What is the Alphabetical Inequality Test?

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1
down vote

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Mathematica can sort "b","d","a","c" into "a","b","c","d" with a simple application of Sort. What ordering function/command is being used?

It isn't <: "a" < "b" doesn't return True or False, just a < b.

I'm trying to sort a large data set that contains both strings and numeric values. An example:

data = 9, 8, "b", 4, 2, "d", 0, 3, "a", 4, 9, "c".

I can sort by the second element of each set:

Sort[data, #2[[2]] > #1[[2]] &] returns

4, 2, "d", 0, 3, "a", 9, 8, "b", 4, 9, "c".

But Sorting by the third element doesn't work:

Sort[data, #2[[3]] > #1[[3]] &] returns data unchanged:

9, 8, "b", 4, 2, "d", 0, 3, "a", 4, 9, "c".

It feels like a hack, but I can sort using Ordering and OrderedQ:

data[[Ordering[data[[All, 3]]]]] returns

0, 3, "a", 9, 8, "b", 4, 9, "c", 4, 2, "d", as does

Sort[data, OrderedQ[#1[[3]], #2[[3]]] &].

Neither feels natural. Is there a lexicographical/alphabetical "inequality" command, or is it just OrderedQ?

asked 4 hours ago

GregH

565516

add a commentÂ |Â

up vote
1
down vote

favorite

Mathematica can sort "b","d","a","c" into "a","b","c","d" with a simple application of Sort. What ordering function/command is being used?

It isn't <: "a" < "b" doesn't return True or False, just a < b.

I'm trying to sort a large data set that contains both strings and numeric values. An example:

data = 9, 8, "b", 4, 2, "d", 0, 3, "a", 4, 9, "c".

I can sort by the second element of each set:

Sort[data, #2[[2]] > #1[[2]] &] returns

4, 2, "d", 0, 3, "a", 9, 8, "b", 4, 9, "c".

But Sorting by the third element doesn't work:

Sort[data, #2[[3]] > #1[[3]] &] returns data unchanged:

9, 8, "b", 4, 2, "d", 0, 3, "a", 4, 9, "c".

It feels like a hack, but I can sort using Ordering and OrderedQ:

data[[Ordering[data[[All, 3]]]]] returns

0, 3, "a", 9, 8, "b", 4, 9, "c", 4, 2, "d", as does

Sort[data, OrderedQ[#1[[3]], #2[[3]]] &].

Neither feels natural. Is there a lexicographical/alphabetical "inequality" command, or is it just OrderedQ?

asked 4 hours ago

GregH

565516

add a commentÂ |Â

up vote
1
down vote

favorite

Mathematica can sort "b","d","a","c" into "a","b","c","d" with a simple application of Sort. What ordering function/command is being used?

It isn't <: "a" < "b" doesn't return True or False, just a < b.

I'm trying to sort a large data set that contains both strings and numeric values. An example:

data = 9, 8, "b", 4, 2, "d", 0, 3, "a", 4, 9, "c".

I can sort by the second element of each set:

Sort[data, #2[[2]] > #1[[2]] &] returns

4, 2, "d", 0, 3, "a", 9, 8, "b", 4, 9, "c".

But Sorting by the third element doesn't work:

Sort[data, #2[[3]] > #1[[3]] &] returns data unchanged:

9, 8, "b", 4, 2, "d", 0, 3, "a", 4, 9, "c".

It feels like a hack, but I can sort using Ordering and OrderedQ:

data[[Ordering[data[[All, 3]]]]] returns

0, 3, "a", 9, 8, "b", 4, 9, "c", 4, 2, "d", as does

Sort[data, OrderedQ[#1[[3]], #2[[3]]] &].

Neither feels natural. Is there a lexicographical/alphabetical "inequality" command, or is it just OrderedQ?

asked 4 hours ago

GregH

565516

Mathematica can sort "b","d","a","c" into "a","b","c","d" with a simple application of Sort. What ordering function/command is being used?

