{"id":28824117,"url":"https://github.com/lm-cyber/symkell","last_synced_at":"2026-03-07T05:05:27.065Z","repository":{"id":290230536,"uuid":"961064744","full_name":"lm-cyber/symkell","owner":"lm-cyber","description":"A computer algebra system written in Haskell ","archived":false,"fork":false,"pushed_at":"2025-05-13T23:38:49.000Z","size":119,"stargazers_count":31,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"master","last_synced_at":"2025-05-14T01:45:37.619Z","etag":null,"topics":["computer-algebra-system","haskell","math"],"latest_commit_sha":null,"homepage":"","language":"Haskell","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"other","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/lm-cyber.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}},"created_at":"2025-04-05T17:15:38.000Z","updated_at":"2025-05-13T23:38:52.000Z","dependencies_parsed_at":"2025-05-14T00:52:15.423Z","dependency_job_id":null,"html_url":"https://github.com/lm-cyber/symkell","commit_stats":null,"previous_names":["lm-cyber/symkell"],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/lm-cyber/symkell","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/lm-cyber%2Fsymkell","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/lm-cyber%2Fsymkell/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/lm-cyber%2Fsymkell/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/lm-cyber%2Fsymkell/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/lm-cyber","download_url":"https://codeload.github.com/lm-cyber/symkell/tar.gz/refs/heads/master","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/lm-cyber%2Fsymkell/sbom","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":260660096,"owners_count":23043487,"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":["computer-algebra-system","haskell","math"],"created_at":"2025-06-19T01:03:41.974Z","updated_at":"2026-03-07T05:05:27.057Z","avatar_url":"https://github.com/lm-cyber.png","language":"Haskell","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Symkell\n\nSymkell is a symbolic mathematics library written in Haskell with Python bindings. It provides powerful tools for symbolic computation, including differentiation, integration, limits, polynomial operations, and more.\n\n## Overview\n\nSymkell enables symbolic mathematical operations through a well-structured Haskell core with FFI bindings to make the functionality accessible from Python. The project is designed for researchers, educators, and developers working with symbolic mathematics.\n\n## TODO\n\n- [ ] Fix FFI implementation for better interoperability with Python\n- [ ] Refactor codebase to improve maintainability and performance\n- [ ] Fix and enhance limits computation algorithm\n- [ ] Improve Series expansion functionality\n- [ ] Implement CI/CD pipeline for automated testing and deployment\n\n## Project Structure\n\n- **symkell_core**: The Haskell core library implementing symbolic mathematics operations\n- **ffi_export_lib**: FFI (Foreign Function Interface) library for exporting Haskell functions\n- **pysymkell**: Python bindings for accessing Symkell functionality from Python\n\n## Features\n\n- Symbolic expression representation and manipulation\n- Differentiation of expressions\n- Integration (with support for various techniques)\n- Symbolic limits\n- Series expansions\n- Polynomial operations (including rational functions)\n- Expression simplification\n- LaTeX conversion for displaying expressions\n- Haskell expression generation\n\n## Algorithms\n\n### Symbolic Integration\n\nSymkell implements a sophisticated symbolic integration algorithm:\n\n1. **Preprocessing \u0026 Simplification**\n   - Numerical evaluation of constants\n   - Symbolic simplification and canonicalization\n   - Term collection and ordering\n\n2. **Basic Integration Methods**\n   - Table lookup for known integrals\n   - Linearity application for sums/differences\n\n3. **Advanced Techniques**\n   - Integration by substitution (u-substitution)\n   - Integration by parts\n   - Specialized handling for rational functions\n   - Trigonometric, exponential, and logarithmic integration\n\n4. **Structural Methods**\n   - Partial implementation of Risch algorithm for determining elementary antiderivatives\n   - Special function handling for non-elementary integrals\n\n### Symbolic Limits\n\nSymkell uses a multi-step approach for computing limits:\n\n1. **Preprocessing**\n   - Handling limit direction and infinite limits\n   - Resolving trivial cases\n\n2. **Core Algorithms**\n   - Leading term analysis\n   - Series expansion techniques (similar to Gruntz algorithm)\n   - L'Hôpital's rule for indeterminate forms\n\n3. **Recursive Methods**\n   - Term-wise limit computation when possible\n   - Algebraic simplifications for resolving indeterminacies\n\n\n## Installation\n\n### Prerequisites\n\n- GHC (Glasgow Haskell Compiler)\n- Stack (Haskell build tool)\n- Python 3.6+\n\n### Building from Source\n\n1. Clone the repository:\n   ```\n   git clone https://github.com/yourusername/symkell.git\n   cd symkell\n   ```\n\n2. Build the Haskell core and FFI libraries:\n   ```\n   cd symkell\n   stack build\n   ```\n\n3. Build and install the Python package:\n   ```\n   cd ../pysymkell\n   pip install -e .\n   ```\n\n## Usage\n\n### Haskell API\n\n```haskell\nimport Symkell\n\n-- Create a symbolic expression\n-- Perform differentiation\nexpr = ...\ndiff = differentiate \"x\" expr\n\n-- Perform integration\nintegral = integrate \"x\" expr\n\n-- Convert to LaTeX\nlatex = toLaTeX expr\n\n-- Simplify an expression\nsimplified = simplify expr\n```\n\n### Python API\n\n```python\nimport pysymkell as sk\n\n# Create symbolic expressions\n# Perform operations on them\n# Output results\n```\n\n## Development\n\nThis project is built using Stack with GHC and uses standard Python package development tools.\n\n## License\n\nThis project is licensed under the BSD 3-Clause License - see the LICENSE file for details. 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