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I am having a lot of issues trying to import data into mathematica and then clean the data so that mathematica recognises it. The data is a set of permutations, which I would like to express as Cycles.

This is how (a section) of the data appears in the .txt file:

(),(20,21),(19,20),(19,20,21),(19,21,20),(19,21),(17,18),(17,18)(20,21),(17,18)(19,20),(17,18)(19,20,21),

(17,18)(19,21,20),(17,18)(19,21),(16,17),(16,17)(20,21),(16,17)(19,20),(16,17)(19,20,21),(16,17)(19,21,20),

(16,17)(19,21),(16,17,18),(16,17,18)(20,21),(16,17,18)(19,20),(16,17,18)(19,20,21),(16,17,18)(19,21,20),

When I import this into mathematica via:

list=Import["pathname.txt","Data"]//InputForm

This outputs the following:

{{"(),(20,21),(19,20),(19,20,21),(19,21,20),(19,21),(17,18),(17,18)(20,21),(17,18)(19,20),(17,18)(19,20,21),"}, 
 {"(17,18)(19,21,20),(17,18)(19,21),(16,17),(16,17)(20,21),(16,17)(19,20),(16,17)(19,20,21),(16,17)(19,21,20),"}, 
 {"(16,17)(19,21),(16,17,18),(16,17,18)(20,21),(16,17,18)(19,20),(16,17,18)(19,20,21),(16,17,18)(19,21,20),"},

I am not able to get mathematica to remove the line breaks, so that it reads as one long list of permutations, seperated only by commas. I have tried StringRemove StringReplace with no luck. I have also attempted ImportString[ToString[list],"CSV"] but this has not worked either.

I cannot manually remove the line breaks in the .txt file as the actual set of permutations is far too large.

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2
  • $\begingroup$ Perhaps try, Flatten[list] prior to string operations. $\endgroup$
    – Craig Carter
    Commented Jul 16 at 11:02
  • 2
    $\begingroup$ Import it as a pure text, namely t = Import[file, "String"], then you should be able to do StringReplace[t, "\n" -> ""]. $\endgroup$
    – Domen
    Commented Jul 16 at 11:16

2 Answers 2

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3
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Maybe a little bit laborious, but it works (at least for the given examples):

imp = StringReplace[Import["Cycles_test.txt", "Text"], WhitespaceCharacter .. -> ""]
(* 
"(),(20,21),(19,20),(19,20,21),(19,21,20),(19,21),(17,18),(17,18)(20,21),(17,18)(19,20),(17,18)(19,20,21),(17,18)(19,21,20),(17,18)(19,21),(16,17),(16,17)(20,21),(16,17)(19,20),(16,17)(19,20,21),(16,17)(19,21,20),(16,17)(19,21),(16,17,18),(16,17,18)(20,21),(16,17,18)(19,20),(16,17,18)(19,20,21),(16,17,18)(19,21,20)"
*)

then multiple string replacements:

cycleStrings = StringReplace[StringReplace[StringReplace[StringSplit[StringReplace[imp, "),(" -> ");("], ";"], {"(" -> "{",")" -> "}"}], "}{" -> "},{"], s__ :> "{" ~~ s ~~ "}"]

and finally:

Cycles[ToExpression[#]] & /@ cycleStrings

yields:

{Cycles[{}], Cycles[{{20, 21}}], Cycles[{{19, 20}}], 
 Cycles[{{19, 20, 21}}], Cycles[{{19, 21, 20}}], Cycles[{{19, 21}}], 
 Cycles[{{17, 18}}], Cycles[{{17, 18}, {20, 21}}], 
 Cycles[{{17, 18}, {19, 20}}], Cycles[{{17, 18}, {19, 20, 21}}], 
 Cycles[{{17, 18}, {19, 21, 20}}], Cycles[{{17, 18}, {19, 21}}], 
 Cycles[{{16, 17}}], Cycles[{{16, 17}, {20, 21}}], 
 Cycles[{{16, 17}, {19, 20}}], Cycles[{{16, 17}, {19, 20, 21}}], 
 Cycles[{{16, 17}, {19, 21, 20}}], Cycles[{{16, 17}, {19, 21}}], 
 Cycles[{{16, 17, 18}}], Cycles[{{16, 17, 18}, {20, 21}}], 
 Cycles[{{16, 17, 18}, {19, 20}}], Cycles[{{16, 17, 18}, {19, 20, 21}}],
  Cycles[{{16, 17, 18}, {19, 21, 20}}]}

