| Name | symmetria JSON |
| Version |
0.3.1
JSON |
| download |
| home_page | None |
| Summary | Symmetria provides an intuitive, thorough, and comprehensive framework for interacting with the symmetric group and its elements. |
| upload_time | 2024-12-16 15:09:39 |
| maintainer | Vasco Schiavo |
| docs_url | None |
| author | Vasco Schiavo |
| requires_python | <3.13,>=3.9 |
| license | None |
| keywords |
math
mathematics
symmetry
permutation
|
| VCS |
 |
| bugtrack_url |
|
| requirements |
No requirements were recorded.
|
| Travis-CI |
No Travis.
|
| coveralls test coverage |
No coveralls.
|
<a href="https://symmetria.readthedocs.io/en/latest/"><img src="./docs/source/_static/symmetria.png" width="200" align="right" /></a>
## **Welcome to symmetria**
Symmetria provides an intuitive, thorough, and comprehensive framework for interacting
with the symmetric group and its elements.
- 📦 - installable via pip
- 🐍 - compatible with Python **3.9**, **3.10**, **3.11** and **3.12**
- 👍 - intuitive **API**
- 🧮 - a lot of functionalities already implemented
- ✅ - 100% of test coverage
You can give a look at how to work with symmetria in the section [quickstart](#quickstart),
or you can directly visit the [docs](https://symmetria.readthedocs.io/en/latest/).
Pull requests are welcome. For major changes, please open an issue first
to discuss what you would like to change, and give a look to the
[contribution guidelines](https://github.com/VascoSch92/symmetria/blob/main/CONTRIBUTING.md).
---
- [Installation](#installation)
- [Quickstart](#quickstart)
- [Command Line Interface](#command-line-interface)
- [Overview](#overview)
---
## Installation
Symmetria can be comfortably installed from PyPI using the command
```text
$ pip install symmetria
```
or directly from the source GitHub code with
```text
$ pip install git+https://github.com/VascoSch92/symmetria@xxx
```
where `xxx` is the name of the branch or the tag you would like to install.
You can check that `symmetria` was successfully installed by typing the command
```text
$ symmetria --version
```
## Quickstart
Let's get started with symmetria. First and foremost, we can import the `Permutation`
class from `symmetria`. The Permutation class serves as the fundamental class for
working with elements of the symmetric group, representing permutations as
bijective maps. Otherwise, you can utilize the `Cycle` class and `CycleDecomposition`
class to work with cycle permutations and permutations represented as cycle
decompositions, respectively.
Let's start by defining a permutation and exploring how we can represent it in various formats.
```python
from symmetria import Permutation
permutation = Permutation(1, 3, 4, 5, 2, 6)
permutation # Permutation(1, 3, 4, 5, 2, 6)
str(permutation) # (1, 3, 4, 5, 2, 6)
permutation.cycle_notation() # (1)(2 3 4 5)(6)
permutation.one_line_notation() # 134526
```
Permutation objects are easy to manipulate. They implement nearly every standard functionality of basic Python objects.
As a rule of thumb, if something seems intuitively possible, you can probably do it.
```python
from symmetria import Permutation
idx = Permutation(1, 2, 3)
permutation = Permutation(1, 3, 2)
if permutation:
print(f"The permutation {permutation} is not the identity.")
if idx == Permutation(1, 2, 3):
print(f"The permutation {idx} is the identity permutation.")
if permutation != idx:
print(f"The permutations {permutation} and {idx} are different.")
# The permutation (1, 3, 2) is not the identity.
# The permutation (1, 2, 3) is the identity permutation.
# The permutations (1, 3, 2) and (1, 2, 3) are different.
```
Basic arithmetic operations are implemented.
```python
from symmetria import Permutation
permutation = Permutation(3, 1, 4, 2)
multiplication = permutation * permutation # Permutation(4, 3, 2, 1)
power = permutation ** 2 # Permutation(4, 3, 2, 1)
inverse = permutation ** -1 # Permutation(2, 4, 1, 3)
identity = permutation * inverse # Permutation(1, 2, 3, 4)
```
Actions on different objects are also implemented.
```python
from symmetria import Permutation
permutation = Permutation(3, 2, 4, 1)
permutation(3) # 4
permutation("abcd") # 'dbac'
permutation(["I", "love", "Python", "!"]) # ['!', 'love', 'I', 'Python']
```
Moreover, many methods are already implemented. If what you are looking for is not available,
let us know as soon as possible.
