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# Vocabulary/acapdot - J Wiki
[\>>](https://code.jsoftware.com/wiki/Vocabulary/bdot "Vocabulary/bdot") [<<](https://code.jsoftware.com/wiki/Vocabulary/aco "Vocabulary/aco") [Back to: Vocabulary](https://code.jsoftware.com/wiki/NuVoc "NuVoc") [Thru to: Dictionary](https://www.jsoftware.com/help/dictionary/dacapdot.ht... | acpadot.md | [
{
"role": "user",
"content": "What does the monadic function A. y compute according to the J Wiki?\n\nEvidence:\n<tt>A. y</tt> Anagram Index"
},
{
"role": "assistant",
"content": "Anagram Index"
}
] |
THIS IMPORTANT?](https://code.jsoftware.com/wiki/Vocabulary/RankInfoIsImportant "Vocabulary/RankInfoIsImportant")
---
A. y converts the [permutation](https://code.jsoftware.com/wiki/Vocabulary/ccapdot "Vocabulary/ccapdot") y into its permutation number (also called its _anagram index_).
```
A. 3 1 2 0
21
```
A ... | acpadot.md | [
{
"role": "user",
"content": "What does A. y do to a permutation y?\n\nEvidence:\nA. y converts the permutation y into its permutation number (also called its anagram index)."
},
{
"role": "assistant",
"content": "converts the permutation y into its permutation number (also called its anagram in... |
://code.jsoftware.com/wiki/Vocabulary/ccapdot#incomplete "Vocabulary/ccapdot") before the anagram index is calculated.
```
N=: 4 NB. Confine attention to permutations on 4 points
A=: 'ABCD' NB. N points provided for a given permutation to act on
p=: 2 0 1 3 NB. a given permutation on N points
\] ... | acpadot.md | [
{
"role": "user",
"content": "What is the anagram index (AI) of the permutation p = 2 0 1 3 on 4 points?\n\nEvidence:\n A. p NB. The AI of permutation: p
12"
},
{
"role": "assistant",
"content": "12"
}
] |
ing the permutation number instead of the permutation itself.
2\. Explore the subgroups of a given permutation group.
Example: the _symmetric group_ of all permutations on 4 points, known as Sym(4) or S4.
Representing each permutation by its AI, we can represent the set S4 in J as follows:
```
N=: 4
\] S4=: i... | acpadot.md | [
{
"role": "user",
"content": "What is the J definition of the mul function between AIs?\n\nEvidence:\nmul=: {{A. (a2p x) { (a2p y)}}"0 NB. (AI) mul (AI) --> (AI)"
},
{
"role": "assistant",
"content": "mul=: {{A. (a2p x) { (a2p y)}}"0 NB. (AI) mul (AI) --> (AI)"
}
] |
lement in S4.
The set of all permutations on N points forms a mathematical _group_ under the operation: mul. That is:
- the set is _closed_ under mul
```
z=: S4 mul/ S4
~. ,z
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
```
- The operation is _associative_, i.e. expressions in mul can be b... | acpadot.md | [
{
"role": "user",
"content": "What is the identity element in S4?\n\nEvidence:\nThere exists a unique _identity_ element. In S4 this is 0."
},
{
"role": "assistant",
"content": "0"
}
] |
://en.wikipedia.org/wiki/Cayley_table "wikipedia:Cayley table") of the subgroup of S4 generated by the AI: 9 under mul
```
9 mul 9
16
9 mul 9 mul 9
18
9 mul 9 mul 9 mul 9
0
S=: 0 9 16 18 NB. Define candidate set S
```
Does S form a group under mul? If so then (S mul/ S) will contain only [items](https:... | acpadot.md | [
{
"role": "user",
"content": "Does the chunk refer to S as a subgroup under mul?\n\nEvidence:\nNB. the Cayley Table of subgroup S"
},
{
"role": "assistant",
"content": "Yes"
}
] |
e expressed in either [cycle or direct form](https://code.jsoftware.com/wiki/Vocabulary/ccapdot "Vocabulary/ccapdot").
