MaplePrimes - answers and comments on Question, efficient way to work out exterior products

with(difforms)

Axel Vogt — Mon, 17 Sep 2012 00:05:23 Z

I almost never used it (it is quite inconvenient, but you may try with(difforms)
and then &^( (e1 -e2+ e3), (e2-e4)), for which you have to supply degrees
by defform(e1=p, ...)

May be DifferentialGeometry[ExteriorDerivative] is your friend ... starting by
with(DifferentialGeometry), looking up DifferentialGeometry[algebraic operations]
Which does not really invite me to use it (I miss a simple 'overloading' for the
operators). But I am simply not used to that package, I guess.

Thanks, I tried restart; with(difforms

fredbel6 — Mon, 17 Sep 2012 01:48:34 Z

Thanks,

I tried

restart; with(difforms);
defform(e1 = 1, e2 = 1);
`&^`(e1, e3)+`&^`(e3, e1)+`&^`(e1, e1);

And I get e1&^e3+ e3&^e1 as output, in other words, he knows he can cancel e1&^e1, but not that there is antisymmetry?

Kind regards.

simplify

Axel Vogt — Mon, 17 Sep 2012 12:22:38 Z

Seems it does not simplify automatically, so continue by

  simpform(%);

                            wdegree(e3)
                   (1 + (-1)           ) (e1 &^ e3)

And you see, that it depends on the degree of e3.

PS: I am not sure, whether they always mean "pure degree".

Edited: 
the terminus in Algebra is "anti-commutativ" or "alternating"
(in this case), not "anti-symmetric"