# Unexpected result {“.a”, “co”, “.m”} from Sort[{“.m”, “.a”, “co”}]

I came across the following situation:

Evaluating

Sort[{".m", ".a", "co"}]


Results in

{".a", "co", ".m"}


I wondering: What was the criterion that Mathematica use to output this? According to the documentation:

...Sort orders strings as in a dictionary, with uppercase...

After reading this, I expect a dictionary sort like this:

{".a", ".m", "co"}


Or

{"co", ".a", ".m"}


Can anyone explain me what was the criterion used by Mathematica to perform this sort?

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As noted in the popup for that tag, please do not add bugs until what you say has been verified by other people. –  Ｊ. Ｍ. Jun 13 '13 at 16:19
@PedroR What do you mean by the ""Pythonic" way to workaround the translation"? –  Alexey Popkov Jun 15 '13 at 7:05

According to The Chicago Manual of Style, para. 18.57/18.58, punctation marks are ignored.

18.57

The letter-by-letter system. In the letter-by-letter system, alphabetizing continues up to the first parenthesis or comma; it then starts again after the punctuation point. Word spaces and all other punctuation marks are ignored. Both open and hyphenated compounds such as New York or self-pity are treated as single words. The order of precedence is one word, word followed by a parenthesis, and word followed by a comma, number, or letters. The index to this manual, in accordance with Chicago’s traditional preference, is arranged letter by letter.

I won't say it's a definitive answer, but it supports Mathematica's behavior to a certain extent.

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Sort orders strings as in a dictionary, with uppercase versions of letters coming after lowercase ones.Sort places ordinary letters first, followed in order by script, Gothic, double - struck, Greek, and Hebrew.Mathematical operators appear in order of decreasing precedence.

Sort[list, p] applies the function p to pairs of elements in list to determine whether they are in order.The default function p is OrderedQ[{#1, #2}] &.

OrderedQ[h[Subscript[e, 1], Subscript[e, 2], [Ellipsis]]] gives True if the Subscript[e, i] are in canonical order, and False otherwise.

# Some Test

## Just one Sort without function

Let' s see the CharacterCode of sampleList1

1. (*Input 1 ==< *)
sampleList1 = {compute, Tes, ., , Etz, .a, .m, a, z, T, .T, wha, {};
ToCharacterCode[sampleList1]

2. (*
Output 1 ==>
{{99,111,109,112,117,116,101},{84,101,115},{46},{},{69,116,122},{46,97},{46,109},{97},{122
},{84},{46,84},{119,104,97},{123}}
*)

3. (*Input 2 ==< *)
Sort[sampleList1]

4. (*
Output 2 ==>
{,{,.,.a,a,compute,Etz,.m,.T,T,Tes,wha,z}
*)

5. (*Input 3 ==< *)
ToCharacterCode[%]

6. (*
Output 3 ==>
{{},{123},{46},{46,97},{97},{99,111,109,112,117,116,101},{69,116,122},{46,109},{46,84},{84
},{84,101,115},{119,104,97},{122}}
*)

7. (*Input 4 ==< *)
Total /@ %

8. (*
Output 4 ==>
{0,123,46,143,97,765,307,155,130,84,300,320,122}
*)


### My thoughts

I do not know whether the default order of Sort is related with CharacterCode.

I guess Mathematica treats some characters orderless and skips some characters in sorting strings with Sort.

I think some characters are treated as trivial elements, and are put before the alphabet.

Though there maybe one order table for all characters whichIdon't know.

### My opinion

Firstly, you should show what's the correct answer for a variety lists, as @JonathanShock mentioned in the comment.

Otherwise, each time you come up one result differ from Python, then ask why Mathematica does not work like Python.

I think that is ....

The important thing is how to get the results as expected.

## Sort with one function

1. (*Input 5 ==< *)
Sort[sampleList1, ToCharacterCode[#1] & ]

2. (*
Output 5 ==>
{compute,Tes,.,,Etz,.a,.m,a,z,T,.T,wha,{}
*)

3. (*Input 6 ==< *)
ToCharacterCode[%]

4. (*
Output 6 ==>
{{99,111,109,112,117,116,101},{84,101,115},{46},{},{69,116,122},{46,97},{46,109},{97},{122
},{84},{46,84},{119,104,97},{123}}
*)

5. (*Input 7 ==< *)
Total /@ %

6. (*
Output 7 ==>
{765,300,46,0,307,143,155,97,122,84,130,320,123}
*)

7. (*Input 8 ==< *)
First /@ %%

8. (*
Output 8 ==>
{99,84,46,First[{}],69,46,46,97,122,84,46,119,123}
*)


Still does not work well, of course, it maybe wrong, forTotalis not the correct criteria of order.

