In order to establish if two expressions are equal, sage performs a "default wash machine program" and in case there is a **proof** for the `True`

value, it returns this True. Else it returns False.

In such cases, one should help sage to find the truth.

In our case:

```
sage: expression = abs(-1+sqrt(2)) != abs(1-sqrt(2))
sage: bool(expression)
True
sage: bool(expression.simplify_full())
False
```

Just tell `sage`

to perfom a simplification of the expression!

Note: One can find many "bugs" like the posted one, just try for instance:

```
sage: bool( abs(-1+sqrt(2)) != abs(1-sqrt(2)) )
True
sage: bool( abs(-1+sqrt(2)) == abs(1-sqrt(2)) )
True
```

it looks like a bug to me, and also why it does this: