You could redefine the `norm`

function in a subclass. Note that your `e0`

is an object of class `Vector_rational_dense`

:

```
sage: V=VectorSpace(QQ,2,inner_product_matrix=SP)
sage: e0=V.0
sage: type(e0)
<type 'sage.modules.vector_rational_dense.Vector_rational_dense'>
```

So you can create a subclass, with a new `norm`

function:

```
sage: from sage.modules.vector_rational_dense import Vector_rational_dense as Vrd
sage: class MyVector(Vrd):
....: def norm(self):
....: return sqrt(self.inner_product(self))
....:
```

and write a helper function to take objects from the old class and make ones in the new class:

```
sage: def improve_norm(v):
....: return MyVector(v.parent(),v.list())
....:
```

Here's how you could use it:

```
sage: f0 = improve_norm(e0)
sage: e0.norm()
1
sage: f0.norm()
sqrt(2)
```

Since `MyVector`

is a subclass of `Vector_rational_dense`

, the two should behave entirely the same, except for the new methods of `MyVector`

:

```
sage: e0.parent() == f0.parent()
True
sage: e0 == f0
True
```

Be careful though; unless you do a bit more work, arithmetic with `MyVector`

objects will produce `Vector_rational_dense`

objects by default:

```
sage: type(f0)
<class '__main__.MyVector'>
sage: type(e0 + f0)
<type 'sage.modules.vector_rational_dense.Vector_rational_dense'>
sage: type(f0+f0)
<type 'sage.modules.vector_rational_dense.Vector_rational_dense'>
sage: type(3*f0)
<type 'sage.modules.vector_rational_dense.Vector_rational_dense'>
```

this is because the addition and multiplication methods are still those of `Vector_rational_dense`

, which return an object of that type. If you want to fix this, you could also redefine `_rmul_`

, `_add_`

, etc.