Ordering of String

Clash Royale CLAN TAG#URR8PPP

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5
down vote

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I don't find these results coherent :

OrderedQ["a","A"]

True

OrderedQ["a2","A1"]

False

Is there any explanation of that somewhere ? (in fact not necessarily related to Mathematica, maybe there are some standards or established conventions about this).

One could think that the explanation is :

• "a" and "A" are equivalent




• As OrderedQ["A","A"] returns True

it's normal.

But in that case OrderedQ["A","a"] shouldn't return False.

string-manipulation sorting

share|improve this question

edited 1 hour ago

asked 3 hours ago

andre

11.5k12248

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  OrderedQ >> Details: By default, OrderedQ uses canonical order as described in the notes for Sort. _ and Sort >> Details: _Sort orders strings as in a dictionary, with uppercase versions of letters coming after lowercase ones.
  – kglr
  3 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @kglr This behaviour is quite puzzling to me because the ordering is clearly not lexicographic. By "lexicographic" I mean an ordering of strings of tokens that is based on an ordering of the tokens themselves. I.e., with pseudocode notation, string[1] > string2[1] implies that string1 > string2. This is clearly not the case here. Mathematica uses some more complex and more confusing ordering.
  – Szabolcs
  38 mins ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Also consider OrderedQ["a", "2", "A", "1"] --> True. If upper/lowecase is treated specially, does that mean that: (1) ordering is language dependent (consider Turkish dotted uppercase Ä° and dotless lowercase ı)? If yes, what language does M use? (2) ordering is not well-defined for certain scripts?
  – Szabolcs
  35 mins ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Example: Sort["I2", "İ2", "i2", "ı2", "I1", "İ1", "i1", "ı1"] --> "İ1", "İ2", "i1", "ı1", "I1", "i2", "ı2", "I2". My point is that the note in the documentation does not give an unambiguous description of what is going on.
  – Szabolcs
  31 mins ago
  

  
  
  
  

add a comment | 

up vote
5
down vote

favorite

1

I don't find these results coherent :

OrderedQ["a","A"]

True

OrderedQ["a2","A1"]

False

Is there any explanation of that somewhere ? (in fact not necessarily related to Mathematica, maybe there are some standards or established conventions about this).

One could think that the explanation is :

• "a" and "A" are equivalent




• As OrderedQ["A","A"] returns True

it's normal.

But in that case OrderedQ["A","a"] shouldn't return False.

string-manipulation sorting

share|improve this question

edited 1 hour ago

asked 3 hours ago

andre

11.5k12248

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  OrderedQ >> Details: By default, OrderedQ uses canonical order as described in the notes for Sort. _ and Sort >> Details: _Sort orders strings as in a dictionary, with uppercase versions of letters coming after lowercase ones.
  – kglr
  3 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @kglr This behaviour is quite puzzling to me because the ordering is clearly not lexicographic. By "lexicographic" I mean an ordering of strings of tokens that is based on an ordering of the tokens themselves. I.e., with pseudocode notation, string[1] > string2[1] implies that string1 > string2. This is clearly not the case here. Mathematica uses some more complex and more confusing ordering.
  – Szabolcs
  38 mins ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Also consider OrderedQ["a", "2", "A", "1"] --> True. If upper/lowecase is treated specially, does that mean that: (1) ordering is language dependent (consider Turkish dotted uppercase Ä° and dotless lowercase ı)? If yes, what language does M use? (2) ordering is not well-defined for certain scripts?
  – Szabolcs
  35 mins ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Example: Sort["I2", "İ2", "i2", "ı2", "I1", "İ1", "i1", "ı1"] --> "İ1", "İ2", "i1", "ı1", "I1", "i2", "ı2", "I2". My point is that the note in the documentation does not give an unambiguous description of what is going on.
  – Szabolcs
  31 mins ago
  

  
  
  
  

add a comment | 

up vote
5
down vote

favorite

1

up vote
5
down vote

favorite

1

1

I don't find these results coherent :

OrderedQ["a","A"]

True

OrderedQ["a2","A1"]

False

Is there any explanation of that somewhere ? (in fact not necessarily related to Mathematica, maybe there are some standards or established conventions about this).