2\. The _permutation number_ of a permutation is the index of the direct form of the permutation in the [table](https://code.jsoftware.com/wiki/Vocabulary/AET#Table "Vocabulary/AET") whose rows are al... | acpadot.md | [
{
"role": "user",
"content": "What is the permutation number also called?\n\nEvidence:\nThe permutation number is also called the _anagram index_."
},
{
"role": "assistant",
"content": "The anagram index."
}
] |
are.com/wiki/Vocabulary/Glossary#ExtendedInteger "Vocabulary/Glossary").
---
### Details
1\. A. y can be modeled as
```
ai =: (>:@i.@-@x:@# #. (+/@:< {.)\\.) @: (C.^:(2 1 {~ L.))
```
---
<table class="wikitable"><tbody><tr><td><tt>x A. y</tt></td><td>Anagram</td></tr></tbody></table>
[Rank 0 \_](https://code.... | acpadot.md | [
{
"role": "user",
"content": "What does x A. y do to the items of y?\n\nEvidence:\nx A. y reorders the items of y by applying the permutation of length #y whose permutation number is x."
},
{
"role": "assistant",
"content": "reorders the items of y by applying the permutation of length #y whose ... |
iki/Vocabulary/AET#Item "Vocabulary/AET") of y by applying the permutation of length #y whose permutation number is x.
A permutation of the letters of a word is called an _anagram_.
```
A. 2 3 1 0 NB. Calculate permutation number of a permutation
17
17 A. 'abcd' NB. Use it to permute abcd
cdba
2 ... | acpadot.md | [
{
"role": "user",
"content": "What is the permutation of length 6 with anagram index 26?\n\nEvidence:\n26 A. i. N NB. What is permutation having AI of 26?
0 2 1 4 3 5"
},
{
"role": "assistant",
"content": "0 2 1 4 3 5"
}
] |
0 2 1 4 3 5
A. 0 2 1 4 3 5 NB. permutation --> AI
26
```
2\. Generate all the distinct permutations of 4 items
```
n=: !N=: 4 NB. number of distinct permutations on N=4 points
(i.n) A. i. N NB. the permutations corresponding to the list of AI's: (i.n)
0 1 2 3
0 1 3 2
0 2 1 3
0 2 3 1
0 3 1 2
0 3 2... | acpadot.md | [
{
"role": "user",
"content": "What is the anagram index for the permutation 0 2 1 4 3 5?\n\nEvidence:\n0 2 1 4 3 5 A. 0 2 1 4 3 5 NB. permutation --> AI
26"
},
{
"role": "assistant",
"content": "26"
}
] |
lary/AET") of the anagram indexes of S4 (the symmetric group on 4 points) with their corresponding direct permutations
```
S4 NB. The AI's contained in S4
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
$ t=: S4 A. i NB. list of corresponding permutations
24 4
(,.S4) ; t
+--+-----... | acpadot.md | [
{
"role": "user",
"content": "What is the direct permutation corresponding to anagram index 5 in S4?\n\nEvidence:\n| 5|0 3 2 1|"
},
{
"role": "assistant",
"content": "0 3 2 1"
}
] |
3 1 2 0|
|22|3 2 0 1|
|23|3 2 1 0|
+--+-------+
```
### Details
1\. x A. i. y can be modeled as (though improvable)
```
del1=: \] ({.~ , \[ }.~ >:@\]) i.~
aiD =: (2 {:: ((0}.@{:: \]) ; 1&{:: ((del1~ {:); \]) 2&{:: , 1&{:: {~ 0 {.@{:: \])^:(0 < 0 #@{:: \])(^:\_)@:(i.@0: (, <)~ i.@\[ ;~ >:@i.@-@x:@\[ #. inv \]... | acpadot.md | [
{
"role": "user",
"content": "What does 5 aiD 95 return?\n\nEvidence:\n 5 aiD 95
3 4 2 1 0"
},
{
"role": "assistant",
"content": "3 4 2 1 0"
}
] |
# Vocabulary/adot - J Wiki
[\>>](https://code.jsoftware.com/wiki/Vocabulary/aco "Vocabulary/aco") [<<](https://code.jsoftware.com/wiki/Vocabulary/querydot "Vocabulary/querydot") [Back to: Vocabulary](https://code.jsoftware.com/wiki/NuVoc "NuVoc") [Thru to: Dictionary](https://www.jsoftware.com/help/dictionary/dadot.... | adot.md | [
{
"role": "user",
"content": "What is a. in the J language?\n\nEvidence:\nThe _alphabet_ of the J language — a built-in list of all [bytes](https://code.jsoftware.com/wiki/Vocabulary/Glossary#Byte "Vocabulary/Glossary")"
},
{
"role": "assistant",
"content": "The alphabet, a built-in list of all ... |
guage — a built-in list of all [bytes](https://code.jsoftware.com/wiki/Vocabulary/Glossary#Byte "Vocabulary/Glossary")
i.e. [atoms](https://code.jsoftware.com/wiki/Vocabulary/AET#Atom "Vocabulary/AET") of [type:](https://code.jsoftware.com/wiki/Vocabulary/Glossary#Type "Vocabulary/Glossary") [character](https://code.j... | adot.md | [
{
"role": "user",
"content": "What does $ a. return?\n\nEvidence:\n $ a.