It isn't <: "a" < "b" doesn't return True or False, just a < b.

I'm trying to sort a large data set that contains both strings and numeric values. An example:

data = 9, 8, "b", 4, 2, "d", 0, 3, "a", 4, 9, "c".

I can sort by the second element of each set:

Sort[data, #2[[2]] > #1[[2]] &] returns

4, 2, "d", 0, 3, "a", 9, 8, "b", 4, 9, "c".

But Sorting by the third element doesn't work:

Sort[data, #2[[3]] > #1[[3]] &] returns data unchanged:

9, 8, "b", 4, 2, "d", 0, 3, "a", 4, 9, "c".

It feels like a hack, but I can sort using Ordering and OrderedQ:

data[[Ordering[data[[All, 3]]]]] returns

0, 3, "a", 9, 8, "b", 4, 9, "c", 4, 2, "d", as does

Sort[data, OrderedQ[#1[[3]], #2[[3]]] &].

Neither feels natural. Is there a lexicographical/alphabetical "inequality" command, or is it just OrderedQ?

sorting

asked 4 hours ago

GregH

565516

asked 4 hours ago

GregH

565516

asked 4 hours ago

GregH

565516

asked 4 hours ago

GregH

565516

asked 4 hours ago

GregH

565516

add a commentÂ |Â

2 Answers
2

active

oldest

votes

up vote
4
down vote

accepted

You can use AlphabeticOrder:

data = 9, 8, "b", 4, 2, "d", 0, 3, "a", 4, 9, "c";

Sort[
 data, 
 AlphabeticOrder[ #1[[3]], #2[[3]] ]&
]

0, 3, "a", 9, 8, "b", 4, 9, "c", 4, 2, "d"

answered 3 hours ago

gwr

6,97622457

That's it. I didn't seem to be using the right search terms online to find that command.
â€“Â GregH
3 hours ago

add a commentÂ |Â

up vote
2
down vote

AlphabeticOrder does not exist in version 10.1 which I use, but I don't believe it is necessary here. I argue that Order and OrderedQ are the more canonical (and certainly general) functions.

Additionally, where possible you should make use of SortBy (e.g. SortBy[data, #[[3]] &]) or Ordering (as you already did) rather than Sort, as these are more efficient methods.

An alternative to OrderedQ if you have need of Sort itself:

Sort[data, 0 < Order[#[[3]], #2[[3]]] &]
Sort[data, 0 > Order[#[[3]], #2[[3]]] &]

0, 3, "a", 9, 8, "b", 4, 9, "c", 4, 2, "d"
4, 2, "d", 4, 9, "c", 9, 8, "b", 0, 3, "a"

This is actually more concise than AlphabeticOrder.

answered 1 hour ago

Mr.Wizardâ™¦

228k294671023

2

In law they say "lex specialis derogat legi generali": Sometimes the more special function has its merits and is maybe is less abstract? AlphabeticOrder on the other hand is more general than Order because English is not the only language out there... ;-)
â€“Â gwr
59 mins ago

@gwr I didn't notice that AlphabeticOrder handled different languages; that's nice! I have already voted for your answer. And thanks for the Latin lesson.
â€“Â Mr.Wizardâ™¦
50 mins ago

add a commentÂ |Â

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2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

up vote
4
down vote

accepted

You can use AlphabeticOrder:

data = 9, 8, "b", 4, 2, "d", 0, 3, "a", 4, 9, "c";

Sort[
 data, 
 AlphabeticOrder[ #1[[3]], #2[[3]] ]&
]

0, 3, "a", 9, 8, "b", 4, 9, "c", 4, 2, "d"

answered 3 hours ago

gwr

6,97622457

That's it. I didn't seem to be using the right search terms online to find that command.
â€“Â GregH
3 hours ago

add a commentÂ |Â

up vote
4
down vote

accepted

You can use AlphabeticOrder:

data = 9, 8, "b", 4, 2, "d", 0, 3, "a", 4, 9, "c";

