[doc] Update README.

README.md

@@ -1,3 +1,50 @@
 # Simplex dictionary
 
-Small package to manipulate a simplex dictionary in python.
+[![Python Versions](https://img.shields.io/badge/python-3.6%20|%203.7-blue.svg)](https://img.shields.io/badge/python-3.6%20|%203.7-blue.svg)
+[![License](https://img.shields.io/badge/license-MIT-green.svg)](https://img.shields.io/badge/license-MIT-green.svg)
+[![Build Status](https://drone.typename.fr/api/badges/mikael.capelle/simplex/status.svg)](https://drone.typename.fr/mikael.capelle/simplex)
+
+`simplex` is a small python module that implements a `simplex_dictionary` structure representing
+a dictionary for the [Simplex algorithm](https://en.wikipedia.org/wiki/Simplex_algorithm).
+
+# Basic usage
+
+The following code creates a simplex dictionary with 5 variables:
+
+```python
+from simplex import simplex_dictionary
+
+# The list of variables (can be anything):
+x1, x2, x3, x4, x5 = ('x_{}'.format(i + 1) for i in range(5))
+variables = [x1, x2, x3, x4, x5]
+
+# The simplex dictionary with B = (x3, x4, x5):
+sdict = simplex_dictionary(B=[x3, x4, x5], N=[x1, x2])
+
+# Set the values of the basic variables:
+sdict.b = {x3: 18, x4: 42, x5: 24}
+
+# Coefficients of the non-basic variables in the dictionary (we represent
+# the positive coefficients):
+sdict.a = {
+    x3: {x1: 2, x2: 1},
+    x4: {x1: 2, x2: 3},
+    x5: {x1: 3, x2: 1}
+}
+
+# Current value of the objective:
+sdict.z = 0
+
+# Coefficients of the non-basic variables in the objective function:
+sdict.c[x1] = 3
+sdict.c[x2] = 2
+```
+
+When using the `simplex` module within a jupyter notebook, the `display()` method outputs
+a latex version of the dictionary:
+
+```python
+sdict.display(name='S_0')
+```
+
+<a href="https://www.codecogs.com/eqnedit.php?latex=\displaystyle&space;S_0&space;=&space;\left.\begin{array}{r||r|r|r|r|}&space;&&space;b&space;&&space;x_{1}&space;&&space;x_{2}\\\hline&space;x_{3}&space;&&space;18&space;&-2&space;&&space;-1\\x_{4}&space;&&space;42&space;&-2&space;&&space;-3\\x_{5}&space;&&space;24&space;&-3&space;&&space;-1\\\hline\hline&space;z&0&3&2\\\hline\end{array}\right." target="_blank"><img src="https://latex.codecogs.com/gif.latex?\displaystyle&space;S_0&space;=&space;\left.\begin{array}{r||r|r|r|r|}&space;&&space;b&space;&&space;x_{1}&space;&&space;x_{2}\\\hline&space;x_{3}&space;&&space;18&space;&-2&space;&&space;-1\\x_{4}&space;&&space;42&space;&-2&space;&&space;-3\\x_{5}&space;&&space;24&space;&-3&space;&&space;-1\\\hline\hline&space;z&0&3&2\\\hline\end{array}\right." title="\displaystyle S_0 = \left.\begin{array}{r||r|r|r|r|} & b & x_{1} & x_{2}\\\hline x_{3} & 18 &-2 & -1\\x_{4} & 42 &-2 & -3\\x_{5} & 24 &-3 & -1\\\hline\hline z&0&3&2\\\hline\end{array}\right." /></a>