Question: efficient way to work out exterior products



I am reading

and I was wondering : what is the most efficient way to work out basic combinations of bivectors (or trivectors...)


Suppose for instance I have a 4-dimensional space with basis (e1,e2,e3,e4) and I would want to work out

(e_1 -e2+ e3) wedge (e_2-e_4),


how could I do this?

(I just think working with big tables with many zero entries is a bit over the top for my purposes)


Many thanks!

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