256"
},
{
"role": "assistant",
"content": "256"
}
] |
.
256
```
Bytes 0 to 127 are (mostly) the [ASCII characters](https://en.wikipedia.org/wiki/ASCII "wikipedia:ASCII").
[Bytes](https://code.jsoftware.com/wiki/Vocabulary/Glossary#Byte "Vocabulary/Glossary") in J serve two purposes:
- To store [ASCII](https://code.jsoftware.com/wiki/Vocabulary/Glossary#ASCII "Vocabu... | adot.md | [
{
"role": "user",
"content": "What are bytes 0 to 127 mostly?\n\nEvidence:\nBytes 0 to 127 are (mostly) the [ASCII characters](https://en.wikipedia.org/wiki/ASCII "wikipedia:ASCII")."
},
{
"role": "assistant",
"content": "the ASCII characters"
}
] |
Vocabulary/Glossary") indexes 32 to 127)
- To store 8-bit bytes for interacting with external hardware and software.
Though a. is a simple [list](https://code.jsoftware.com/wiki/Vocabulary/AET#List "Vocabulary/AET"), **displaying** it is a challenge because only half of it contains displayable ASCII characters, and ... | adot.md | [
{
"role": "user",
"content": "Why is displaying the list a challenge?\n\nEvidence:\ndisplaying it is a challenge because only half of it contains displayable ASCII characters, and a quarter of the ASCII codes are control characters that mess up the display."
},
{
"role": "assistant",
"content": ... |
t and Input](https://code.jsoftware.com/wiki/Vocabulary/ScreenOutputInput "Vocabulary/ScreenOutputInput") for details.
**_Note:_** [Unicode characters](http://www.unicode.org/) may be stored in [character](https://code.jsoftware.com/wiki/Vocabulary/Glossary#Character "Vocabulary/Glossary") [nouns](https://code.jsoftwa... | adot.md | [
{
"role": "user",
"content": "Are bytes using UTF-8 encoding automatically recognized as representing Unicode characters in J?\n\nEvidence:\n_Bytes_ using UTF-8 encoding are **not** automatically recognized as representing Unicode characters; you must explicitly [convert them to unicode precision](https://c... |
plicitly [convert them to unicode precision](https://code.jsoftware.com/wiki/Vocabulary/uco#precision "Vocabulary/uco") using (u:).
---
### Common uses
1\. Find the _ASCII code(s)_ of any letter (or [string](https://code.jsoftware.com/wiki/Vocabulary/Glossary#String "Vocabulary/Glossary")). This **converts from char... | adot.md | [
{
"role": "user",
"content": "What is the result of executing a. i. 'AZaz09'?\n\nEvidence:\n a. i. 'AZaz09'
65 90 97 122 48 57"
},
{
"role": "assistant",
"content": "65 90 97 122 48 57"
}
] |
rstuvwxyz
a. {~ 48+i.10
0123456789
```
See the stdlib verbs: tolower and toupper for their use of this construct.