One could think that the explanation is :

• "a" and "A" are equivalent




• As OrderedQ["A","A"] returns True

it's normal.

But in that case OrderedQ["A","a"] shouldn't return False.

string-manipulation sorting

share|improve this question

edited 1 hour ago

asked 3 hours ago

andre

11.5k12248

I don't find these results coherent :

OrderedQ["a","A"]

True

OrderedQ["a2","A1"]

False

Is there any explanation of that somewhere ? (in fact not necessarily related to Mathematica, maybe there are some standards or established conventions about this).

One could think that the explanation is :

• "a" and "A" are equivalent




• As OrderedQ["A","A"] returns True

it's normal.

But in that case OrderedQ["A","a"] shouldn't return False.

string-manipulation sorting

string-manipulation sorting

share|improve this question

edited 1 hour ago

asked 3 hours ago

andre

11.5k12248

share|improve this question

edited 1 hour ago

asked 3 hours ago

andre

11.5k12248

share|improve this question

share|improve this question

edited 1 hour ago

edited 1 hour ago

edited 1 hour ago

asked 3 hours ago

andre

11.5k12248

asked 3 hours ago

andre

11.5k12248

asked 3 hours ago

andre

11.5k12248

11.5k12248

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  OrderedQ >> Details: By default, OrderedQ uses canonical order as described in the notes for Sort. _ and Sort >> Details: _Sort orders strings as in a dictionary, with uppercase versions of letters coming after lowercase ones.
  – kglr
  3 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @kglr This behaviour is quite puzzling to me because the ordering is clearly not lexicographic. By "lexicographic" I mean an ordering of strings of tokens that is based on an ordering of the tokens themselves. I.e., with pseudocode notation, string[1] > string2[1] implies that string1 > string2. This is clearly not the case here. Mathematica uses some more complex and more confusing ordering.
  – Szabolcs
  38 mins ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Also consider OrderedQ["a", "2", "A", "1"] --> True. If upper/lowecase is treated specially, does that mean that: (1) ordering is language dependent (consider Turkish dotted uppercase Ä° and dotless lowercase ı)? If yes, what language does M use? (2) ordering is not well-defined for certain scripts?
  – Szabolcs
  35 mins ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Example: Sort["I2", "İ2", "i2", "ı2", "I1", "İ1", "i1", "ı1"] --> "İ1", "İ2", "i1", "ı1", "I1", "i2", "ı2", "I2". My point is that the note in the documentation does not give an unambiguous description of what is going on.
  – Szabolcs
  31 mins ago
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  OrderedQ >> Details: By default, OrderedQ uses canonical order as described in the notes for Sort. _ and Sort >> Details: _Sort orders strings as in a dictionary, with uppercase versions of letters coming after lowercase ones.
  – kglr
  3 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @kglr This behaviour is quite puzzling to me because the ordering is clearly not lexicographic. By "lexicographic" I mean an ordering of strings of tokens that is based on an ordering of the tokens themselves. I.e., with pseudocode notation, string[1] > string2[1] implies that string1 > string2. This is clearly not the case here. Mathematica uses some more complex and more confusing ordering.
  – Szabolcs
  38 mins ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Also consider OrderedQ["a", "2", "A", "1"] --> True. If upper/lowecase is treated specially, does that mean that: (1) ordering is language dependent (consider Turkish dotted uppercase Ä° and dotless lowercase ı)? If yes, what language does M use? (2) ordering is not well-defined for certain scripts?
  – Szabolcs
  35 mins ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Example: Sort["I2", "İ2", "i2", "ı2", "I1", "İ1", "i1", "ı1"] --> "İ1", "İ2", "i1", "ı1", "I1", "i2", "ı2", "I2". My point is that the note in the documentation does not give an unambiguous description of what is going on.
  – Szabolcs
  31 mins ago
  