```python
from symmetria import Permutation
permutation = Permutation(3, 2, 4, 1)
permutation.order() # 3
permutation.support() # {1, 3, 4}
permutation.sgn() # 1
permutation.cycle_decomposition() # CycleDecomposition(Cycle(1, 3, 4), Cycle(2))
permutation.cycle_type() # (1, 3)
permutation.is_derangement() # False
permutation.is_regular() # False
permutation.inversions() # [(1, 2), (1, 4), (2, 4), (3, 4)]
permutation.ascents() # [2]
permutation.descents() # [1, 3]
```
If you can't decide what you want, just print everything
```python
from symmetria import Permutation
print(Permutation(3, 2, 4, 1).describe())
```
in a nice formatted table:
```text
+----------------------------------------------------------------------------+
| Permutation(3, 2, 4, 1) |
+----------------------------------------------------------------------------+
| order | 3 |
+--------------------------------------+-------------------------------------+
| degree | 4 |
+--------------------------------------+-------------------------------------+
| is derangement | False |
+--------------------------------------+-------------------------------------+
| inverse | (4, 2, 1, 3) |
+--------------------------------------+-------------------------------------+
| parity | +1 (even) |
+--------------------------------------+-------------------------------------+
| cycle notation | (1 3 4)(2) |
+--------------------------------------+-------------------------------------+
| cycle type | (1, 3) |
+--------------------------------------+-------------------------------------+
| inversions | [(1, 2), (1, 4), (2, 4), (3, 4)] |
+--------------------------------------+-------------------------------------+
| ascents | [2] |
+--------------------------------------+-------------------------------------+
| descents | [1, 3] |
+--------------------------------------+-------------------------------------+
| excedencees | [1, 3] |
+--------------------------------------+-------------------------------------+
| records | [1, 3] |
+--------------------------------------+-------------------------------------+
```
Click [here](https://symmetria.readthedocs.io/en/latest/pages/API_reference/elements/index.html) for an overview of
all the functionalities implemented in `symmetria`.
## Command Line Interface
Symmetria also provides a simple command line interface to find all what you need just with a line.
```text
$ symmetria 132
+------------------------------------------------------+
| Permutation(1, 3, 2) |
+------------------------------------------------------+
| order | 2 |
+---------------------------+--------------------------+
| degree | 3 |
+---------------------------+--------------------------+
| is derangement | False |
+---------------------------+--------------------------+
| inverse | (1, 3, 2) |
+---------------------------+--------------------------+
| parity | -1 (odd) |
+---------------------------+--------------------------+
| cycle notation | (1)(2 3) |
+---------------------------+--------------------------+
| cycle type | (1, 2) |
+---------------------------+--------------------------+
| inversions | [(2, 3)] |
+---------------------------+--------------------------+
| ascents | [1] |
+---------------------------+--------------------------+
| descents | [2] |
+---------------------------+--------------------------+
| excedencees | [2] |
+---------------------------+--------------------------+
| records | [1, 2] |
+---------------------------+--------------------------+
```
Check it out.
```text
$ symmetria --help
Symmetria, an intuitive framework for working with the symmetric group and its elements.
Usage: symmetria <ARGUMENT> [OPTIONS]
Options:
-h, --help Print help
-v, --version Print version
Argument (optional):
permutation A permutation you want to learn more about.
The permutation must be given in its one-line format, i.e.,
for the permutation Permutation(2, 3, 1), write 231.
