{"id":21595771,"url":"https://github.com/wigging/exponential-sums","last_synced_at":"2025-03-18T11:13:14.309Z","repository":{"id":102016152,"uuid":"197978184","full_name":"wigging/exponential-sums","owner":"wigging","description":"Generate plots and animations of exponential sums","archived":false,"fork":false,"pushed_at":"2020-04-11T04:27:40.000Z","size":1733,"stargazers_count":2,"open_issues_count":0,"forks_count":1,"subscribers_count":0,"default_branch":"master","last_synced_at":"2025-01-24T17:33:55.594Z","etag":null,"topics":["math","matplotlib","python"],"latest_commit_sha":null,"homepage":"https://gavinw.me/exponential-sums","language":"Python","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"mit","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/wigging.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2019-07-20T20:29:45.000Z","updated_at":"2023-07-31T17:14:38.000Z","dependencies_parsed_at":null,"dependency_job_id":"67877025-8acf-4506-a21c-b6d63334ed2b","html_url":"https://github.com/wigging/exponential-sums","commit_stats":null,"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/wigging%2Fexponential-sums","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/wigging%2Fexponential-sums/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/wigging%2Fexponential-sums/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/wigging%2Fexponential-sums/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/wigging","download_url":"https://codeload.github.com/wigging/exponential-sums/tar.gz/refs/heads/master","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":244207747,"owners_count":20416109,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["math","matplotlib","python"],"created_at":"2024-11-24T17:43:56.728Z","updated_at":"2025-03-18T11:13:14.291Z","avatar_url":"https://github.com/wigging.png","language":"Python","funding_links":["https://www.paypal.me/gavinwiggins"],"categories":[],"sub_categories":[],"readme":"# Exponential Sums\n\nExponential 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.\n\nAn exponential sum is represented by the following equation\n\n\u003cimg src=\"assets/expsum.png\" height=\"80\"/\u003e\n\nwhere 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.\n\nThis project is inspired by John Cook's article \"[Exponential sums make pretty pictures][1]\".\n\n## Installation and Usage\n\nRequires Python 3, NumPy, and Matplotlib.\n\nClone this repository and run the following command:\n\n```bash\n\u003e\u003e\u003e python expsum func1 2000 10 7 17\n```\n\nCreate an animated plot by passing the optional `--anim` argument:\n\n```bash\n\u003e\u003e\u003e python expsum func1 2000 10 7 17 --anim\n```\n\n## Examples\n\nExamples of the functions available in the `expsum` package are shown below.\n\n### Function 1\n\n\u003cimg src=\"assets/func1eq.png\" height=\"45\"/\u003e\n\n```bash\n\u003e\u003e\u003e python expsum func1 2000 10 7 17\n```\n\n\u003cimg src=\"assets/func1a.png\" height=\"400\"/\u003e\n\n```bash\n\u003e\u003e\u003e python expsum func1 8000 11 21 31\n```\n\n\u003cimg src=\"assets/func1b.png\" height=\"400\"/\u003e\n\n### Function 2\n\n\u003cimg src=\"assets/func2eq.png\" height=\"45\"/\u003e\n\n```bash\n\u003e\u003e\u003e python expsum func2 1200 100\n```\n\n\u003cimg src=\"assets/func2a.png\" height=\"400\"/\u003e\n\n```bash\n\u003e\u003e\u003e python expsum func2 4000 800\n```\n\n\u003cimg src=\"assets/func2b.png\" height=\"400\"/\u003e\n\n### Function 3\n\n\u003cimg src=\"assets/func3eq.png\" height=\"25\"/\u003e\n\n```bash\n\u003e\u003e\u003e python expsum func3 1000\n```\n\n\u003cimg src=\"assets/func3a.png\" height=\"400\"/\u003e\n\n```bash\n\u003e\u003e\u003e python expsum func3 4000\n```\n\n\u003cimg src=\"assets/func3b.png\" height=\"400\"/\u003e\n\n### Function 4\n\n\u003cimg src=\"assets/func4eq.png\" height=\"22\"/\u003e\n\n```bash\n\u003e\u003e\u003e python expsum func4 4000 4\n```\n\n\u003cimg src=\"assets/func4a.png\" height=\"400\"/\u003e\n\n### Function 5\n\n\u003cimg src=\"assets/func5eq.png\" height=\"45\"/\u003e\n\n```bash\npython expsum func5 4000 50 100\n```\n\n\u003cimg src=\"assets/func5a.png\" height=\"400\"/\u003e\n\n### Function 6\n\n\u003cimg src=\"assets/func6eq.png\" height=\"48\"/\u003e\n\n```bash\n\u003e\u003e\u003e python expsum func6 2000 4\n```\n\n\u003cimg src=\"assets/func6a.png\" height=\"400\"/\u003e\n\n### Function 7\n\n\u003cimg src=\"assets/func7eq.png\" height=\"48\"/\u003e\n\n```bash\n\u003e\u003e\u003e python expsum func7 8000 4\n```\n\n\u003cimg src=\"assets/func7a.png\" height=\"400\"/\u003e\n\n## Contributing\n\nSubmit a Pull Request if you would like to contribute to this project. Questions and other comments can be submitted on the Issues page.\n\n## Support\n\nSupport this project by making a donation at [paypal.me/gavinwiggins](https://www.paypal.me/gavinwiggins). Thank you 😁\n\n## References\n\n1. John D. Cook. [Exponential sums make pretty pictures][1]. October 7, 2017.\n2. David Angell. [Exponential sums][2]. School of Mathematics and Statistics, UNSW. Accessed July 7, 2019.\n3. Wikipedia contributors. [Exponential sum][3]. In Wikipedia, The Free Encyclopedia. Accessed July 20, 2019.\n\n[1]: https://www.johndcook.com/blog/2017/10/07/exponential-sums-make-pretty-pictures/\n[2]: https://www.maths.unsw.edu.au/about/exponential-sums\n[3]: https://en.wikipedia.org/wiki/Exponential_sum\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fwigging%2Fexponential-sums","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fwigging%2Fexponential-sums","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fwigging%2Fexponential-sums/lists"}