  
  
  
  

3

3

OrderedQ >> Details: By default, OrderedQ uses canonical order as described in the notes for Sort. _ and Sort >> Details: _Sort orders strings as in a dictionary, with uppercase versions of letters coming after lowercase ones.
– kglr
3 hours ago

OrderedQ >> Details: By default, OrderedQ uses canonical order as described in the notes for Sort. _ and Sort >> Details: _Sort orders strings as in a dictionary, with uppercase versions of letters coming after lowercase ones.
– kglr
3 hours ago

1

1

@kglr This behaviour is quite puzzling to me because the ordering is clearly not lexicographic. By "lexicographic" I mean an ordering of strings of tokens that is based on an ordering of the tokens themselves. I.e., with pseudocode notation, string[1] > string2[1] implies that string1 > string2. This is clearly not the case here. Mathematica uses some more complex and more confusing ordering.
– Szabolcs
38 mins ago

@kglr This behaviour is quite puzzling to me because the ordering is clearly not lexicographic. By "lexicographic" I mean an ordering of strings of tokens that is based on an ordering of the tokens themselves. I.e., with pseudocode notation, string[1] > string2[1] implies that string1 > string2. This is clearly not the case here. Mathematica uses some more complex and more confusing ordering.
– Szabolcs
38 mins ago

1

1

Also consider OrderedQ["a", "2", "A", "1"] --> True. If upper/lowecase is treated specially, does that mean that: (1) ordering is language dependent (consider Turkish dotted uppercase Ä° and dotless lowercase ı)? If yes, what language does M use? (2) ordering is not well-defined for certain scripts?
– Szabolcs
35 mins ago

Also consider OrderedQ["a", "2", "A", "1"] --> True. If upper/lowecase is treated specially, does that mean that: (1) ordering is language dependent (consider Turkish dotted uppercase Ä° and dotless lowercase ı)? If yes, what language does M use? (2) ordering is not well-defined for certain scripts?
– Szabolcs
35 mins ago

Example: Sort["I2", "İ2", "i2", "ı2", "I1", "İ1", "i1", "ı1"] --> "İ1", "İ2", "i1", "ı1", "I1", "i2", "ı2", "I2". My point is that the note in the documentation does not give an unambiguous description of what is going on.
– Szabolcs
31 mins ago

Example: Sort["I2", "İ2", "i2", "ı2", "I1", "İ1", "i1", "ı1"] --> "İ1", "İ2", "i1", "ı1", "I1", "i2", "ı2", "I2". My point is that the note in the documentation does not give an unambiguous description of what is going on.
– Szabolcs
31 mins ago

add a comment | 

1 Answer
1

active

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up vote
4
down vote

I think you have a good question. It seems that Sort treats "a" and "A" equivalently, and then sorts the elements that are equivalent. Here is an example that perhaps clarifies the issue:

Sort[
 "a2a1","A1a1","A2a1","a1a1","a2A1","A1A1","A2A1","a1A1",
 "a2a2","A1a2","A2a2","a1a2","a2A2","A1A2","A2A2","a1A2"
]

"a1a1", "a1A1", "A1a1", "A1A1", "a1a2", "a1A2", "A1a2", "A1A2", "a2a1",
"a2A1", "A2a1", "A2A1", "a2a2", "a2A2", "A2a2", "A2A2"

Notice how the x1x1 terms come first, then the x1x2 terms, etc. Within each grouping the sort of the equivalent letters goes as "aa", "aA", "Aa", "AA" as expected.

share|improve this answer

answered 1 hour ago

Carl Woll

60.3k279155

add a comment | 

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1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
4
down vote

I think you have a good question. It seems that Sort treats "a" and "A" equivalently, and then sorts the elements that are equivalent. Here is an example that perhaps clarifies the issue:

