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The goal of matrixmodp is to make two matrix algebra tasks easier
when working with the fields \(\mathbb{F}_p\). Specifically, this package
provides two functions: rref_p() calculates the reduced-row
echelon form of a matrix, and inv_p() calculates the
inverse of a (square, invertible) matrix.
You can install the public released version of
matrixmodp from CRAN with:
install.packages("matrixmodp")
#> Installing package into 'C:/Users/rhigginbottom/AppData/Local/Temp/Rtmpc35hmI/temp_libpath93c0442736d5'
#> (as 'lib' is unspecified)
#> Warning: package 'matrixmodp' is not available for this version of R
#>
#> A version of this package for your version of R might be available elsewhere,
#> see the ideas at
#> https://cran.r-project.org/doc/manuals/r-patched/R-admin.html#Installing-packagesYou can install the development version of matrixmodp from GitHub with:
# install.packages("devtools")
devtools::install_github("rhigginbottom/matrixmodp")We first provide an example of finding the RREF of a matrix with entries in \(\mathbb{F}_5\).
library(matrixmodp)
entries <- c(4, 1, 2, 0, 0, 3, 4, 0, 0, 1, 4, 1)
A <- matrix(entries, 3, 4)
rref_p(A, 5)
#> [,1] [,2] [,3] [,4]
#> [1,] 1 0 0 4
#> [2,] 0 1 0 1
#> [3,] 0 0 1 0We now show how to find the inverse of a \(3\times 3\) matrix over \(\mathbb{F}_7\).
library(matrixmodp)
entries <- c(3, 3, 3, 2, 0, 2, 1, 2, 5)
A <- matrix(entries, 3, 3)
inv_p(A, 7)
#> [,1] [,2] [,3]
#> [1,] 6 5 1
#> [2,] 3 3 1
#> [3,] 5 0 2Some of the code for the rref_p() function was taken
from the echelon() function in the matlib
package. Because of the different way row operations need to work when
using entries in \(\mathbb{F}_p\), no
functions could be copied entirely. This makes attribution somewhat
difficult. The license chosen for this package was specifically chosen
to be compatible with the license in use for the matlib
package because of this overlap in code.
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.