Update docs.

docs/source/_theory/algebra.rst

@@ -15,7 +15,9 @@ While this is in fact Algebra the concept goes far beyond replacing some numbers
 with letters and torturing students for hours on end with systems of linear
 equations.
 
-*More to come*
+An algebra in general is some structure made up of elements that one can add,
+multiply by each other, and scale. These can take many forms, one of which
+is directly related to the symmetry detection work performed by SymDet.
 
 Lie Algebra
 ^^^^^^^^^^^

docs/source/_theory/detecting_symmetry_groups.rst

@@ -1,2 +1,17 @@
 Detecting Symmetry Groups
-=========================
+=========================
+Now we can get into some of the fun part of this package. How do we use
+machine learning to detect symmetry groups in large data-sets. This is a direct
+implementation of Sven Krippendorf and Marc Syvaeri's paper on
+`Detecting symmetries with neural networks <https://iopscience.iop.org/article/10.1088/2632-2153/abbd2d>`_.
+and I refer readers to the original work for a full treatment of the problem
+from the authors. Here I will discuss the theory and implementation as best I
+can.
+
+In a system related by some symmetry such as a harmonic oscillator potential it does not
+take a human long to identify that symmetry exists. If we then train a neural
+network to classify points along this potential, it seems intuitive that on some
+level the machine learning model should also identify this symmetry. Unfortunately,
+the representation of the symmetry will be buried somewhere in a very high-dimensional
+space that we cannot simply visualize. That's where the tSNE visualization we
+discussed comes in.