4\. Translate one set of characters to another
```
lc =: 'abcdefghijklmnopqrstuvwxyz'
uc =: 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'
tolow =: (lc,a.) {~ (uc,a.) i. \] NB. a. fills in the other charact... | adot.md | [
{
"role": "user",
"content": "What is the definition of the tolow verb using lc, uc and a.?\n\nEvidence:\n tolow =: (lc,a.) {~ (uc,a.) i. \] NB. a. fills in the other characters"
},
{
"role": "assistant",
"content": "tolow =: (lc,a.) {~ (uc,a.) i. \]"
}
] |
performance](https://code.jsoftware.com/wiki/Vocabulary/SpecialCombinations "Vocabulary/SpecialCombinations") include:
<table class="wikitable"><tbody><tr><td><b>What it does</b></td><td><b>Type;<br></b><p><b>Precisions;<br>Ranks</b></p></td><td><b><a title="Vocabulary/SpecialCombinations" href="/wiki/Vocabulary/Speci... | adot.md | [
{
"role": "user",
"content": "What benefit does using u&.(a.&i.) y provide for bitwise operations on bytes?\n\nEvidence:\navoids conversion to integer"
},
{
"role": "assistant",
"content": "avoids conversion to integer"
}
] |
</tr><tr><td><tt>(m b.)/&.(a.&i.) y</tt><p><tt>x (m b.)&.(a.&i.) y</tt></p></td><td><tt>m</tt> is 16 to 31</td></tr></tbody></table>
--- | adot.md | [
{
"role": "user",
"content": "What is the value range specified for m in the given expressions?\n\nEvidence:\n<tt>m</tt> is 16 to 31"
},
{
"role": "assistant",
"content": "16 to 31"
}
] |
# Vocabulary/ampdotco - J Wiki
[\>>](https://code.jsoftware.com/wiki/Vocabulary/query "Vocabulary/query") [<<](https://code.jsoftware.com/wiki/Vocabulary/ampco "Vocabulary/ampco") [Back to: Vocabulary](https://code.jsoftware.com/wiki/NuVoc "NuVoc") [Thru to: Dictionary](https://www.jsoftware.com/help/dictionary/d631... | amdotco.md | [
{
"role": "user",
"content": "What does the J conjunction [x] u&.:v y represent?\n\nEvidence:\n<tt>[x] u&.:v y</tt></td><td>Under</td><td>Conjunction</td></tr>"
},
{
"role": "assistant",
"content": "Under"
}
] |
THIS IMPORTANT?](https://code.jsoftware.com/wiki/Vocabulary/RankInfoIsImportant "Vocabulary/RankInfoIsImportant")
---
Executes v on the [argument](https://code.jsoftware.com/wiki/Vocabulary/AET#Argument "Vocabulary/AET")(s); then executes u on the [result](https://code.jsoftware.com/wiki/Vocabulary/Glossary#Result "V... | amdotco.md | [
{
"role": "user",
"content": "What is u&.:v equivalent to?\n\nEvidence:\nu&.:v is equivalent to v^:_1@:(u&:v). That is,"
},
{
"role": "assistant",
"content": "v^:_1@:(u&:v)"
}
] |
lent to v^:\_1@:(u&:v). That is,
```
u&.:v y <--> v^:\_1 u (v y)
x u&.:v y <--> v^:\_1 (v x) u (v y)
```
**Example:** Addition (+) _applied under_ logarithm (^.) gives multiplication
```
u =: +
v =: ^.
