I’m specifically interested in the TensorProduct,TensorWedge, HodgeDual and certain build in functions to do tensor arithmetic like TensorReduce, TensorExpand.

I would like to do exterior algebra calculations where I can choose to work with basis vectors as symbolic objects (and where I can choose to work without basis vectors).

To be explicit, I would like mathematica to do this input:

`v = {v1, v2}; w = {w1, w2}; v\[TensorWedge]w `

desired output:

`(v1 w2 - v2 v1) e1 \[TensorWedge] e2 `

actual output (in normal form):

`{{0, -v2 w1 + v1 w2}, {v2 w1 - v1 w2, 0}} `

If this is not possible what source gives the best advice on how to use mathematica to deal with exterior algebra related differential geometry topics ? A simple example code, video, guide or tutorial on the wolfram site would be optimal.