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# cellComplexTorus -- gives a torus as a cell complex

- Usage:
    `cellComplexTorus(R,n)`
- Inputs:
  - R, a ring, that specifies the base ring
  - n, an integer, that specifies the dimension of the torus
- Outputs:
  - a cell complex, the n-dimensional torus

## Description

This function returns the n-dimensional torus as a cell complex in the usual way: the product of n copies of $S^1$.

    i1 : T3 = cellComplexTorus(QQ,3)

    o1 = T3

    o1 : CellComplex

    i2 : cells(T3)

    o2 = HashTable{0 => {Cell of dimension 0 with label 1}                                                                    }
                   1 => {Cell of dimension 1 with label 1, Cell of dimension 1 with label 1, Cell of dimension 1 with label 1}
                   2 => {Cell of dimension 2 with label 1, Cell of dimension 2 with label 1, Cell of dimension 2 with label 1}
                   3 => {Cell of dimension 3 with label 1}

    o2 : HashTable

    i3 : prune homology T3

           3       3       1
    o3 = QQ  <-- QQ  <-- QQ

         1       2       3

    o3 : Complex

## See also

- cellComplexSphere -- gives a sphere as a cell complex
- cellComplexRPn -- gives a $RP^n$ as a cell complex

## Ways to use cellComplexTorus:

- `cellComplexTorus(Ring,ZZ)`

## For the programmer

The object cellComplexTorus is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/CellularResolutions/doc.m2:1201:0.