Docs: intro page

docs/src/index.md

@@ -1,3 +1,35 @@
 # Hodge.jl
 
-Documentation for Hodge.jl
+This package exports two main types,
+[`SimplicialComplex`](@ref) and [`Cochain`](@ref),
+together with methods to work with their topological and algebraic properties.
+
+The topological operations on this package
+are all done via the discrete laplacian operator.
+This includes the method [`betti`](@ref),
+which calculates the Betti numbers of a simplicial complex,
+and the method [`hodge`](@ref)
+which calculates the discrete Hodge decomposition of a cochain.
+
+## Installation
+This package can be installed using the Julia Package Manager. Simply open the REPL, enter `]` and run
+
+```julia
+pkg> add https://github.com/iagoleal/Hodge.jl.git
+```
+
+## Bibliography
+
+`Hodge.jl` is based on a scientific initiation
+that I did with Prof. João Paixão
+while an undergraduate at UFRJ.
+
+The simplicial complex type is built upon
+the __Simplex Tree__ data structure,
+described on the [paper](https://hal.inria.fr/hal-00707901v1/document):
+- Jean-Daniel Boissonnat, Clément Maria. The Simplex Tree: An Efficient Data Structure for General Simplicial Complexes. [Research Report] RR-7993, 2012, pp.20. hal-00707901v1
+
+The idea of representing cochains as skew-symmetric tensors
+and using them to write the discrete Hodge decomposition was taken from
+the [paper](https://link.springer.com/article/10.1007%2Fs10107-010-0419-x):
+- Jiang, X., Lim, L., Yao, Y. et al. Statistical ranking and combinatorial Hodge theory. Math. Program. 127, 203–244 (2011). https://doi.org/10.1007/s10107-010-0419-x