Objects ex, ey, and ez in the stokes package

Robin K. S. Hankin

ex <- e(1,3)
ey <- e(2,3)
ez <- e(3,3)

Convenience objects ex, ey, and ez are discussed here. Elementary forms dx, dy and dz are discussed in dx.Rmd.

The dual basis to \((dx,dy,dz)\) 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)
##      [,1] [,2] [,3]
## [1,]    1    0    0
## [2,]    0    1    0
## [3,]    0    0    1

Above we see that the matrix \(dx^i\frac{\partial}{\partial x^j}\) is the identity, showing that ex, ey, ez are indeed conjugate to \(dx,dy,dz\).

Package dataset

Following lines create exeyez.rda, residing in the data/ directory of the package.