stokes (version 1.2-1)

hodge: Hodge star operator

Description

Given a \(k\)-form, return its Hodge dual

Usage

hodge(K, n=dovs(K), g, lose=TRUE)

Value

Given a \(k\)-form, in an \(n\)-dimensional space, return a \((n-k)\)-form.

Arguments

K

Object of class kform

n

Dimensionality of space, defaulting the the largest element of the index

g

Diagonal of the metric tensor, with missing default being the standard metric of the identity matrix. Currently, only entries of \(\pm 1\) are accepted

lose

Boolean, with default TRUE meaning to coerce to a scalar if appropriate

Author

Robin K. S. Hankin

See Also

wedge

Examples

(o <- kform_general(5,2,1:10))
hodge(o)
o == hodge(hodge(o))

Faraday <- kform_general(4,2,runif(6)) # Faraday electromagnetic tensor
mink <- c(-1,1,1,1)  # Minkowski metric
hodge(Faraday,g=mink)

Faraday  == Faraday |>
      hodge(g=mink) |>
      hodge(g=mink) |>
      hodge(g=mink) |>
      hodge(g=mink)

hodge(dx,3) == dy^dz


## Some edge-cases:
hodge(scalar(1),2)
hodge(zeroform(5),9)
hodge(volume(5))
hodge(volume(5),lose=TRUE)
hodge(scalar(7),n=9)