# How to generate this map in sage

Okay this is my code so far.

```
F.<x,y,z> = FreeGroup()
A = F.algebra(QQ)
Y = A(y)
Yinv = A(y^-1)
Z = A(z)
Z2 = A(Z)
X = A(x)
X2 = A(X)
X2inv = A(X^-1)
Xinv = A(x^-1)
Y2 = A(Y)
def functionMap(X,Y,Z,Xinv):
X = A(X2 * Y2 * X2inv)
Y = A(X2 * Z2 * X2inv)
Z = A((Z2 * Y2 + 1)*X2inv)
print(X)
print(Y)
print(Z)
X2 = A(X)
X2inv = A(X2^-1)
Y2 = A(Y)
Z2 = A(Z)
for i in range(6):
functionMap(X,Y,Z,Xinv)
```

As you can see, I'm trying to repeatedly take the map x,y,z to xyx^-1, xzx^-1, (zy+1)x^-1 repeatedly. I'm getting a lot of errors though. Does anyone know how to fix my code? I think It might have something to do with the multiple variables calling the symbol 'x' but idk how else to not cause issues when I'm doing the three different parts of my map (like if I change X then the middle part has the wrong iteration of x)

okay wow that formatted terriably lemme do this.

Your function has no

`return`

anywhere. You should rather make a function taking a triple as input and returning a triple.The given function does not use its arguments but rather overwrites them with new values. Is that intended?