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# cellComplexSphere -- gives a sphere as a cell complex

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

## Description

This function constructs an n-dimensional sphere in the typical way for a CW-complex: a single n-dimensional cell attached to a single 0-dimensional cell.

    i1 : S = cellComplexSphere(QQ,3)

    o1 = S

    o1 : CellComplex

    i2 : cells(S)

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

    o2 : HashTable

    i3 : complex S

           1       1                   1
    o3 = QQ  <-- QQ  <-- 0 <-- 0 <-- QQ

         -1      0       1     2     3

    o3 : Complex

    i4 : prune homology S

           1
    o4 = QQ

         3

    o4 : Complex

## See also

- cellComplexRPn -- gives a $RP^n$ as a cell complex
- cellComplexTorus -- gives a torus as a cell complex

## Ways to use cellComplexSphere:

- `cellComplexSphere(Ring,ZZ)`

## For the programmer

The object cellComplexSphere is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/CellularResolutions/doc.m2:1141:0.