docs: improve README, add pre-commit badge (ComPWA#29)

* docs: add pre-commit badge
* docs: improve README.md text

README.md

@@ -4,37 +4,36 @@
 [![Codacy Badge](https://api.codacy.com/project/badge/Grade/db355758fb0e4654818b85997f03e3b8)](https://www.codacy.com/gh/ComPWA/expertsystem)
 [![Documentation build status](https://readthedocs.org/projects/expertsystem/badge/?version=latest)](https://pwa.readthedocs.io/projects/expertsystem/)
 [![Code style: black](https://img.shields.io/badge/code%20style-black-000000.svg)](https://github.com/psf/black)
+[![pre-commit](https://img.shields.io/badge/pre--commit-enabled-brightgreen)](https://github.com/pre-commit/pre-commit)
 
 # PWA Expert System
 
 The goal is to build state transition graphs, going from an initial state to a
-final state
+final state. A state transition graph consists of nodes and edges/lines (in
+correspondence to Feynman graphs):
 
-A state transition graph consists of nodes and edges/lines (in correspondence
-to Feynman graphs):
-
-- The connection lines we call particle lines, which are basically a list of
-  quantum numbers (QN) that define the particle state (That list can be empty
-  at first).
-- The nodes are of type InteractionNode, that contain all information for the
-  transition of this specific step. An interaction node has M ingoing lines and
-  N outgoing lines (M, N = Integer & M > 0, N > 0) .
+- We call the connection lines **particle lines**. These are basically a list
+  of quantum numbers (QN) that define the particle state. (This list can be
+  empty at first).
+- The nodes are of type `InteractionNode` and contain all information for the
+  transition of this specific step. An interaction node has 𝑀 ingoing lines
+  and 𝑁 outgoing lines (𝑀, 𝑁 ∈ 𝕫, 𝑀 > 0, 𝑁 > 0).
 
 ## Concept of building graphs
 
 ### Step 1
-Building of all possible topologies. A topology is a graph, in which the edges
-and nodes are empty (no QN information). See the topology sub-modules.
+Building of all possible topologies. A **topology** is a graph, in which the
+edges and nodes are empty (no QN information). See the topology sub-modules.
 
 ### Step 2
-Filling the toplogy graphs with QN information. This means initializing the
-topology graphs with the initial and final state quantum numbers and
-propagating these through the complete graph. Here also the combinatorics of
-the initial and final state should be taken into account.
+Filling the topology graphs with QN information. This means initializing the
+topology graphs with the initial and final state QNs and *propagating* these
+numbers through the complete graph. Here, the combinatorics of the initial and
+final state should also be taken into account.
 
 ### Step 3
 Duplicate the graphs and insert concrete particles for the edges (inserting the
 mass variable).
 
 ### Step 4
-Output to XML model file.
+Write output to XML model file.

doc/index.rst

@@ -19,8 +19,12 @@
   :target: https://pwa.readthedocs.io/projects/expertsystem/
 
 .. image:: https://img.shields.io/badge/code%20style-black-000000.svg
-   :alt: Code style: black
-   :target: https://github.com/psf/black
+  :alt: Code style: black
+  :target: https://github.com/psf/black
+
+.. image:: https://img.shields.io/badge/pre--commit-enabled-brightgreen?logo=pre-commit&logoColor=white
+  :target: https://github.com/pre-commit/pre-commit
+  :alt: pre-commit
 
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