OrderQ with string arguments

Clash Royale CLAN TAG#URR8PPP

up vote
9
down vote

favorite

1

I don't find these results consistent:

OrderedQ["a", "A"]

True

OrderedQ["a2", "A1"]

False

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

One could think that the explanation is: since "a" and "A" are equivalent

and as OrderedQ["A", "A"] returns True, it's normal. But in that case OrderedQ["A", "a"] shouldn't return False.

EDIT

(Thanks to @Michael E2 comments)

It turns out that this question has nothing to do with the fact that "1" and "2" are digit characters. The same thing happens if one replaces "1" by "c" and "2" by "d" for example.

string-manipulation sorting

share|improve this question

edited 10 mins ago

m_goldberg

82.6k870190

asked 9 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
  9 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  @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
  7 hours 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
  7 hours 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
  7 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Szabolcs, all good points.
  – kglr
  4 hours ago
  

  
  
  
  

 | 
show 1 more comment

up vote
9
down vote

favorite

1

I don't find these results consistent:

OrderedQ["a", "A"]

True

OrderedQ["a2", "A1"]

False

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

One could think that the explanation is: since "a" and "A" are equivalent

and as OrderedQ["A", "A"] returns True, it's normal. But in that case OrderedQ["A", "a"] shouldn't return False.

EDIT

(Thanks to @Michael E2 comments)

It turns out that this question has nothing to do with the fact that "1" and "2" are digit characters. The same thing happens if one replaces "1" by "c" and "2" by "d" for example.

string-manipulation sorting

share|improve this question

edited 10 mins ago

m_goldberg

82.6k870190

asked 9 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
  9 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  @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
  7 hours 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
  7 hours 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
  7 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Szabolcs, all good points.
  – kglr
  4 hours ago
  

  
  
  
  

 | 
show 1 more comment

up vote
9
down vote

favorite

1

up vote
9
down vote

favorite

1

1

I don't find these results consistent:

OrderedQ["a", "A"]

True

OrderedQ["a2", "A1"]

False

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

One could think that the explanation is: since "a" and "A" are equivalent

and as OrderedQ["A", "A"] returns True, it's normal. But in that case OrderedQ["A", "a"] shouldn't return False.

EDIT

(Thanks to @Michael E2 comments)

It turns out that this question has nothing to do with the fact that "1" and "2" are digit characters. The same thing happens if one replaces "1" by "c" and "2" by "d" for example.

string-manipulation sorting

share|improve this question

edited 10 mins ago

m_goldberg

82.6k870190

asked 9 hours ago

andre

11.5k12248

I don't find these results consistent:

OrderedQ["a", "A"]

True

OrderedQ["a2", "A1"]

False

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

One could think that the explanation is: since "a" and "A" are equivalent

and as OrderedQ["A", "A"] returns True, it's normal. But in that case OrderedQ["A", "a"] shouldn't return False.

EDIT

(Thanks to @Michael E2 comments)

It turns out that this question has nothing to do with the fact that "1" and "2" are digit characters. The same thing happens if one replaces "1" by "c" and "2" by "d" for example.

string-manipulation sorting

string-manipulation sorting

share|improve this question

edited 10 mins ago

m_goldberg

82.6k870190

asked 9 hours ago

andre

11.5k12248

share|improve this question

edited 10 mins ago

m_goldberg

82.6k870190

asked 9 hours ago

andre

11.5k12248

share|improve this question

share|improve this question

edited 10 mins ago

m_goldberg

82.6k870190

edited 10 mins ago

m_goldberg

82.6k870190

edited 10 mins ago

m_goldberg

82.6k870190

82.6k870190

asked 9 hours ago

andre

11.5k12248

asked 9 hours ago

andre

11.5k12248

asked 9 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
  9 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  @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
  7 hours 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
  7 hours 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
  7 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Szabolcs, all good points.
  – kglr
  4 hours ago
  

  
  
  
  

 | 
show 1 more 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
  9 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  @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
  7 hours 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
  7 hours 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
  7 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Szabolcs, all good points.
  – kglr
  4 hours 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
9 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
9 hours ago

2

2

@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
7 hours 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
7 hours 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
7 hours 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
7 hours 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
7 hours 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
7 hours ago

