matrixmodp

Functions for Working with Matrices over Finite Prime Fields

https://github.com/rhigginbottom/matrixmodp

Repository

Functions for Working with Matrices over Finite Prime Fields

README.Rmd

---
output: github_document
---



```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.path = "man/figures/README-",
  out.width = "100%"
)
```

# matrixmodp


[![R-CMD-check](https://github.com/rhigginbottom/matrixmodp/actions/workflows/R-CMD-check.yaml/badge.svg)](https://github.com/rhigginbottom/matrixmodp/actions/workflows/R-CMD-check.yaml)


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.

## Installation

You can install the public released version of `matrixmodp` from CRAN with:

```{r}
install.packages("matrixmodp")
```

You can install the development version of matrixmodp from [GitHub](https://github.com/) with:

``` r
# install.packages("devtools")
devtools::install_github("rhigginbottom/matrixmodp")
```

## Example

We first provide an example of finding the RREF of a matrix with entries in $\mathbb{F}_5$.

```{r example}
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)
```

We now show how to find the inverse of a $3\times 3$ matrix over $\mathbb{F}_7$.

```{r}
library(matrixmodp)
entries <- c(3, 3, 3, 2, 0, 2, 1, 2, 5)
A <- matrix(entries, 3, 3)
inv_p(A, 7)
```

## Note

Some 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.

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