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One thing I would like to do in many instances is arrange input/output in columns for comparison. I expect that I need to use Grid to do this, but have not been able to figure out the right commands. For example, if I have the following type of function and two different possibilities:

Table[GCD[fun1[c^a], fun1[c^b]], {a, 1, 3}, {b, 1, 3}, {c, 1, 3}]

Table[GCD[fun2[c^a], fun2[c^b]], {a, 1, 3}, {b, 1, 3}, {c, 1, 3}]

Here, I have two custom functions fun1 and fun2 which take multiple inputs over ranges (27 possibilities in all). I want the output to be rearranged so I have the following columns:

a, b, c, GCD[fun1[c^a], fun1[c^b]], GCD[fun2[c^a], fun1[c^b]], difference

In otherwords I want to see the combination of inputs being used in the leftmost columns, the ouptuts from the two possible expressions, one using fun1, the other using fun2, then optionally a final column showing the difference between the two possible outputs for each of the 27 possibilities.

How can I do this?

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Table[{a, b, c, GCD[fun1[c^a], fun1[c^b]], GCD[fun2[c^a], fun2[c^b]]}, 
    {a, 1, 3}, {b, 1, 3}, {c, 1, 3}] // TableForm

and with the final differences:

Table[{a, b, c, x = GCD[fun1[c^a], fun1[c^b]], y = GCD[fun2[c^a], fun2[c^b]], x - y}, 
     {a, 1, 3}, {b, 1, 3}, {c, 1, 3}] // TableForm

You can reformat the table by

Flatten[Table[{a, b, c, x = GCD[fun1[c^a], fun1[c^b]],  
   y = GCD[fun2[c^a], fun2[c^b]], x - y}, {a, 1, 3}, {b, 1, 3}, {c, 1, 3}], 2] //TableForm

as suggested by cormullion to get it into single columns.

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  • $\begingroup$ This does not make a single set of columns of the results. It creates 3 separate columns which wrap around. $\endgroup$ – Tyler Durden Oct 21 '13 at 15:34
  • $\begingroup$ @TylerDurden Try Flatten[Table[...], 2] // TableForm perhaps? $\endgroup$ – cormullion Oct 21 '13 at 15:56
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If I understand you:

{fun1, fun2} = {Prime, Fibonacci};

Table[
   {a, b, c, #, #2, # - #2} &[
    GCD[fun1[c^a], fun1[c^b]],
    GCD[fun2[c^a], fun2[c^b]]
   ],
   {a, 3}, {b, 3}, {c, 3}
] ~Flatten~ 2 // Grid

Also look at Outer and Array. For the example above I needed to Flatten, so I might consider using Tuples instead, which always produces a flat list:

{fun1, fun2} = {Prime, Fibonacci};

row[{a_, b_, c_}] := {a, b, c, #, #2, # - #2} &[
  GCD[fun1[c^a], fun1[c^b]],
  GCD[fun2[c^a], fun2[c^b]]
 ]

row /@ Tuples[Range@{3, 3, 3}] // Grid
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