# Replacing For loop with multiple iterator with Table

I have written code for calculating cristofell symbol using for loop with 3 iterators for each coordinate

A = {
{1, 0, 0},
{0, r^2, 0},
{0, 0, 1}
} ;
Kor[n_] := \[Piecewise] {
{(r), n == 1},
{(\[Theta]), n == 2},
{(z), n == 3}
}
ChristoffelSymbol1[i_, j_, k_] :=
1/2 (-D[A[[i, j]], Korr[k]] + D[A[[j, k]], Korr[i]] +
D[A[[k, i]], Korr[j]])
For[i = 1, i < 4, i++,
For[j = 1, j < 4, j++,
For[k = 1, k < 4, k++,

Print[Subscript[\[CapitalGamma], i, j, k], " = ",
ChristoffelSymbol1[i, j, k]]

]
]
]


I was wandering if I could use Map/Table to do the same without changing the functions too much. As far as I could tell I need to make the Piecewise function return symbols for i, j, k when they are entered instead of number so I dont get an error when I do ChristoffelSymbol1[1,j,k] and (this I don't know how) somehow define what happens when I try to access the matrix A with A[[1,j]] for example , so it doesn't give me "expression j cannot be used as a part specification" and leave it in symbolic notation so it can be used when j iterators start.

• if you actually want to Print like that you would use Do. I dont see why you would have the part issue you are imagining -- try it. I wouldn't bother with that Piecewise by the way , just do Kor[1]=r;Kor[2]=theta;Kor[3]=z or do Kor={r,theta,z} and reference it as a list. – george2079 Sep 28 '17 at 18:22
• You can use for example Tuples and then Map function over the obtained list. However, it is unclear from your question what exactly you want to do? – ercegovac Sep 28 '17 at 18:58
• I want a table of {Symbol,value} pairs outputted in 1 cell,but for the symbol to keep the formatting from print. – Andrej Licanin Sep 28 '17 at 19:26

\[CapitalGamma]ddd[i_, j_, k_] :=
1/2 (-D[A[[i, j]], Kor[[k]]] + D[A[[j, k]], Kor[[i]]] +
D[A[[k, i]], Kor[[j]]])

A = DiagonalMatrix[{1, r^2, 1}]
Kor = {r, \[Theta], z}

Table[{Subscript[\[CapitalGamma], i, j, k], \[CapitalGamma]ddd[i, j,
k]}, {i, 1, 3}, {j, 1, 3}, {k, 1, 3}] // TableForm


Got it

 A = {
{1, 0, 0},
{0, r^2, 0},
{0, 0, 1}
} ;  B = {
{1, 0, 0},
{0, 1/r^2, 0},
{0, 0, 1}
};
Kor[n_] := \[Piecewise] {
{(r), n == 1},
{(\[Theta]), n == 2},
{(z), n == 3}
}
ChristoffelSymbol1[i_, j_, k_] :=
1/2 (-D[A[[i, j]], Kor[k]] + D[A[[j, k]], Kor[i]] +
D[A[[k, i]], Kor[j]])
ChristoffelSymbol2[i_, j_, m_] :=
Sum[B[[k, m]] ChristoffelSymbol1[i, j, k], {k, 1, 3}]
TableForm[
Table[{Subscript[\[CapitalGamma], i, j, k],
ChristoffelSymbol1[i, j, k]}, {i, 1, 3}, {j, 1, 3}, {k, 1, 3}]]
TableForm[
Table[{Subscript[Superscript[\[CapitalGamma], m], i, j],
ChristoffelSymbol2[i, j, m]}, {i, 1, 3}, {j, 1, 3}, {m, 1, 3}]]


When i tried to replace For with Table i just copied the iterators,they were going from 1-4 in the loop and the marix is 3x3 so it bugged out :p