given a vector in sage

```
sage: a,b=var('a,b')
sage: sv=vector(SR,[1,a,b^2])
```

then why is this a meaningful operation

```
sage: sv/sv
1
```

To my (utterly humble) understanding, I always thought, that if vector multiplication '*' is defined via the scalar product - as it seems to be in sage

```
sage: sv*sv
a^2 + b^4 + 1
```

then, division cannot be defined meaningfully?

[Just as a sideremark along that line: I have no problem with numpy's element wise array-arithmetic

```
In [1]: v=array([1.,2.,3.]) # vector
In [2]: e=array([1.,1.,1.]) # unity is a vector
In [3]: e*v == v # multiplication by unity
Out[4]: array([ True, True, True], dtype=bool)
In [5]: vi=v**(-1) # inverse is a vector
In [6]: e/v == vi # unity/vector == inverse
Out[7]: array([ True, True, True], dtype=bool)
In [8]: e == v*vi # vector * inverse == unity
Out[9]: array([ True, True, True], dtype=bool)
```

In my layman's world, this type of division makes perfect sense. (Moreover I'm curious why sage seems to not adopt this pythonic way of array arithmetic)]