{"id":50445288,"url":"https://github.com/jlmsc/gaussian-elimination","last_synced_at":"2026-05-31T21:02:40.879Z","repository":{"id":355501779,"uuid":"1219483669","full_name":"JLMSC/gaussian-elimination","owner":"JLMSC","description":"Python implementation of the Gaussian Elimination method for solving systems of linear equations.","archived":false,"fork":false,"pushed_at":"2026-05-03T22:48:34.000Z","size":11,"stargazers_count":0,"open_issues_count":0,"forks_count":0,"subscribers_count":0,"default_branch":"main","last_synced_at":"2026-05-04T00:32:40.498Z","etag":null,"topics":["algorithms","back-substitution","educational","gaussian-elimination","linear-algebra","linear-systems","math","matrix","numerical-methods","numpy","pysimplegui","python","row-echelon-form","scientific-computing","sympy"],"latest_commit_sha":null,"homepage":"","language":"Python","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"unlicense","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/JLMSC.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,"zenodo":null,"notice":null,"maintainers":null,"copyright":null,"agents":null,"dco":null,"cla":null}},"created_at":"2026-04-23T23:30:21.000Z","updated_at":"2026-05-03T22:48:37.000Z","dependencies_parsed_at":null,"dependency_job_id":null,"html_url":"https://github.com/JLMSC/gaussian-elimination","commit_stats":null,"previous_names":["jlmsc/gaussian-elimination"],"tags_count":null,"template":false,"template_full_name":null,"purl":"pkg:github/JLMSC/gaussian-elimination","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/JLMSC%2Fgaussian-elimination","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/JLMSC%2Fgaussian-elimination/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/JLMSC%2Fgaussian-elimination/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/JLMSC%2Fgaussian-elimination/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/JLMSC","download_url":"https://codeload.github.com/JLMSC/gaussian-elimination/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/JLMSC%2Fgaussian-elimination/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":33748607,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-05-26T15:22:16.424Z","status":"online","status_checked_at":"2026-05-31T02:00:06.040Z","response_time":95,"last_error":null,"robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":true,"can_crawl_api":true,"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":["algorithms","back-substitution","educational","gaussian-elimination","linear-algebra","linear-systems","math","matrix","numerical-methods","numpy","pysimplegui","python","row-echelon-form","scientific-computing","sympy"],"created_at":"2026-05-31T21:02:35.480Z","updated_at":"2026-05-31T21:02:40.866Z","avatar_url":"https://github.com/JLMSC.png","language":"Python","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Gaussian Elimination Algorithm\n\nThis work presents a computational implementation of the Gaussian Elimination method for solving systems of linear equations. The system accepts user-defined equations in symbolic string format, converts them into an augmented matrix representation, and applies elementary row operations to obtain a row echelon form. The final solution is computed via back substitution. A graphical interface is provided to facilitate user interaction.\n\n## Introduction\n\nThis project implements the method programmatically using Python, with the following objectives:\n\n* Accept arbitrary linear systems as input (string format)\n* Convert symbolic equations into matrix representation\n* Apply Gaussian Elimination to obtain a Row Echelon Form (REF)\n* Compute solutions using Back Substitution\n* Provide a simple graphical user interface (GUI)\n\n## Problem Representation\n\nA linear system is represented as:\n\n$$ A\\mathbf{x} = \\mathbf{B} $$\n\nWhere:\n* $A \\in \\mathbb{R}^{n \\times n}$ : coefficient matrix\n* $\\mathbf{x} \\in \\mathbb{R}^n$ : vector of variables\n* $\\mathbf{B} \\in \\mathbb{R}^n$ : constant vector\n\nThe system is internally transformed into an augmented matrix:\n\n$$ [A \\mid \\mathbf{B}] $$\n\n## Gaussian Elimination\n\nThe algorithm transforms the augmented matrix into Row Echelon Form (REF) using elementary row operations:\n\n* **Row Swapping** (pivoting)\n* **Row Scaling** (normalizing pivots)\n* **Row Elimination** (zeroing values below pivots)\n\nThis process is implemented in the primary routine:\n`row_echelon_form(A, B)`\n\n## Back Substitution\n\nOnce the matrix is in row echelon form, back substitution is applied to compute the solution vector.\n\nImplemented in:\n`back_substitution(M)`\n\n**Steps:**\n1. Traverse rows in reverse order.\n2. Eliminate coefficients above pivots.\n3. Extract the solution from the last column.\n\n## Input Parsing\n\nUser-provided equations are parsed using symbolic computation:\n`string_to_augmented_matrix(equations)`\n\n**Responsibilities:**\n* Extract variable names dynamically.\n* Convert expressions using symbolic algebra.\n* Build the coefficient matrix $A$ and vector $\\mathbf{B}$.\n\n**Example Input:**\n```text\n3*x + 6*y + 6*w + 8*z = 1\n5*x + 3*y + 6*w = -10\n4*y - 5*w + 8*z = 8\n4*w + 8*z = 9\n```\n\n## Graphical Interface\n\nA simple GUI is implemented using PySimpleGUI:\n* Multiline input for equations\n* Submit / Cancel controls\n* Popup display for results or errors\n\n**Features:**\n* Input validation\n* Automatic enabling/disabling of controls\n* Error handling for singular or invalid systems\n\n## Results\n\nThe system successfully computes solutions for valid, non-singular linear systems.\n\nOutput is formatted as:\n```text\nx = -1.5414\ny = -0.5223\nw = -0.1210\nz = 1.1855\n```\n\nInvalid or singular systems trigger appropriate error messages.\n\n## Limitations\n\n* Only supports systems with a unique solution.\n* Numerical instability may occur for ill-conditioned matrices (no full pivoting).\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fjlmsc%2Fgaussian-elimination","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fjlmsc%2Fgaussian-elimination","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fjlmsc%2Fgaussian-elimination/lists"}