```
## Overview
| **Statistics** |  |
|-------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| **Repository** |    |
| **Size** |   |
| **Issues** |   |
| **Pull Requests** |   |
| **Open Source** | [](https://github.com/VascSch92/symmetria/blob/main/LICENSE) [](https://github.com/VascSch92/symmetria/blob/main/CONTRIBUTING.md) [](https://github.com/VascSch92/symmetria/blob/main/CODE_OF_CONDUCT.md) |
| **DOCS** |  |
| **CI/CD** |    |
| **Code** | [](https://pypi.org/project/symmetria/) [](https://www.python.org/) [](https://github.com/astral-sh/ruff) |
| **Downloads** | [)](https://pepy.tech/project/symmetria) [)](https://pepy.tech/project/symmetria) [)](https://pepy.tech/project/symmetria) |
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"description": "<a href=\"https://symmetria.readthedocs.io/en/latest/\"><img src=\"./docs/source/_static/symmetria.png\" width=\"200\" align=\"right\" /></a>\n\n## **Welcome to symmetria**\n\nSymmetria provides an intuitive, thorough, and comprehensive framework for interacting\nwith the symmetric group and its elements.\n\n- \ud83d\udce6 - installable via pip\n- \ud83d\udc0d - compatible with Python **3.9**, **3.10**, **3.11** and **3.12**\n- \ud83d\udc4d - intuitive **API**\n- \ud83e\uddee - a lot of functionalities already implemented\n- \u2705 - 100% of test coverage\n\nYou can give a look at how to work with symmetria in the section [quickstart](#quickstart),\nor you can directly visit the [docs](https://symmetria.readthedocs.io/en/latest/).\n\nPull requests are welcome. For major changes, please open an issue first\nto discuss what you would like to change, and give a look to the\n[contribution guidelines](https://github.com/VascoSch92/symmetria/blob/main/CONTRIBUTING.md).\n\n---\n\n- [Installation](#installation)\n- [Quickstart](#quickstart)\n- [Command Line Interface](#command-line-interface)\n- [Overview](#overview)\n\n---\n## Installation\n\nSymmetria can be comfortably installed from PyPI using the command\n\n```text\n$ pip install symmetria\n```\n\nor directly from the source GitHub code with\n\n```text\n$ pip install git+https://github.com/VascoSch92/symmetria@xxx\n```\n\nwhere `xxx` is the name of the branch or the tag you would like to install.\n\nYou can check that `symmetria` was successfully installed by typing the command\n\n```text\n$ symmetria --version\n```\n\n## Quickstart\n\nLet's get started with symmetria. First and foremost, we can import the `Permutation`\nclass from `symmetria`. The Permutation class serves as the fundamental class for\nworking with elements of the symmetric group, representing permutations as\nbijective maps. Otherwise, you can utilize the `Cycle` class and `CycleDecomposition`\nclass to work with cycle permutations and permutations represented as cycle\ndecompositions, respectively.\n\nLet's start by defining a permutation and exploring how we can represent it in various formats.\n\n```python\nfrom symmetria import Permutation\n\npermutation = Permutation(1, 3, 4, 5, 2, 6)\n\npermutation # Permutation(1, 3, 4, 5, 2, 6)\nstr(permutation) # (1, 3, 4, 5, 2, 6)\npermutation.cycle_notation() # (1)(2 3 4 5)(6)\npermutation.one_line_notation() # 134526\n```\n\nPermutation objects are easy to manipulate. They implement nearly every standard functionality of basic Python objects. \nAs a rule of thumb, if something seems intuitively possible, you can probably do it.\n\n```python\nfrom symmetria import Permutation\n\nidx = Permutation(1, 2, 3)\npermutation = Permutation(1, 3, 2)\n\nif permutation:\n print(f\"The permutation {permutation} is not the identity.\")\nif idx == Permutation(1, 2, 3):\n print(f\"The permutation {idx} is the identity permutation.\")\nif permutation != idx:\n print(f\"The permutations {permutation} and {idx} are different.\")\n\n# The permutation (1, 3, 2) is not the identity.\n# The permutation (1, 2, 3) is the identity permutation.\n# The permutations (1, 3, 2) and (1, 2, 3) are different.\n```\n\nBasic arithmetic operations are implemented.\n\n```python\nfrom symmetria import Permutation\n\npermutation = Permutation(3, 1, 4, 2)\n\nmultiplication = permutation * permutation # Permutation(4, 3, 2, 1)\npower = permutation ** 2 # Permutation(4, 3, 2, 1)\ninverse = permutation ** -1 # Permutation(2, 4, 1, 3)\nidentity = permutation * inverse # Permutation(1, 2, 3, 4)\n```\n\nActions on different objects are also implemented.\n\n```python\nfrom symmetria import Permutation\n\npermutation = Permutation(3, 2, 4, 1)\n\npermutation(3) # 4\npermutation(\"abcd\") # 'dbac'\npermutation([\"I\", \"love\", \"Python\", \"!\"]) # ['!', 'love', 'I', 'Python']\n```\n\nMoreover, many methods are already implemented. If what you are looking for is not available, \nlet us know as soon as possible.