Ask Your Question

Revision history [back]

click to hide/show revision 1
initial version

manifolds: antisymmetrize a tensor field creates a vector field i/o a tensor field

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)

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) KA.symmetries()

click to hide/show revision 2
None

manifolds: antisymmetrize a tensor field creates a vector field i/o a tensor field

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

manifolds: antisymmetrize a tensor field creates a vector field i/o a tensor field

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)