Sort[
 "a2a1","A1a1","A2a1","a1a1","a2A1","A1A1","A2A1","a1A1",
 "a2a2","A1a2","A2a2","a1a2","a2A2","A1A2","A2A2","a1A2"
]

"a1a1", "a1A1", "A1a1", "A1A1", "a1a2", "a1A2", "A1a2", "A1A2", "a2a1",
"a2A1", "A2a1", "A2A1", "a2a2", "a2A2", "A2a2", "A2A2"

Notice how the x1x1 terms come first, then the x1x2 terms, etc. Within each grouping the sort of the equivalent letters goes as "aa", "aA", "Aa", "AA" as expected.

share|improve this answer

answered 1 hour ago

Carl Woll

60.3k279155

add a comment | 

up vote
4
down vote

I think you have a good question. It seems that Sort treats "a" and "A" equivalently, and then sorts the elements that are equivalent. Here is an example that perhaps clarifies the issue:

Sort[
 "a2a1","A1a1","A2a1","a1a1","a2A1","A1A1","A2A1","a1A1",
 "a2a2","A1a2","A2a2","a1a2","a2A2","A1A2","A2A2","a1A2"
]

"a1a1", "a1A1", "A1a1", "A1A1", "a1a2", "a1A2", "A1a2", "A1A2", "a2a1",
"a2A1", "A2a1", "A2A1", "a2a2", "a2A2", "A2a2", "A2A2"

Notice how the x1x1 terms come first, then the x1x2 terms, etc. Within each grouping the sort of the equivalent letters goes as "aa", "aA", "Aa", "AA" as expected.

share|improve this answer

answered 1 hour ago

Carl Woll

60.3k279155

add a comment | 

up vote
4
down vote

up vote
4
down vote

I think you have a good question. It seems that Sort treats "a" and "A" equivalently, and then sorts the elements that are equivalent. Here is an example that perhaps clarifies the issue:

Sort[
 "a2a1","A1a1","A2a1","a1a1","a2A1","A1A1","A2A1","a1A1",
 "a2a2","A1a2","A2a2","a1a2","a2A2","A1A2","A2A2","a1A2"
]

"a1a1", "a1A1", "A1a1", "A1A1", "a1a2", "a1A2", "A1a2", "A1A2", "a2a1",
"a2A1", "A2a1", "A2A1", "a2a2", "a2A2", "A2a2", "A2A2"

Notice how the x1x1 terms come first, then the x1x2 terms, etc. Within each grouping the sort of the equivalent letters goes as "aa", "aA", "Aa", "AA" as expected.

share|improve this answer

answered 1 hour ago

Carl Woll

60.3k279155

I think you have a good question. It seems that Sort treats "a" and "A" equivalently, and then sorts the elements that are equivalent. Here is an example that perhaps clarifies the issue:

Sort[
 "a2a1","A1a1","A2a1","a1a1","a2A1","A1A1","A2A1","a1A1",
 "a2a2","A1a2","A2a2","a1a2","a2A2","A1A2","A2A2","a1A2"
]

"a1a1", "a1A1", "A1a1", "A1A1", "a1a2", "a1A2", "A1a2", "A1A2", "a2a1",
"a2A1", "A2a1", "A2A1", "a2a2", "a2A2", "A2a2", "A2A2"

Notice how the x1x1 terms come first, then the x1x2 terms, etc. Within each grouping the sort of the equivalent letters goes as "aa", "aA", "Aa", "AA" as expected.

share|improve this answer

answered 1 hour ago

Carl Woll

60.3k279155

share|improve this answer

share|improve this answer

answered 1 hour ago

Carl Woll

60.3k279155

answered 1 hour ago

Carl Woll

60.3k279155

answered 1 hour ago

Carl Woll

60.3k279155

60.3k279155

add a comment | 

add a comment | 

 

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