This could be converted into permutations by PermutationList:

{{}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 
  19, 21, 20}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
   17, 18, 20, 19}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 
  15, 16, 17, 18, 20, 21, 19}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,
   13, 14, 15, 16, 17, 18, 21, 19, 20}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 
  10, 11, 12, 13, 14, 15, 16, 17, 18, 21, 20, 19}, {1, 2, 3, 4, 5, 6, 
  7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 17}, {1, 2, 3, 4, 5, 6, 7, 
  8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 17, 19, 21, 20}, {1, 2, 3, 4, 
  5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 17, 20, 19}, {1, 2, 
  3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 17, 20, 21, 
  19}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 17,
   21, 19, 20}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 
  16, 18, 17, 21, 20, 19}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,
   14, 15, 17, 16}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 
  15, 17, 16, 18, 19, 21, 20}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,
   13, 14, 15, 17, 16, 18, 20, 19}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 
  11, 12, 13, 14, 15, 17, 16, 18, 20, 21, 19}, {1, 2, 3, 4, 5, 6, 7, 
  8, 9, 10, 11, 12, 13, 14, 15, 17, 16, 18, 21, 19, 20}, {1, 2, 3, 4, 
  5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 16, 18, 21, 20, 19}, {1, 
  2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 16}, {1, 2, 
  3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 16, 19, 21, 
  20}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 16,
   20, 19}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 
  18, 16, 20, 21, 19}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,
   15, 17, 18, 16, 21, 19, 20}}
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4
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Another way:

dataFile = (* String representation of input file *)
  "(),(20,21),(19,20),(19,20,21),(19,21,20),(19,21),(17,18),(17,18)(20,21),(17,18)(19,20),(17,18)(19,20,21),
(17,18)(19,21,20),(17,18)(19,21),(16,17),(16,17)(20,21),(16,17)(19,20),(16,17)(19,20,21),(16,17)(19,21,20),
(16,17)(19,21),(16,17,18),(16,17,18)(20,21),(16,17,18)(19,20),(16,17,18)(19,20,21),(16,17,18)(19,21,20),";
input = ImportString[dataFile, "Text"];

Then after Import[] file as "Text":

StringCases[input,
 cycs : ("(" ~~ RegularExpression["[^()]*"] ~~ ")") .. :>
  Cycles[ToExpression[
    "{" <> StringReplace[cycs, {")(" -> "},{", "(" -> "{", ")" -> "}"}] <> "}"]]
 ]

(*
{Cycles[{}], Cycles[{{20, 21}}], Cycles[{{19, 20}}], 
 Cycles[{{19, 20, 21}}], Cycles[{{19, 21, 20}}], Cycles[{{19, 21}}], 
 Cycles[{{17, 18}}], Cycles[{{17, 18}, {20, 21}}], 
 Cycles[{{17, 18}, {19, 20}}], Cycles[{{17, 18}, {19, 20, 21}}], 
 Cycles[{{17, 18}, {19, 21, 20}}], Cycles[{{17, 18}, {19, 21}}], 
 Cycles[{{16, 17}}], Cycles[{{16, 17}, {20, 21}}], 
 Cycles[{{16, 17}, {19, 20}}], Cycles[{{16, 17}, {19, 20, 21}}], 
 Cycles[{{16, 17}, {19, 21, 20}}], Cycles[{{16, 17}, {19, 21}}], 
 Cycles[{{16, 17, 18}}], Cycles[{{16, 17, 18}, {20, 21}}], 
 Cycles[{{16, 17, 18}, {19, 20}}], Cycles[{{16, 17, 18}, {19, 20, 21}}],
 Cycles[{{16, 17, 18}, {19, 21, 20}}]}
*)
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