set.seed(0) library("stokes") knitr::opts_chunk$set(echo = TRUE) options(rmarkdown.html_vignette.check_title = FALSE)
knitr::include_graphics(system.file("help/figures/stokes.png", package = "stokes"))
ex <- e(1,3) ey <- e(2,3) ez <- e(3,3)
To cite the stokes
package in publications, please use
@hankin2022_stokes. Convenience objects ex
, ey
, and ez
are
discussed here (related package functionality is discussed in
dx.Rmd
). The dual basis to $(\mathrm{d}x,\mathrm{d}y,\mathrm{d}z)$
is, depending on context, written $(e_x,e_y,e_z)$, or $(i,j,k)$ or
sometimes $\left(\frac{\partial}{\partial x},\frac{\partial}{\partial
x},\frac{\partial}{\partial x}\right)$. 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)
Above we see that the matrix $\mathrm{d}x^i\frac{\partial}{\partial
x^j}$ is the identity, showing that ex
, ey
, ez
are indeed
conjugate to $\mathrm{d}x,\mathrm{d}y,\mathrm{d}z$.
Following lines create exeyez.rda
, residing in the data/
directory of
the package.
save(ex,ey,ez,file="exeyez.rda")
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