Science Score: 13.0%
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○Scientific vocabulary similarity
Low similarity (8.6%) to scientific vocabulary
Keywords
arithmetic
cyclotomic-numbers
r
Last synced: 6 months ago
·
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Repository
The field of cyclotomic numbers.
Statistics
- Stars: 1
- Watchers: 2
- Forks: 1
- Open Issues: 1
- Releases: 2
Topics
arithmetic
cyclotomic-numbers
r
Created almost 3 years ago
· Last pushed over 2 years ago
Metadata Files
Readme
Changelog
README.Rmd
---
title: "cyclotomic"
output: github_document
---
[](https://github.com/stla/cyclotomic/actions/workflows/R-CMD-check.yaml)
```{r setup, include=FALSE}
knitr::opts_chunk$set(collapse = TRUE)
```
*The field of cyclotomic numbers.*
___
The set of cyclotomic numbers is a field obtained by extending the set of
rational numbers with the complex roots of unity. The main function used to
construct a cyclotomic number in this package is `zeta`, it returns a primitive
root of the unity. For example `zeta(4)` is the primitive fourth root of unity,
that is the imaginary unit.
```{r}
library(cyclotomic)
im <- zeta(4)
im^2
```
Arithmetic on cyclotomic numbers can be performed with this package.
It is exact. In particular it allows to deal with the Gaussian rational numbers:
the complex numbers whose both real and imaginary part are rational.
```{r}
a <- as.cyclotomic(5)
b <- as.cyclotomic("3/2")
(a + im * b)^2
```
Note that while `zeta(4)` is printed as `zeta(4)`, this is not the case for all
roots of unity:
```{r}
zeta(9)
```
The set of cyclotomic numbers contains all the square roots of rational numbers,
and therefore the package allows exact calculations on such square roots. For
example, using float numbers, the following equality does not hold true:
```{r}
sqrt(5/3) == sqrt(5) / sqrt(3)
```
But it holds true using the cyclotomic arithmetic:
```{r}
cycSqrt("5/3") == cycSqrt(5) / cycSqrt(3)
```
The set of cyclotomic numbers also contains the cosine and the sine of the
rational multiples of pi. In particular, it contains the cosine and the sine
of any rational number when this number represents an angle given in degrees.
```{r}
cosDeg(60)
sinDeg(60) == cycSqrt(3) / 2
```
___
This package is a port of the Haskell library **cyclotomic**, written by
Scott N. Walck.
Owner
- Login: stla
- Kind: user
- Repositories: 244
- Profile: https://github.com/stla
GitHub Events
Total
- Watch event: 1
Last Year
- Watch event: 1
Committers
Last synced: about 1 year ago
Top Committers
| Name | Commits | |
|---|---|---|
| Stéphane Laurent | l****p@y****r | 83 |
Issues and Pull Requests
Last synced: 6 months ago
All Time
- Total issues: 1
- Total pull requests: 0
- Average time to close issues: N/A
- Average time to close pull requests: N/A
- Total issue authors: 1
- Total pull request authors: 0
- Average comments per issue: 9.0
- Average comments per pull request: 0
- Merged pull requests: 0
- Bot issues: 0
- Bot pull requests: 0
Past Year
- Issues: 0
- Pull requests: 0
- Average time to close issues: N/A
- Average time to close pull requests: N/A
- Issue authors: 0
- Pull request authors: 0
- Average comments per issue: 0
- Average comments per pull request: 0
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- Bot issues: 0
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Top Authors
Issue Authors
- joelcourtheyn (1)
Pull Request Authors
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Packages
- Total packages: 1
-
Total downloads:
- cran 244 last-month
- Total dependent packages: 0
- Total dependent repositories: 0
- Total versions: 4
- Total maintainers: 1
cran.r-project.org: cyclotomic
The Field of Cyclotomic Numbers
- Homepage: https://github.com/stla/cyclotomic
- Documentation: http://cran.r-project.org/web/packages/cyclotomic/cyclotomic.pdf
- License: GPL-3
-
Latest release: 1.3.0
published over 2 years ago
Rankings
Dependent packages count: 29.6%
Dependent repos count: 35.3%
Average: 51.5%
Downloads: 89.7%
Maintainers (1)
Last synced:
6 months ago