# manifolds: antisymmetrize a tensor field creates a vector field instead of a tensor field [closed]

Tensor.antisymmetrize(...) creates a vector field instead of a tensor field as expected. See example below: CODE:

```
M = Manifold(3, 'M')
c_xyz.<x,y,z> = M.chart()
e_=c_xyz.frame()
K =M.tensor_field(2,0,{e_:[[0,1,2],[4,5,6],[8,9,10],[12,13,14]]},name='K')
print('K :',K)
K.symmetries()
KS=K.symmetrize(0,1);print('KS:',KS)
KS.symmetries()
KA=K.antisymmetrize(0,1);print('KA:',KA)
KA.symmetries()
```

OUTPUT print :

```
K : Tensor field K of type (2,0) on the 3-dimensional differentiable manifold M
no symmetry; no antisymmetry
KS: Tensor field of type (2,0) on the 3-dimensional differentiable manifold M
symmetry: (0, 1); no antisymmetry
KA: 2-vector field on the 3-dimensional differentiable manifold M
no symmetry; antisymmetry: (0, 1)
```

Got it. Thanks.