complexR

Overview

complexR is a tool for easily computing and visualizing transformations on complex numbers:

• circle_transform() performs and visualizes any kind of transformation on circles

• line_transform() performs and visualizes any kind of transformation on lines

• quad_transform() performs and visualizes any kind of transformation on squares and rectangles

• disc_transform() performs and visualizes any kind of transformation on discs

• plane_to_sphere() and sphere_to_plane() compute stereographic projections

• st_sphere_plot() and st_plane_plot() visualize them.

These functions combine other intermediary functions like cart_to_polar() and polar_to_cart() to execute their operations. You can learn more about them in vignette("complexR").

Installation

Use this code to download the development version of complexR.

devtools::install_github("Swaha294/complexR")

## Downloading GitHub repo Swaha294/complexR@HEAD

## 
##      checking for file ‘/private/var/folders/0p/hkwpsbqj047d4nq34kz3_wdr0000gn/T/Rtmpy8jJo1/remotesf58d78bf1442/Swaha294-complexR-d60dad2/DESCRIPTION’ ...  ✔  checking for file ‘/private/var/folders/0p/hkwpsbqj047d4nq34kz3_wdr0000gn/T/Rtmpy8jJo1/remotesf58d78bf1442/Swaha294-complexR-d60dad2/DESCRIPTION’ (341ms)
##   ─  preparing ‘complexR’:
##      checking DESCRIPTION meta-information ...  ✔  checking DESCRIPTION meta-information
##   ─  checking for LF line-endings in source and make files and shell scripts
##   ─  checking for empty or unneeded directories
##   ─  building ‘complexR_1.0.0.tar.gz’
##      
## 

Usage

Visualize the transformation $f(z) = 2xy + iy^2$ on the unit circle centered at $(1, 0)$

library(complexR)
circle_transform(
  x0 = 1, 
  x_new = expression(2*x*y), 
  y_new = expression(y^2),
  annotations = c(complex(real = 2, imaginary = 0), complex(real = 1, imaginary = 1))
  )

Visualize the transformation $f(x + iy) = (x^3 - y^2) + i(2xy)$ on the disc $|z| < 1, \theta \in [0, \pi/3]$

disc_transform(
  x0 = 1, 
  y0 = 1, 
  x_new = expression(x^3 - y^2),
  y_new = expression(2*x*y), 
  theta_min = 0, 
  theta_max = pi/3
  )

Visualize the stereographic projection of z = 2 + 3i in $\mathbb{C}$ onto the Riemann sphere $\mathbb{C}^*$

st_sphere_plot(2, 3)