I have been trying to do some oscillator algebra in Mathematica and having troubles with sorting and simplifying expressions. I am using the NCAlgebra package which helps to improve the properties of
NonCommutativeMultiply in Mathematica. However I have to create a huge list of rules to replace terms using the algebra. This quickly becomes impractical since I get these enormous expressions and I have to sift through the terms to see what simplifies and add more rules.
I have been wondering if there is a way to write a sorting function that would take an elementary expression and change it to a list and then permute the elements of list to sort the expression. I am fairly new to Mathematica but I would eventually like to write a small package which would allow me to these kind of manipulations.
For example, I have terms like $a**b**c**a^\dagger$ where $a$, $b$, $c$, etc. commute with each other but $a**a^\dagger-a^\dagger**a =1$. So I would like to sort things such that all dagger operators are to the left and have Mathematica use the fact that $a$, $b$, $c$ commute to rewrite the expressions. Right now I am assigning rules for every type of term that appears in my calculation but the number of terms has become unmanageable.