Saving solutions of equations with indexed variables to a table

Question

I am trying to solve a set of equations which are very ugly and have indexed variables. I have a vector of expressions

{c[0, 4, 0] + (3221 c[0, 4, 2])/11520 + (5956135 c[0, 4, 4])/
  37158912 + (280835610335 c[0, 4, 6])/1748974436352 + c[2, 0, 0] - (
  47 c[2, 0, 2])/2304 - (24863 c[2, 0, 4])/5308416 - (
  27473615 c[2, 0, 6])/12230590464, 
 23/48 c[0, 4, 2] + (23207 c[0, 4, 4])/55296 + (
  6316272121 c[0, 4, 6])/12145655808 + 23/48 c[2, 0, 2] + (
  5543 c[2, 0, 4])/55296 + (3892727 c[2, 0, 6])/84934656, 
 1/4 c[0, 4, 2] + (689 c[0, 4, 4])/1536 + (57501463 c[0, 4, 6])/
  77856768 + 1/4 c[2, 0, 2] + (433 c[2, 0, 4])/1536 + (
  1288613 c[2, 0, 6])/7077888, 
 23/96 c[0, 4, 4] + (1718215 c[0, 4, 6])/2875392 + 
  23/96 c[2, 0, 4] + (60835 c[2, 0, 6])/221184, 
 1/16 c[0, 4, 4] + (47825 c[0, 4, 6])/159744 + 1/16 c[2, 0, 4] + (
  2645 c[2, 0, 6])/12288, 23/256 c[0, 4, 6] + 23/256 c[2, 0, 6], 
 1/64 c[0, 4, 6] + 1/64 c[2, 0, 6]}

which I equate to the vector

{494/(6561 Sqrt[\[Pi]]), 31579/(51030 Sqrt[\[Pi]]), 33529/(
 17010 Sqrt[\[Pi]]), 5359/(1701 Sqrt[\[Pi]]), 508/(
 189 Sqrt[\[Pi]]), 368/(315 Sqrt[\[Pi]]), 64/(315 Sqrt[\[Pi]])}

and then use Solve to solve for the c[p,q,r]. The thing is that I would like to save these values, say in a table such that C[[p,q,r]] returns me the value c[p,q,r] which I obtained above. How can one do this? Note that the number of independent equations in the above are actually less than the number of unknowns so the system is under-constrained. I would like to set the excess number of variables to zero and then get the rest in terms of the ones set to 0 and store that so that I can access them easily.

How can one do this?

Answer 1

First, use Solve to get the solution:

sol = First@Solve[{c[0, 4, 0] + ...} == {494/(6561 Sqrt[π]), ...}];

Now iterate through the values and put them in another symbol. Instead of putting them in a table, I suggest using downvalues. And I will avoid capital C by using cc instead:

(Evaluate[cc @@ #1] = (#2 /. c[__] -> 0)) & @@@ sol

The solutions are now stored inside cc.

Definition[cc]
(* 
 cc[2, 0, 0] = 429/(4096 Sqrt[π])
 cc[2, 0, 2] = 47/(112 Sqrt[π])
 cc[2, 0, 4] = -(16/(9 Sqrt[π]))
 cc[2, 0, 6] = 4096/(315 Sqrt[π])
*)