The following is what you expected? note theStringLengthof characters.

1. (*Input 9 ==< *)
FromCharacterCode[Sort[ToCharacterCode[sampleList1]]]

2. (*
Output 9 ==>
{,.,T,a,z,{,.T,.a,.m,Etz,Tes,wha,compute}
*)

3. (*Input 10 ==< *)
Sort[ToCharacterCode[sampleList1]]

4. (*
Output 10 ==>
{{},{46},{84},{97},{122},{123},{46,84},{46,97},{46,109},{69,116,122},{84,101,115},{119,104
,97},{99,111,109,112,117,116,101}}
*)

5. (*Input 11 ==< *)
First /@ %

6. (*
Output 11 ==>
{First[{}],46,84,97,122,123,46,46,46,69,84,119,99}
*)


update

Note: totalList here is neither ascending nor descending.

1. (*Input 12 ==< *)
totalList = Total /@ %%

2. (*
Output 12 ==>
{0,46,84,97,122,123,130,143,155,307,300,320,765}
*)

3. (*Input 13 ==< *)
Transpose[{totalList, Sort[totalList]}]

4. (*
Output 13 ==>
{{0,0},{46,46},{84,84},{97,97},{122,122},{123,123},{130,130},{143,143},{155,155},{307,300}
,{300,307},{320,320},{765,765}}
*)


The above is the same to that use SortBy

1. (*Input 14 ==< *)
SortBy[sampleList1, ToCharacterCode]

2. (*
Output 14 ==>
{,.,T,a,z,{,.T,.a,.m,Etz,Tes,wha,compute}
*)


update

As@MichaelE2 mentioned in the comment,

Note that SortBy[sampleList1, ToCharacterCode] effectively orders them by length first. - Michael E2

one method in Rojo's comment

1. (*Input 15 ==< *)
yourSort = Max[StringLength[#1]] /. len_ :> SortBy[#1, PadRight[ToCharacterCode[#1], len] & ] & ;


### My conclusion

So the conclusion maybe the canonical order in Mathematica is different from that in Python.

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Dictionary order is correctly used in: Evaluating Sort[{"a", ".", "m", "c"}] result in {".", "a", "c", "m"}. It's skip some characters? The answer is no! Every element is a string and should be treated as in dictionary order. WMath should not ignore any characters. Segundo a documentação: "...Sort orders strings as in a dictionary, with uppercase...". I'm thing this is a bug. –  Pedro Vagner Jun 13 '13 at 16:44
@PedroR I think some characters are in different orders in different encodings. And we can use a sort function in Sort or SortBy to get any result. –  HyperGroups Jun 13 '13 at 16:49
@PedroR How to compare the order of { and . ? See one example in my edit. –  HyperGroups Jun 13 '13 at 17:00
@PedroR If you wanna do that translation. Use one function is easy to done. SortBy[lista,ToCharacterCode[#]&] –  HyperGroups Jun 13 '13 at 17:11
+1 for making effort on formatting :) –  Silvia Jun 14 '13 at 6:07

Since there is perhaps an implicit question of how to get a sort more along the lines you expect, as I proposed here you might use:

asciisort = #[[Ordering @ PadRight @ ToCharacterCode @ #]] &;

asciisort @ {".m", ".ast", "co"}

{".ast", ".m", "co"}


Or with the default character-wise order:

charsort = #[[Ordering @ PadRight @ Characters @ #]] &;

charsort @ {".m", ".ast", "co"}

{".ast", ".m", "co"}


If you are comfortable with shorter strings being ordered first you can also use:

SortBy[{".ast", ".m", "co"}, Characters]

{".m", "co", ".ast"}

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Or you could call it a Unicode sort. –  Michael E2 Jun 18 '13 at 18:43
@Michael Good point. –  Mr.Wizard Jun 18 '13 at 22:05