\n\n```python\nfrom symmetria import Permutation\n\npermutation = Permutation(3, 2, 4, 1)\n\npermutation.order() # 3\npermutation.support() # {1, 3, 4}\npermutation.sgn() # 1\npermutation.cycle_decomposition() # CycleDecomposition(Cycle(1, 3, 4), Cycle(2))\npermutation.cycle_type() # (1, 3)\npermutation.is_derangement() # False\npermutation.is_regular() # False\npermutation.inversions() # [(1, 2), (1, 4), (2, 4), (3, 4)]\npermutation.ascents() # [2]\npermutation.descents() # [1, 3]\n```\n\nIf you can't decide what you want, just print everything\n\n```python\nfrom symmetria import Permutation\n\nprint(Permutation(3, 2, 4, 1).describe())\n```\n\nin a nice formatted table:\n\n```text\n+----------------------------------------------------------------------------+\n| Permutation(3, 2, 4, 1) |\n+----------------------------------------------------------------------------+\n| order | 3 |\n+--------------------------------------+-------------------------------------+\n| degree | 4 |\n+--------------------------------------+-------------------------------------+\n| is derangement | False |\n+--------------------------------------+-------------------------------------+\n| inverse | (4, 2, 1, 3) |\n+--------------------------------------+-------------------------------------+\n| parity | +1 (even) |\n+--------------------------------------+-------------------------------------+\n| cycle notation | (1 3 4)(2) |\n+--------------------------------------+-------------------------------------+\n| cycle type | (1, 3) |\n+--------------------------------------+-------------------------------------+\n| inversions | [(1, 2), (1, 4), (2, 4), (3, 4)] |\n+--------------------------------------+-------------------------------------+\n| ascents | [2] |\n+--------------------------------------+-------------------------------------+\n| descents | [1, 3] |\n+--------------------------------------+-------------------------------------+\n| excedencees | [1, 3] |\n+--------------------------------------+-------------------------------------+\n| records | [1, 3] |\n+--------------------------------------+-------------------------------------+\n```\n\nClick [here](https://symmetria.readthedocs.io/en/latest/pages/API_reference/elements/index.html) for an overview of \nall the functionalities implemented in `symmetria`.\n\n\n## Command Line Interface\nSymmetria also provides a simple command line interface to find all what you need just with a line.\n\n```text\n$ symmetria 132\n+------------------------------------------------------+\n| Permutation(1, 3, 2) |\n+------------------------------------------------------+\n| order | 2 |\n+---------------------------+--------------------------+\n| degree | 3 |\n+---------------------------+--------------------------+\n| is derangement | False |\n+---------------------------+--------------------------+\n| inverse | (1, 3, 2) |\n+---------------------------+--------------------------+\n| parity | -1 (odd) |\n+---------------------------+--------------------------+\n| cycle notation | (1)(2 3) |\n+---------------------------+--------------------------+\n| cycle type | (1, 2) |\n+---------------------------+--------------------------+\n| inversions | [(2, 3)] |\n+---------------------------+--------------------------+\n| ascents | [1] |\n+---------------------------+--------------------------+\n| descents | [2] |\n+---------------------------+--------------------------+\n| excedencees | [2] |\n+---------------------------+--------------------------+\n| records | [1, 2] |\n+---------------------------+--------------------------+\n```\n\nCheck it out.\n\n```text\n$ symmetria --help\nSymmetria, an intuitive framework for working with the symmetric group and its elements.\n\n\nUsage: symmetria <ARGUMENT> [OPTIONS] \n\nOptions: \n -h, --help Print help \n -v, --version Print version \n\nArgument (optional): \n permutation A permutation you want to learn more about. \n The permutation must be given in its one-line format, i.e., \n for the permutation Permutation(2, 3, 1), write 231. \n```\n\n\n## Overview\n\n| **Statistics** |  |\n|-------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|\n| **Repository** |    |\n| **Size** |   |\n| **Issues** |   |\n| **Pull Requests** |   | \n| **Open Source** | [](https://github.com/VascSch92/symmetria/blob/main/LICENSE) [](https://github.com/VascSch92/symmetria/blob/main/CONTRIBUTING.md) [](https://github.com/VascSch92/symmetria/blob/main/CODE_OF_CONDUCT.md) |\n| **DOCS** |  | \n| **CI/CD** |    |\n| **Code** | [](https://pypi.org/project/symmetria/) [](https://www.python.org/) [](https://github.com/astral-sh/ruff) |\n| **Downloads** | [)](https://pepy.tech/project/symmetria) [)](https://pepy.tech/project/symmetria) [)](https://pepy.tech/project/symmetria) |\n",
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