Multivariable functions symmetric in their arguments/representing indexed coefficients

Question

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.

Answer 1

At the beginning of your notebook, set the attribute of c to be Orderless.

SetAttributes[c, Orderless];

Then, all arguments of c will be sorted canonically, allowing you to solve for c in your subsequent equations.