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Readme.md

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<h1 align="center">
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<br>
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<picture>
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<source media="(prefers-color-scheme: dark)" srcset="https://symbolica.io/logo_dark.svg">
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<source media="(prefers-color-scheme: light)" srcset="https://symbolica.io/logo.svg">
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<img src="https://symbolica.io/logo.svg" alt="logo" width="200">
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</picture>
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<br>
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</h1>
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# <h1 align="center"> Disclaimer </h1>
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<p align="center">
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<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>
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<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>
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<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>
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<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>
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</p>
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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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# 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.
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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>
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<source media="(prefers-color-scheme: dark)" srcset="https://symbolica.io/resources/demo.dark.svg">
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<source media="(prefers-color-scheme: light)" srcset="https://symbolica.io/resources/demo.light.svg">
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<img width="600" alt="A demo of Symbolica" src="https://symbolica.io/resources/demo.light.svg">
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</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>
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<source media="(prefers-color-scheme: dark)" srcset="https://symbolica.io/resources/completion.png">
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<source media="(prefers-color-scheme: light)" srcset="https://symbolica.io/resources/completion_light.png">
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<img width="600" alt="A demo of Symbolica" src="https://symbolica.io/resources/completion.png">
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</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
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pip install symbolica
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```
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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`:
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```toml
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[dependencies]
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symbolica = "0.15"
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```
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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.
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In the following example we try to match the pattern `f(w1_,w2_)`:
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```python
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from symbolica import *
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x, y, w1_, w2_, f = S('x','y','w1_','w2_', 'f')
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e = f(3,x)*y**2+5
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r = e.replace_all(f(w1_,w2_), f(w1_ - 1, w2_**2))
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print(r)
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```
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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
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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(
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[f(c)*x + y + c, y + c**2], [x, y])
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print('x =', x_r, ', y =', y_r)
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```
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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
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from symbolica import *
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e = E('exp(5+x)/(1-x)').series(S('x'), 0, 3)
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print(e)
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```
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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:
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```python
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from symbolica import *
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p = E('(x*y^2*5+5)^2/(2*x+5)+(x+4)/(6*x^2+1)').to_rational_polynomial()
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print(p)
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```
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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)!
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Make sure to instead use the original codebase available [here](https://github.com/benruijl/symbolica).

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