Sort[
 data, 
 AlphabeticOrder[ #1[[3]], #2[[3]] ]&
]

0, 3, "a", 9, 8, "b", 4, 9, "c", 4, 2, "d"

answered 3 hours ago

gwr

6,97622457

That's it. I didn't seem to be using the right search terms online to find that command.
â€“Â GregH
3 hours ago

add a commentÂ |Â

up vote
4
down vote

accepted

You can use AlphabeticOrder:

data = 9, 8, "b", 4, 2, "d", 0, 3, "a", 4, 9, "c";

Sort[
 data, 
 AlphabeticOrder[ #1[[3]], #2[[3]] ]&
]

0, 3, "a", 9, 8, "b", 4, 9, "c", 4, 2, "d"

answered 3 hours ago

gwr

6,97622457

You can use AlphabeticOrder:

data = 9, 8, "b", 4, 2, "d", 0, 3, "a", 4, 9, "c";

Sort[
 data, 
 AlphabeticOrder[ #1[[3]], #2[[3]] ]&
]

0, 3, "a", 9, 8, "b", 4, 9, "c", 4, 2, "d"

answered 3 hours ago

gwr

6,97622457

answered 3 hours ago

gwr

6,97622457

answered 3 hours ago

gwr

6,97622457

answered 3 hours ago

gwr

6,97622457

That's it. I didn't seem to be using the right search terms online to find that command.
â€“Â GregH
3 hours ago

add a commentÂ |Â

That's it. I didn't seem to be using the right search terms online to find that command.
â€“Â GregH
3 hours ago

That's it. I didn't seem to be using the right search terms online to find that command.
â€“Â GregH
3 hours ago

add a commentÂ |Â

up vote
2
down vote

AlphabeticOrder does not exist in version 10.1 which I use, but I don't believe it is necessary here. I argue that Order and OrderedQ are the more canonical (and certainly general) functions.

Additionally, where possible you should make use of SortBy (e.g. SortBy[data, #[[3]] &]) or Ordering (as you already did) rather than Sort, as these are more efficient methods.

An alternative to OrderedQ if you have need of Sort itself:

Sort[data, 0 < Order[#[[3]], #2[[3]]] &]
Sort[data, 0 > Order[#[[3]], #2[[3]]] &]

0, 3, "a", 9, 8, "b", 4, 9, "c", 4, 2, "d"
4, 2, "d", 4, 9, "c", 9, 8, "b", 0, 3, "a"

This is actually more concise than AlphabeticOrder.

answered 1 hour ago

Mr.Wizardâ™¦

228k294671023

2

In law they say "lex specialis derogat legi generali": Sometimes the more special function has its merits and is maybe is less abstract? AlphabeticOrder on the other hand is more general than Order because English is not the only language out there... ;-)
â€“Â gwr
59 mins ago

@gwr I didn't notice that AlphabeticOrder handled different languages; that's nice! I have already voted for your answer. And thanks for the Latin lesson.
â€“Â Mr.Wizardâ™¦
50 mins ago

add a commentÂ |Â

up vote
2
down vote

AlphabeticOrder does not exist in version 10.1 which I use, but I don't believe it is necessary here. I argue that Order and OrderedQ are the more canonical (and certainly general) functions.

Additionally, where possible you should make use of SortBy (e.g. SortBy[data, #[[3]] &]) or Ordering (as you already did) rather than Sort, as these are more efficient methods.

