update readme

README.md

@@ -1,7 +1,7 @@
 
 <div align="center">
   <a href="https://github.com/asanchezyali/Zmodn#readme">
-    <img src="logo/logo.svg" alt="Logo" width="100%" height="140">
+    <img src="logo/heading.svg" alt="Logo" width="100%" height="140">
   </a>
   <a href="https://github.com//Zmodn/actions/workflows/docs.yaml"><img src="https://github.com/mhostetter/galois/actions/workflows/docs.yaml/badge.svg"></a>
   <a href="https://github.com//Zmodn/actions/workflows/lint.yaml"><img src="https://github.com/mhostetter/galois/actions/workflows/lint.yaml/badge.svg"></a>
@@ -105,5 +105,5 @@ If this library was useful to you in your research, please cite us. Following th
 ### APA
 
 ```
-Sánchez, A. (2023). Zmodn: Efficient Modulo Arithmetic with NumPy.
+Sánchez, A. (2023). Zmodn: Efficient Modulo Arithmetic with NumPy. [Computer software]. https://github.com/asanchezyali/Zmodn
 ```

docs/index.rst

@@ -1,20 +1,111 @@
-.. Zmodn documentation master file, created by
-   sphinx-quickstart on Thu Nov 23 16:31:16 2023.
-   You can adapt this file completely to your liking, but it should at least
-   contain the root `toctree` directive.
+.. image:: ../logo/heading.svg
+   :align: center
 
-Welcome to Zmodn's documentation!
-=================================
+The :obj:`zmodn` package provides a class for representing integers modulo a given positive integer. This class can be used to applications such as cryptography and computer algebra. It is designed to be easy to use, and to provide a simple interface for working with modular arithmetic.
 
-.. toctree::
-   :maxdepth: 2
-   :caption: Contents:
+Features
+--------
+
+- Perform arithmetic operations (addition, subtraction, multiplication, division, power) on integers modulo a given positive integer.
+- Compute the modular inverse of an integer modulo a given positive integer.
+- Compute the inverse of a square matrix modulo a given positive integer.
+- Compare two integers modulo a given positive integer.
+- Access and modify the representatives of an integer modulo a given positive integer.
+
+Installation
+------------
+The :obj:`zmodn` package can be installed using `pip <https://pip.pypa.io/en/stable/>`_.
+
+.. code-block:: bash
+
+   $ pip install zmodn
+
+Basic Usage
+-----------
+
+Here is a simple example of how to use Zmodn:
+
+.. code-block:: python
+
+   import numpy as np
+   from zmodn import Zmodn
+
+   # Create a Zmodn object with the representatives 2 and 3 modulo 5
+   zmodn = Zmodn([2, 3], 5)
+
+   # Add two Zmodn objects
+   zmodn_sum = zmodn + Zmodn([1, 4], 5)
+
+   # Subtract two Zmodn objects
+   zmodn_difference = zmodn - Zmodn([1, 4], 5)
+
+   # Multiply two Zmodn objects
+   zmodn_product = zmodn * Zmodn([1, 4], 5)
+
+   # Divide two Zmodn objects
+   zmodn_quotient = zmodn / Zmodn([1, 4], 5)
+
+   # Compute the modular inverse of a Zmodn object
+   zmodn_inverse = zmodn.mod_inv()
+
+Documentation
+-------------
+
+For more detailed information about the features and usage of :obj:`zmodn`, please refer to the documentation.
 
+License
+-------
+:obj:`zmodn` is licensed under the terms of the MIT license. See the license file for details.
 
+Contact
+-------
 
-Indices and tables
-==================
+If you have any questions, comments, or issues, please feel free to contact us.
 
-* :ref:`genindex`
-* :ref:`modindex`
-* :ref:`search`
+Contributing
+------------
+
+We welcome contributions to :obj:`zmodn` library! If you have an idea for a new feature or improvement, please feel free to create an issue or submit a pull request.
+
+To contribute to the :obj:`zmodn` library, you will need to:
+
+1. Fork the repository.
+2. Create a new branch for your changes.
+3. Make your changes to the code.
+4. Add tests to ensure that your changes work correctly.
+5. Push your branch to the fork.
+6. Create a pull request to merge your changes into the main repository.
+7. Please be sure to follow the coding style guide and add documentation for any new features or changes that you make.
+
+We appreciate your contributions to the zmodn library!
+
+
+Citation
+--------
+
+If this library was useful to you in your research, please cite us. Following the `GitHub citation standards <https://docs.github.com/en/github/creating-cloning-and-archiving-repositories/creating-a-repository-on-github/about-citation-files>`_, here is the recommended citation.
+
+.. md-tab-set::
+
+   .. md-tab-item:: BibTeX
+
+      .. code-block:: latex
+
+         @software{Sanchez_Alejandro_2020,
+            title = {{Zmodn}: Efficient Modulo Arithmetic with NumPy},
+            author = {Sánchez, Alejandro},
+            month = {11},
+            year = {2023},
+            url = {https://github.com/asanchezyali/Zmodn},
+         }
+
+   .. md-tab-item:: APA
+
+      .. code-block:: text
+
+         Sánchez, A. (2023). Zmodn: Efficient Modulo Arithmetic with NumPy. [Computer software]. https://github.com/asanchezyali/Zmodn
+
+
+.. toctree::
+   :maxdepth: 2
+   :caption: Contents: