# Visualize vector field with singularities

What's the best way to plot vector fields with singularities, for example if I take

```
var('x1 x2')
E1=vector([x1,x2])/(sqrt(x1^2+x2^2))^3
E2=E1.subs(x1=x1-1)
E=(E1-E2)
plot_vector_field(E,(x1,-3,3),(x2,-3,3))
```

I get the following ugly plot:

Is it possible to exclude a region around the singularities?

There are some nice mathematica plots for a similar example in the answers to this question: http://mathematica.stackexchange.com/...

There is certainly room for improvement in the `plot_vector_field` function. If someone implemented a way to customize the arrows based on the properties of the underlying vector you could easily color or filter out arrows who length was larger than a given upper bound which is what is done in one of the answers on the mathematica stack exchange.

http://trac.sagemath.org/sage_trac/ticket/2922 would seem relevant.

Yeah, that would do the trick. I left a comment on the ticket, maybe it'll spur someone into wrapping that mpl function :)