# ApCoCoA-1:Coxeter Group F4

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### Coxeter Group F4

#### Description

The F4 group is a Coxeter group. Their relations results of a Matrix, the Coxetermatrix. The Matrix with i lines and j columns gives the following relations:

```<r_1,...,r_n|(r_ir_j)^m_ij
```

-the relation mii means: (r_ir_i)^1=1 for all i

-and other generators r_i, r_j commute.

F4 has the following presentation:

#### Example in Symbolic Data Format

```<FREEALGEBRA createdAt="2014-07-30" createdBy="strohmeier">
<vars>v,x,y,z</vars>
<basis>
<ncpoly>v*v-1</ncpoly>
<ncpoly>x*x-1</ncpoly>
<ncpoly>y*y-1</ncpoly>
<ncpoly>z*z-1</ncpoly>
<ncpoly>(v*x)^3-1</ncpoly>
<ncpoly>(x*v)^3-1</ncpoly>
<ncpoly>(v*y)^2-1</ncpoly>
<ncpoly>(y*v)^2-1</ncpoly>
<ncpoly>(v*z)^2-1</ncpoly>
<ncpoly>(z*v)^2-1</ncpoly>
<ncpoly>(x*y)^4-1</ncpoly>
<ncpoly>(y*x)^4-1</ncpoly>
<ncpoly>(x*z)^2-1</ncpoly>
<ncpoly>(z*x)^2-1</ncpoly>
<ncpoly>(y*z)^3-1</ncpoly>
<ncpoly>(z*y)^3-1</ncpoly>
</basis>
<Comment>Coxeter_Group_F4</Comment>
</FREEALGEBRA>
```