No, there is no dedicated method to compute the covariant derivative of a tensor field along a given vector field. You have to perform the contraction with the vector field explicitly. Note that you can use the method `contract`

to avoid explicit sums on the indices. For instance, to compute the covariant derivative $\nabla_v T$ of a tensor field $T$ along the vector field $v$, simply write

```
nabla(T).contract(v)
```

It would be desirable though to implement a method `covariant_derivative`

to perform this directly, by writing

```
T.covariant_derivative(v, connection=nabla)
```

which could be shortened to

```
T.covariant_derivative(v)
```

when there exists a default connection, e.g. on a pseudo-Riemannian manifold.
This would be on the same footing as the existing method for the Lie derivative: `T.lie_derivative(v)`

evaluates $\mathcal{L}_v T$.