# Why does sage fail to detect the symmetry here?

```
M = Manifold(4, 'M')
CM.<u,r,θ,φ> = M.chart(r'u r:(0,+oo) θ:(0,pi) φ:(0,2*pi)')
e = CM.coframe()
du = e[0]
dr = e[1]
dθ = e[2]
dφ = e[3]
V = function('V')
β = function('β')
γ = function('γ')
δ = function('δ')
(dθ * dφ + dφ * dθ).symmetries()
(dθ * dφ + dφ * dθ).symmetrize() == (dθ * dφ + dφ * dθ)
```

I want to define a (degenerate) metric:

```
g = M.metric('g')
g.set(dθ * dφ + dφ * dθ)
```

this fails because Sage does not believe the tensor field to be symmetric.