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| <h1 align="center"> | ||
| <br> | ||
| <picture> | ||
| <source media="(prefers-color-scheme: dark)" srcset="https://symbolica.io/logo_dark.svg"> | ||
| <source media="(prefers-color-scheme: light)" srcset="https://symbolica.io/logo.svg"> | ||
| <img src="https://symbolica.io/logo.svg" alt="logo" width="200"> | ||
| </picture> | ||
| <br> | ||
| </h1> | ||
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| <p align="center"> | ||
| <a href="https://symbolica.io"><img alt="Symbolica website" src="https://img.shields.io/static/v1?label=symbolica&message=website&color=orange&style=flat-square"></a> | ||
| <a href="https://reform.zulipchat.com"><img alt="Zulip Chat" src="https://img.shields.io/static/v1?label=zulip&message=discussions&color=blue&style=flat-square"></a> | ||
| <a href="https://github.com/benruijl/symbolica"><img alt="Symbolica website" src="https://img.shields.io/static/v1?label=github&message=development&color=green&style=flat-square&logo=github"></a> | ||
| <a href="https://app.codecov.io/gh/benruijl/symbolica"><img alt="Codecov" src="https://img.shields.io/codecov/c/github/benruijl/symbolica?token=N43MATK5XJ&style=flat-square"></a> | ||
| </p> | ||
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| # Symbolica ⊆ Modern Computer Algebra | ||
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| Symbolica is a blazing fast computer algebra system for Python and Rust, born of a need to push the boundaries of computations in science and enterprise. | ||
| Check out the live [Jupyter Notebook demo](https://colab.research.google.com/drive/1VAtND2kddgBwNt1Tjsai8vnbVIbgg-7D?usp=sharing)! | ||
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| For documentation and more, see [symbolica.io](https://symbolica.io). | ||
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| ## Quick Example | ||
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| Symbolica allows you to build and manipulate mathematical expressions, for example from a Jupyter Notebook: | ||
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| <picture> | ||
| <source media="(prefers-color-scheme: dark)" srcset="https://symbolica.io/resources/demo.dark.svg"> | ||
| <source media="(prefers-color-scheme: light)" srcset="https://symbolica.io/resources/demo.light.svg"> | ||
| <img width="600" alt="A demo of Symbolica" src="https://symbolica.io/resources/demo.light.svg"> | ||
| </picture> | ||
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| You are able to perform these operations from the comfort of a programming language that you (probably) already know, by using Symbolica's bindings to Python and Rust: | ||
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| <picture> | ||
| <source media="(prefers-color-scheme: dark)" srcset="https://symbolica.io/resources/completion.png"> | ||
| <source media="(prefers-color-scheme: light)" srcset="https://symbolica.io/resources/completion_light.png"> | ||
| <img width="600" alt="A demo of Symbolica" src="https://symbolica.io/resources/completion.png"> | ||
| </picture> | ||
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| # Installation | ||
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| Visit the [Get Started](https://symbolica.io/docs/get_started.html) page for detailed installation instructions. | ||
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| ## Python | ||
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| Symbolica can be installed for Python >3.5 using `pip`: | ||
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| ```sh | ||
| pip install symbolica | ||
| ``` | ||
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| ## Rust | ||
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| If you want to use Symbolica as a library in Rust, simply include it in the `Cargo.toml`: | ||
| # <h1 align="center"> Disclaimer </h1> | ||
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| ```toml | ||
| [dependencies] | ||
| symbolica = "0.13" | ||
| ``` | ||
| This fork of the symbolica code is not meant to be used outside of the context of the [γLoop](https://github.com/alphal00p/gammaloop) project as it contains custom modifications that may not be suitable for a generic use. | ||
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| # Examples | ||
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| Below we list some examples of the features of Symbolica. Check the [guide](https://symbolica.io/docs/) for a complete overview. | ||
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| ### Pattern matching | ||
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| Variables ending with a `_` are wildcards that match to any subexpression. | ||
| In the following example we try to match the pattern `f(w1_,w2_)`: | ||
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| ```python | ||
| from symbolica import * | ||
| x, y, w1_, w2_, f = S('x','y','w1_','w2_', 'f') | ||
| e = f(3,x)*y**2+5 | ||
| r = e.replace_all(f(w1_,w2_), f(w1_ - 1, w2_**2)) | ||
| print(r) | ||
| ``` | ||
| which yields `y^2*f(2,x^2)+5`. | ||
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| ### Solving a linear system | ||
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| Solve a linear system in `x` and `y` with a parameter `c`: | ||
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| ```python | ||
| from symbolica import * | ||
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| x, y, c, f = S('x', 'y', 'c', 'f') | ||
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| x_r, y_r = Expression.solve_linear_system( | ||
| [f(c)*x + y + c, y + c**2], [x, y]) | ||
| print('x =', x_r, ', y =', y_r) | ||
| ``` | ||
| which yields `x = (-c+c^2)*f(c)^-1` and `y = -c^2`. | ||
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| ### Series expansion | ||
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| Perform a series expansion in `x`: | ||
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| ```python | ||
| from symbolica import * | ||
| e = E('exp(5+x)/(1-x)').series(S('x'), 0, 3) | ||
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| print(e) | ||
| ``` | ||
| which yields `(exp(5))+(2*exp(5))*x+(5/2*exp(5))*x^2+(8/3*exp(5))*x^3+𝒪(x^4)`. | ||
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| ### Rational arithmetic | ||
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| Symbolica is world-class in rational arithmetic, outperforming Mathematica, Maple, Form, Fermat, and other computer algebra packages. Simply convert an expression to a rational polynomial: | ||
| ```python | ||
| from symbolica import * | ||
| p = E('(x*y^2*5+5)^2/(2*x+5)+(x+4)/(6*x^2+1)').to_rational_polynomial() | ||
| print(p) | ||
| ``` | ||
| which yields `(45+13*x+50*x*y^2+152*x^2+25*x^2*y^4+300*x^3*y^2+150*x^4*y^4)/(5+2*x+30*x^2+12*x^3)`. | ||
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| ## Development | ||
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| Follow the development and discussions on [Zulip](https://reform.zulipchat.com)! | ||
| Make sure to instead use the original codebase available [here](https://github.com/benruijl/symbolica). | ||
| <p align="center"> | ||
| <a href="https://github.com/alphal00p/gammaloop"><img alt="Compatibility tests with gammaLoop" src="https://github.com/alphal00p/symbolica/actions/workflows/symbolica_tests.yml/badge.svg?event=push"></a> | ||
| </p> |