<h1 align="center">
<br>
<img src="https://symbolica.io/logo.svg" alt="logo" width="200">
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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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# Symbolica
Symbolica is a blazing fast and modern computer algebra system which aims to handle huge expressions. It can easily be incorporated into existing projects using its Python, Rust or C++ bindings.
Check out the live [Jupyter Notebook demo](https://colab.research.google.com/drive/1VAtND2kddgBwNt1Tjsai8vnbVIbgg-7D?usp=sharing)!
For documentation and more, see [symbolica.io](https://symbolica.io).
## Quick Example
Symbolica allows you to build and manipulate mathematical expressions through matching and replacing patterns, similar to `regex` for text:
<img width="600" alt="A demo of Symbolica" srcset="https://symbolica.io/resources/demo.light.gif">
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, Rust and C++:
<img width="600" alt="A demo of Symbolica" src="https://symbolica.io/resources/completion.light.png">
# Installation
Visit the [Get Started](https://symbolica.io/docs/get_started.html) page for detailed installation instructions.
## Python
Symbolica can be installed for Python >3.5 using `pip`:
```sh
pip install symbolica
```
The installation may take some time on Mac OS and Windows, as it may have to compile Symbolica.
## Rust
If you want to use Symbolica as a library in Rust, simply include it in the `Cargo.toml`:
```toml
[dependencies]
symbolica = "0.4"
```
# Examples
Below we list some examples of the features of Symbolica. Check the [guide](https://symbolica.io/docs/) for a complete overview.
### Pattern matching
Variables ending with a `_` are wildcards that match to any subexpression.
In the following example we try to match the pattern `f(w1_,w2_)`:
```python
from symbolica import Expression
x, y, w1_, w2_ = Expression.vars('x','y','w1_','w2_')
f = Expression.fun('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`.
### Solving a linear system
Solve a linear system in `x` and `y` with a parameter `c`:
```python
from symbolica import Expression
x, y, c = Expression.vars('x', 'y', 'c')
f = Expression.fun('f')
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`.
### Series expansion
Perform the Taylor series in `x` of an expression that contains a user-defined function `f`:
```python
from symbolica import Expression
x, y = Expression.vars('x', 'y')
f = Expression.fun('f')
e = 2* x**2 * y + f(x)
e = e.taylor_series(x, 0, 2)
print(e)
```
which yields `f(0)+x*der(1,f(0))+1/2*x^2*(4*y+der(2,f(0)))`.
### Rational arithmetic
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 Expression
x, y = Expression.vars('x','y')
p = Expression.parse('(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)`.
## Development
Follow the development and discussions on [Zulip](https://reform.zulipchat.com)!
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"description": "<h1 align=\"center\">\n <br>\n <img src=\"https://symbolica.io/logo.svg\" alt=\"logo\" width=\"200\">\n <br>\n</h1>\n\n<p align=\"center\">\n<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>\n <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>\n <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>\n <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>\n</p>\n\n# Symbolica\n\nSymbolica is a blazing fast and modern computer algebra system which aims to handle huge expressions. It can easily be incorporated into existing projects using its Python, Rust or C++ bindings.\nCheck out the live [Jupyter Notebook demo](https://colab.research.google.com/drive/1VAtND2kddgBwNt1Tjsai8vnbVIbgg-7D?usp=sharing)!\n\nFor documentation and more, see [symbolica.io](https://symbolica.io).\n\n\n\n## Quick Example\n\nSymbolica allows you to build and manipulate mathematical expressions through matching and replacing patterns, similar to `regex` for text:\n\n<img width=\"600\" alt=\"A demo of Symbolica\" srcset=\"https://symbolica.io/resources/demo.light.gif\">\n\nYou 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, Rust and C++:\n\n<img width=\"600\" alt=\"A demo of Symbolica\" src=\"https://symbolica.io/resources/completion.light.png\">\n\n# Installation\n\nVisit the [Get Started](https://symbolica.io/docs/get_started.html) page for detailed installation instructions.\n\n## Python\n\nSymbolica can be installed for Python >3.5 using `pip`:\n\n```sh\npip install symbolica\n```\n\nThe installation may take some time on Mac OS and Windows, as it may have to compile Symbolica.\n\n## Rust\n\nIf you want to use Symbolica as a library in Rust, simply include it in the `Cargo.toml`:\n\n```toml\n[dependencies]\nsymbolica = \"0.4\"\n```\n\n# Examples\n\nBelow we list some examples of the features of Symbolica. Check the [guide](https://symbolica.io/docs/) for a complete overview.\n\n### Pattern matching\n\nVariables ending with a `_` are wildcards that match to any subexpression.\nIn the following example we try to match the pattern `f(w1_,w2_)`:\n\n```python\nfrom symbolica import Expression\nx, y, w1_, w2_ = Expression.vars('x','y','w1_','w2_')\nf = Expression.fun('f')\ne = f(3,x)*y**2+5\nr = e.replace_all(f(w1_,w2_), f(w1_ - 1, w2_**2))\nprint(r)\n```\nwhich yields `y^2*f(2,x^2)+5`.\n\n### Solving a linear system\n\nSolve a linear system in `x` and `y` with a parameter `c`:\n\n```python\nfrom symbolica import Expression\n\nx, y, c = Expression.vars('x', 'y', 'c')\nf = Expression.fun('f')\n\nx_r, y_r = Expression.solve_linear_system(\n [f(c)*x + y + c, y + c**2], [x, y])\nprint('x =', x_r, ', y =', y_r)\n```\nwhich yields `x = (-c+c^2)*f(c)^-1` and `y = -c^2`.\n\n### Series expansion\n\nPerform the Taylor series in `x` of an expression that contains a user-defined function `f`:\n\n```python\nfrom symbolica import Expression\n\nx, y = Expression.vars('x', 'y')\nf = Expression.fun('f')\n\ne = 2* x**2 * y + f(x)\ne = e.taylor_series(x, 0, 2)\n\nprint(e)\n```\nwhich yields `f(0)+x*der(1,f(0))+1/2*x^2*(4*y+der(2,f(0)))`.\n\n### Rational arithmetic\n\nSymbolica is world-class in rational arithmetic, outperforming Mathematica, Maple, Form, Fermat, and other computer algebra packages. Simply convert an expression to a rational polynomial:\n```python\nfrom symbolica import Expression\nx, y = Expression.vars('x','y')\np = Expression.parse('(x*y^2*5+5)^2/(2*x+5)+(x+4)/(6*x^2+1)').to_rational_polynomial()\nprint(p)\n```\nwhich 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)`.\n\n## Development\n\nFollow the development and discussions on [Zulip](https://reform.zulipchat.com)!\n",
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