hodge() interpretation

[RobinHankin]

Something is wrong with my understanding:

> as.kform(matrix(1,1,1)) -> dx
> as.kform(matrix(2,1,1)) -> dy
> as.kform(matrix(3,1,1)) -> dz
> hodge(dx,3)
[1] 1
> hodge(dx^dy,3)
[1] 1
> 

I was expecting hodge(dx,3) to be equal to dx ^ dy and hodge(dx^dy,3) to be dz

[RobinHankin]

Inspired by

https://www.youtube.com/watch?v=tyaWHQO-wSc&t=325s

[RobinHankin]

clearly a bug:

> hodge(7*d(1)^d(2) + 8*d(3)^d(4),5)
An alternating linear map from V^3 to R with V=R^5:
           val
 1 2 5  =    8
 3 4 5  =    7
> hodge(7*d(1)^d(2),5)
[1] 7
> 

The first call to hodge() is fine, but the second should return a 3-form (corresponding to one of the lines of the first), but it returns a scalar.