Context: I have equations for indexed coefficients $C_{ij}$ which I have represented using 2-variable functions in Mathematica. e.g.,
c[2,1]+c[3,0]==0
c[1,2]+2c[2,1]+c[3,0]==0
etc.
Now, my coefficients are symmetric--i.e., $C_{ij}=C_{ji}$ so, when I use functions like Reduce/Solve or Simplify for these equations, I would like Mathematica to recognize $c[1,2]+2c[2,1]=3c[1,2]$, for example.
Question: How does one implement this index symmetry in Mathematica? The implementation of this need not use 2-variable functions; I'd be happy to use a different object type to represent my indexed coefficients.
C
has a built in meaning in Mathematica, see here. It's generally best not to use capitals so you can avoid conflicts. $\endgroup$