I have a system of $n$ linear equations with an equal or smaller number of unknowns stored in a table. The variables are of the form $f[x_1,x_2,x_3]$. For example, the equations are:
f[1,1,1]= 2f[3,2,1] + 4f[2,1,1]
f[1,4,2] = 3f[1,3,1] + 3f[2,4,1] + 3ab
.....
I need to solve those equations for f[1,1,1], f[1,1,2],... in terms of a, b, ... and other constants.
Solve[f[i,j,k]==0, {f[i,j,k], {i,m}, {j,m}, {k,m}}] doesn't work.
Any help is appreciated.
There seem to be two separate questions here, perhaps. The first is, how can one solve an equation in indexed variables? The answer is, like with any other variables. The second question is, how can I produce the list of variables needed by solve? The answer is, any way you would usually produce a list.
ClearAll[f]
vars = Array[f[##] &, 2]
eq1 = f[1] + f[2] == 1
eq2 = f[1] - f[2] == 1
Solve[eq1 && eq2, vars]
f[5] -> 8 so f[5] will have a value of 8 and so on?
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ReplaceAll[solns, {Rule -> Set}], but generally it is better not to do this.
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