer)
Frame[idj]idj-indexed variable the frame vectors
Connection[id]id-variable-connection identifier

Necessary functions.

Load the package:
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Declare some functions:
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Declare some vectors:
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Declare some forms:
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Declare coframe 1-forms:
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Declare frame vectors:
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Declare connection:
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d[expr]expr - any expression
ToBasis[t] t - variable or expression of tensor type
div[expr]expr - any vector expression

Necessary functions.

Using d- procedure:
For functions:
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Obviously that:
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Using ToBasis- procedure:
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Using div- procedure:
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Declare constant :
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Let us declare another coframe 1-forms:
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And another frame vectors:
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