@Szabolcs, all good points.
– kglr
4 hours ago

@Szabolcs, all good points.
– kglr
4 hours ago

 | 
show 1 more comment

1 Answer
1

active

oldest

votes

up vote
9
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 7 hours ago

Carl Woll

60.3k279155

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I would add that "dictionary order" is easier to understand with examples like OrderedQ["ac", "Ab"] instead of the ones and twos. Also punctuation characters are treated differently (and different from my print dictionary) than letter-like characters, to which class digits apparently belong.
  – Michael E2
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I don't understand the plain-English statement "It seems that Sort treats 'a' and 'A' equivalently" -- it does not in the most natural interpretation (to me) agree with the example below. Perhaps you could try phrasing that in a different way?
  – Mr.Wizard♦
  1 hour ago
  

  
  
  
  

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
9
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 7 hours ago

Carl Woll

60.3k279155

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I would add that "dictionary order" is easier to understand with examples like OrderedQ["ac", "Ab"] instead of the ones and twos. Also punctuation characters are treated differently (and different from my print dictionary) than letter-like characters, to which class digits apparently belong.
  – Michael E2
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I don't understand the plain-English statement "It seems that Sort treats 'a' and 'A' equivalently" -- it does not in the most natural interpretation (to me) agree with the example below. Perhaps you could try phrasing that in a different way?
  – Mr.Wizard♦
  1 hour ago
  

  
  
  
  

add a comment | 

up vote
9
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 7 hours ago

Carl Woll

60.3k279155

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I would add that "dictionary order" is easier to understand with examples like OrderedQ["ac", "Ab"] instead of the ones and twos. Also punctuation characters are treated differently (and different from my print dictionary) than letter-like characters, to which class digits apparently belong.
  – Michael E2
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I don't understand the plain-English statement "It seems that Sort treats 'a' and 'A' equivalently" -- it does not in the most natural interpretation (to me) agree with the example below. Perhaps you could try phrasing that in a different way?
  – Mr.Wizard♦
  1 hour ago
  

  
  
  
  

add a comment | 

up vote
9
down vote

up vote
9
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 7 hours 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 7 hours ago

Carl Woll

60.3k279155

share|improve this answer

share|improve this answer

answered 7 hours ago

Carl Woll

60.3k279155

answered 7 hours ago

Carl Woll

60.3k279155

answered 7 hours ago

Carl Woll

60.3k279155

60.3k279155

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I would add that "dictionary order" is easier to understand with examples like OrderedQ["ac", "Ab"] instead of the ones and twos. Also punctuation characters are treated differently (and different from my print dictionary) than letter-like characters, to which class digits apparently belong.
  – Michael E2
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I don't understand the plain-English statement "It seems that Sort treats 'a' and 'A' equivalently" -- it does not in the most natural interpretation (to me) agree with the example below. Perhaps you could try phrasing that in a different way?
  – Mr.Wizard♦
  1 hour ago
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I would add that "dictionary order" is easier to understand with examples like OrderedQ["ac", "Ab"] instead of the ones and twos. Also punctuation characters are treated differently (and different from my print dictionary) than letter-like characters, to which class digits apparently belong.
  – Michael E2
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I don't understand the plain-English statement "It seems that Sort treats 'a' and 'A' equivalently" -- it does not in the most natural interpretation (to me) agree with the example below. Perhaps you could try phrasing that in a different way?
  – Mr.Wizard♦
  1 hour ago
  

  
  
  
  

I would add that "dictionary order" is easier to understand with examples like OrderedQ["ac", "Ab"] instead of the ones and twos. Also punctuation characters are treated differently (and different from my print dictionary) than letter-like characters, to which class digits apparently belong.
– Michael E2
5 hours ago

I would add that "dictionary order" is easier to understand with examples like OrderedQ["ac", "Ab"] instead of the ones and twos. Also punctuation characters are treated differently (and different from my print dictionary) than letter-like characters, to which class digits apparently belong.
– Michael E2
5 hours ago

I don't understand the plain-English statement "It seems that Sort treats 'a' and 'A' equivalently" -- it does not in the most natural interpretation (to me) agree with the example below. Perhaps you could try phrasing that in a different way?
– Mr.Wizard♦
1 hour ago

I don't understand the plain-English statement "It seems that Sort treats 'a' and 'A' equivalently" -- it does not in the most natural interpretation (to me) agree with the example below. Perhaps you could try phrasing that in a different way?
– Mr.Wizard♦
1 hour ago

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