# Quotients of exterior algebras

I am trying to take a quotient of an exterior algebra by a two-sided ideal, and having some trouble. As an easy case to understand the syntax, I tried to compute $\Lambda^\mathbb{Q}[x,y,z]/(x-y)$, where I would expect $\overline{x} = \overline{y}$. However, it seems to not consider `xbar`

and `ybar`

the same.

```
sage: E.<x,y,z> = algebras.Exterior(QQ);
sage: I = E.ideal(x-y);
sage: Q = E.quo(I);
sage: xbar,ybar,zbar = Q.gens();
sage: xbar == ybar
False
```

I thought maybe that was fine because `xbar`

and `ybar`

are generators of the quotient so maybe there is some funkiness going on there. So then I tried to take the image of `x`

and `y`

under the quotient map and check if they are equal, but it still said they were not.

```
sage: q = Q.cover()
sage: q(x) == q(y)
False
```

Am I misunderstanding something in Sage? In the algebra of it? Both?