3 4 u&.:v 5 1
15 4
```
[Under (Dual)](https://code.jsoftware.com/wiki/Vocabulary/ampdot "... | amdotco.md | [
{
"role": "user",
"content": "What does addition applied under logarithm give according to the example?\n\nEvidence:\nAddition (+) _applied under_ logarithm (^.) gives multiplication"
},
{
"role": "assistant",
"content": "multiplication"
}
] |
## Common Uses
1\. Compute the Geometric Mean as: the Arithmetic Mean taken in the "log-domain"
```
y =: 2 4 8 16
mean =: +/ % # NB. The Arithmetic Mean of y
mean y
7.5
^ mean ^. y NB. The Geometric Mean: log (^.), then arithmetic mean, then antilog (^)
5.65685
mean&.:^. y ... | amdotco.md | [
{
"role": "user",
"content": "What does mean&.:^. y return for y =: 2 4 8 16?\n\nEvidence:\n mean&.:^. y
5.65685"
},
{
"role": "assistant",
"content": "5.65685"
}
] |
ean does not have [rank](https://code.jsoftware.com/wiki/Vocabulary/AET#Rank "Vocabulary/AET") 0, it has rank Infinity
```
mean b.0
\_ \_ \_
(mean&.^.) b.0
0 0 0
```
See below: **More Information (1.)**
2\. Compute _standard deviation_ as the root-mean-square of a [list](https://code.jsoftware.com/wiki/Vocabu... | amdotco.md | [
{
"role": "user",
"content": "What rank does mean have?\n\nEvidence:\nean does not have [rank](https://code.jsoftware.com/wiki/Vocabulary/AET#Rank "Vocabulary/AET") 0, it has rank Infinity"
},
{
"role": "assistant",
"content": "inf"
}
] |
um of squares of y
stddev 0 \_3 1 2
1.87083
```
3\. Compute Vector Length (Euclidean Length) in **R**<sup>n</sup>
```
u=. +/
v=. \*:
y=. 6 3 2
u &. v y NB. u is acting on each list item of v y (that wasn't the intension)
6 3 2
u &.: v y NB. u is acting on the result of v y (the whole l... | amdotco.md | [
{
"role": "user",
"content": "What is the result of u &.: v y for y=. 6 3 2 when computing vector length in J?\n\nEvidence:\nu &.: v y NB. u is acting on the result of v y (the whole list)
7"
},
{
"role": "assistant",
"content": "7"
}
] |
one argument, with the other argument being passed unchanged into u. This can be represented by a gerund form where a: indicates which argument is to be used unmodified:
- x u&.:(a:\`v) y is v^:\_1 x u (v y)
- x u&.:(v\`a:) y is v^:\_1 (v x) u y
```
1 +&.:(a:\`^.) 2 3
5.43656 8.15485
^ 1 + ^. 2 3
5.43656 8.1... | amdotco.md | [
{
"role": "user",
"content": "What is the result of evaluating 1 +&.:(a:\`^.) 2 3 ?\n\nEvidence:\n 1 +&.:(a:\`^.) 2 3
5.43656 8.15485"
},
{
"role": "assistant",
"content": "5.43656 8.15485"
}
] |
.jsoftware.com/wiki/Vocabulary/Glossary#Cell "Vocabulary/Glossary"), whereas u&.:v _applies_ u _under_ v to the entire argument(s) (x and) y.
--- | amdotco.md | [
{
"role": "user",
"content": "What does u&.:v apply u under v to?\n\nEvidence:\nwhereas u&.:v _applies_ u _under_ v to the entire argument(s) (x and) y."
},
{
"role": "assistant",
"content": "the entire argument(s) (x and) y"
}
] |
# Vocabulary/ampco - J Wiki
[\>>](https://code.jsoftware.com/wiki/Vocabulary/ampdotco "Vocabulary/ampdotco") [<<](https://code.jsoftware.com/wiki/Vocabulary/ampdot "Vocabulary/ampdot") [Back to: Vocabulary](https://code.jsoftware.com/wiki/NuVoc "NuVoc") [Thru to: Dictionary](https://www.jsoftware.com/help/dictionary... | ampco.md | [
{
"role": "user",
"content": "What is the name of the conjunction denoted by [x] u&:v y ?\n\nEvidence:\n<tt>[x] u&:v y</tt></td><td>Appose</td><td>Conjunction</tr></tbody></table>"
},
{
"role": "assistant",
"content": "Appose"
}
] |
THIS IMPORTANT?](https://code.jsoftware.com/wiki/Vocabulary/RankInfoIsImportant "Vocabulary/RankInfoIsImportant")
---
Applies verb v to each argument, and then applies verb u dyadically between the result(s).
```
u&:v y <--> u (v y)
x u&:v y <--> (v x) u (v y)
```
Example:
```
u =: < ... | ampco.md | [
{
"role": "user",
"content": "What is the expansion of x u&:v y according to the provided definition?\n\nEvidence:\nx u&:v y <--> (v x) u (v y)"
},
{
"role": "assistant",
"content": "(v x) u (v y)"
}
] |
erb u is executed either monadically or dyadically depending whether u&:v has been called monadically or dyadically .
