https://github.com/wigging/exponential-sums
Generate plots and animations of exponential sums
https://github.com/wigging/exponential-sums
math matplotlib python
Last synced: over 1 year ago
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Generate plots and animations of exponential sums
- Host: GitHub
- URL: https://github.com/wigging/exponential-sums
- Owner: wigging
- License: mit
- Created: 2019-07-20T20:29:45.000Z (almost 7 years ago)
- Default Branch: master
- Last Pushed: 2020-04-11T04:27:40.000Z (about 6 years ago)
- Last Synced: 2025-01-24T17:33:55.594Z (over 1 year ago)
- Topics: math, matplotlib, python
- Language: Python
- Homepage: https://gavinw.me/exponential-sums
- Size: 1.65 MB
- Stars: 2
- Watchers: 0
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Exponential Sums
Exponential sums are an area of math represented by a series with terms that are complex exponentials. These types of sums are related to Fourier analysis and number theory. Plotting exponential sums produces various designs based on the type of input function.
An exponential sum is represented by the following equation
where the exponential is a complex number. The function f(n) is a real-valued function defined for a sequence of positive integers. The Python package `expsum` plots the exponential sum in the complex plane as a progression of partial sums. The x-axis on the plot is the real part and the y-axis is the imaginary part.
This project is inspired by John Cook's article "[Exponential sums make pretty pictures][1]".
## Installation and Usage
Requires Python 3, NumPy, and Matplotlib.
Clone this repository and run the following command:
```bash
>>> python expsum func1 2000 10 7 17
```
Create an animated plot by passing the optional `--anim` argument:
```bash
>>> python expsum func1 2000 10 7 17 --anim
```
## Examples
Examples of the functions available in the `expsum` package are shown below.
### Function 1
```bash
>>> python expsum func1 2000 10 7 17
```
```bash
>>> python expsum func1 8000 11 21 31
```
### Function 2
```bash
>>> python expsum func2 1200 100
```
```bash
>>> python expsum func2 4000 800
```
### Function 3
```bash
>>> python expsum func3 1000
```
```bash
>>> python expsum func3 4000
```
### Function 4
```bash
>>> python expsum func4 4000 4
```
### Function 5
```bash
python expsum func5 4000 50 100
```
### Function 6
```bash
>>> python expsum func6 2000 4
```
### Function 7
```bash
>>> python expsum func7 8000 4
```
## Contributing
Submit a Pull Request if you would like to contribute to this project. Questions and other comments can be submitted on the Issues page.
## Support
Support this project by making a donation at [paypal.me/gavinwiggins](https://www.paypal.me/gavinwiggins). Thank you 😁
## References
1. John D. Cook. [Exponential sums make pretty pictures][1]. October 7, 2017.
2. David Angell. [Exponential sums][2]. School of Mathematics and Statistics, UNSW. Accessed July 7, 2019.
3. Wikipedia contributors. [Exponential sum][3]. In Wikipedia, The Free Encyclopedia. Accessed July 20, 2019.
[1]: https://www.johndcook.com/blog/2017/10/07/exponential-sums-make-pretty-pictures/
[2]: https://www.maths.unsw.edu.au/about/exponential-sums
[3]: https://en.wikipedia.org/wiki/Exponential_sum