ex
, ey
,
and ez
in the stokes
packageTo cite the stokes
package in publications, please use
Hankin (2022). Convenience objects
ex
, ey
, and ez
are discussed here
(related package functionality is discussed in dx.Rmd
). The
dual basis to (dx,dy,dz) is,
depending on context, written (ex,ey,ez), or (i,j,k) or sometimes (∂∂x,∂∂x,∂∂x). Here they are denoted ex
,
ey
, and ez
(rather than
i
,j
,k
which cause problems in the
context of R).
fdx <- as.function(dx)
fdy <- as.function(dy)
fdz <- as.function(dz)
matrix(c(
fdx(ex),fdx(ey),fdx(ez),
fdy(ex),fdy(ey),fdy(ez),
fdz(ex),fdz(ey),fdz(ez)
),3,3)
## [,1] [,2] [,3]
## [1,] 1 0 0
## [2,] 0 1 0
## [3,] 0 0 1
Above we see that the matrix dxi∂∂xj is the identity, showing that ex
,
ey
, ez
are indeed conjugate to dx,dy,dz.
Following lines create exeyez.rda
, residing in the
data/
directory of the package.