An alternative to OrderedQ if you have need of Sort itself:

Sort[data, 0 < Order[#[[3]], #2[[3]]] &]
Sort[data, 0 > Order[#[[3]], #2[[3]]] &]

0, 3, "a", 9, 8, "b", 4, 9, "c", 4, 2, "d"
4, 2, "d", 4, 9, "c", 9, 8, "b", 0, 3, "a"

This is actually more concise than AlphabeticOrder.

answered 1 hour ago

Mr.Wizardâ™¦

228k294671023

2

In law they say "lex specialis derogat legi generali": Sometimes the more special function has its merits and is maybe is less abstract? AlphabeticOrder on the other hand is more general than Order because English is not the only language out there... ;-)
â€“Â gwr
59 mins ago

@gwr I didn't notice that AlphabeticOrder handled different languages; that's nice! I have already voted for your answer. And thanks for the Latin lesson.
â€“Â Mr.Wizardâ™¦
50 mins ago

add a commentÂ |Â

up vote
2
down vote

AlphabeticOrder does not exist in version 10.1 which I use, but I don't believe it is necessary here. I argue that Order and OrderedQ are the more canonical (and certainly general) functions.

Additionally, where possible you should make use of SortBy (e.g. SortBy[data, #[[3]] &]) or Ordering (as you already did) rather than Sort, as these are more efficient methods.

An alternative to OrderedQ if you have need of Sort itself:

Sort[data, 0 < Order[#[[3]], #2[[3]]] &]
Sort[data, 0 > Order[#[[3]], #2[[3]]] &]

0, 3, "a", 9, 8, "b", 4, 9, "c", 4, 2, "d"
4, 2, "d", 4, 9, "c", 9, 8, "b", 0, 3, "a"

This is actually more concise than AlphabeticOrder.

answered 1 hour ago

Mr.Wizardâ™¦

228k294671023

AlphabeticOrder does not exist in version 10.1 which I use, but I don't believe it is necessary here. I argue that Order and OrderedQ are the more canonical (and certainly general) functions.

Additionally, where possible you should make use of SortBy (e.g. SortBy[data, #[[3]] &]) or Ordering (as you already did) rather than Sort, as these are more efficient methods.

An alternative to OrderedQ if you have need of Sort itself:

Sort[data, 0 < Order[#[[3]], #2[[3]]] &]
Sort[data, 0 > Order[#[[3]], #2[[3]]] &]

0, 3, "a", 9, 8, "b", 4, 9, "c", 4, 2, "d"
4, 2, "d", 4, 9, "c", 9, 8, "b", 0, 3, "a"

This is actually more concise than AlphabeticOrder.

answered 1 hour ago

Mr.Wizardâ™¦

228k294671023

answered 1 hour ago

Mr.Wizardâ™¦

228k294671023

answered 1 hour ago

Mr.Wizardâ™¦

228k294671023

answered 1 hour ago

Mr.Wizardâ™¦

228k294671023

2

In law they say "lex specialis derogat legi generali": Sometimes the more special function has its merits and is maybe is less abstract? AlphabeticOrder on the other hand is more general than Order because English is not the only language out there... ;-)
â€“Â gwr
59 mins ago

@gwr I didn't notice that AlphabeticOrder handled different languages; that's nice! I have already voted for your answer. And thanks for the Latin lesson.
â€“Â Mr.Wizardâ™¦
50 mins ago

add a commentÂ |Â

2

In law they say "lex specialis derogat legi generali": Sometimes the more special function has its merits and is maybe is less abstract? AlphabeticOrder on the other hand is more general than Order because English is not the only language out there... ;-)
â€“Â gwr
59 mins ago

@gwr I didn't notice that AlphabeticOrder handled different languages; that's nice! I have already voted for your answer. And thanks for the Latin lesson.
â€“Â Mr.Wizardâ™¦
50 mins ago

In law they say "lex specialis derogat legi generali": Sometimes the more special function has its merits and is maybe is less abstract? AlphabeticOrder on the other hand is more general than Order because English is not the only language out there... ;-)
â€“Â gwr
59 mins ago

@gwr I didn't notice that AlphabeticOrder handled different languages; that's nice! I have already voted for your answer. And thanks for the Latin lesson.
â€“Â Mr.Wizardâ™¦
50 mins ago

add a commentÂ |Â

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