See: **More Information** for a visual comparison of [At](https://code.jsoftware.com/wiki/Vocabulary/atco "Vocabulary/atco") (@:), [Atop](https://code.jsoftware.com/wiki/Vocabulary/at "Vocabulary/at")... | ampco.md | [
{
"role": "user",
"content": "What is recommended instead of the monadic use of &:?\n\nEvidence:\n**The monadic use of &: is deprecated. Use @: instead.**"
},
{
"role": "assistant",
"content": "Use @: instead."
}
] |
l code in places where f@:g is recognized, if only the monadic form of the compounds is eligible for special treatment.
2. u&:v is called for when the rank of v is less than the ranks of an argument, but you want to apply u to the **entire result** of v.
In the csm example above, we needed (&:) not (&)
```
\_1 2 ... | ampco.md | [
{
"role": "user",
"content": "In the csm example, why must (&:) be used instead of (&) in the expression +/@:<&:| ?\n\nEvidence:\nBecause | y has rank 0, the entire compound +/@:<&| is applied to each _atom_ of x and y, making the +/ useless since it now operates on each atom individually."
},
{
"... |
:<&| is applied to each _atom_ of x and y, making the +/ useless since it now operates on each atom individually.
---
[Atop](https://code.jsoftware.com/wiki/Vocabulary/at "Vocabulary/at") (@), [At](https://code.jsoftware.com/wiki/Vocabulary/atco "Vocabulary/atco") (@:), [Compose](https://code.jsoftware.com/wiki/Vocab... | ampco.md | [
{
"role": "user",
"content": "What does Compose (u&v) apply v to, in contrast to Appose?\n\nEvidence:\nContrast **Appose** (u&:v) with Compose (u&v) which applies v to **individual cell(s)** and then applies u on the **individual result(s)** of v"
},
{
"role": "assistant",
"content": "individual... |
dual result(s)** of v
An illustration of the process follows, extracted from the series of diagrams referenced below:
[](https://code.jsoftware.com/wiki/File:ApposeFlow.png "flow diagra... | ampco.md | [
{
"role": "user",
"content": "What is the notation for the Appose conjunction mentioned in the chunk?\n\nEvidence:\n**Appose** (u&:v) , [Compose](https://code.jsoftware.com/wiki/Vocabulary/ampv "Vocabulary/ampv") (u&v) , [At](https://code.jsoftware.com/wiki/Vocabulary/atco "Vocabulary/atco") (u@:v) , and [A... |
i/Vocabulary/at "Vocabulary/at") (u@v) are also visualized along with verb application and rank here: [a series of flow diagrams](https://code.jsoftware.com/wiki/File:CompositionConjunctions.png "File:CompositionConjunctions.png")
2\. So what's the difference between [Atop](https://code.jsoftware.com/wiki/Vocabulary/a... | ampco.md | [
{
"role": "user",
"content": "What is the difference between the dyads of Atop (@) and Compose (&)?\n\nEvidence:\nBut the _dyads_ are different:
```
x u&v y ↔ (v x) u (v y)
x u@v y ↔ u x v y
```"
},
{
"role": "assistant",
"content": "x u&v y ↔ (v x) u (v y) while x u@v y ↔ u x v y"
}
] |
y ↔ u v y
u@v y ↔ u v y
```
But the _dyads_ are different:
```
x u&v y ↔ (v x) u (v y)
x u@v y ↔ u x v y
```
According to the [J Dictionary](https://www.jsoftware.com/help/dictionary/d632.htm "jdic:d632") -- &: _is equivalent to_ & _except that the ranks of the resulting function are infinite; the relation i... | ampco.md | [
{
"role": "user",
"content": "According to the J Dictionary, how does &: relate to &?\n\nEvidence:\n&: _is equivalent to_ & _except that the ranks of the resulting function are infinite; the relation is similar to that between_ @: _and_ @"
},
{
"role": "assistant",
"content": "&: is equivalent t... |
# Vocabulary/ampdot - J Wiki
[\>>](https://code.jsoftware.com/wiki/Vocabulary/ampco "Vocabulary/ampco") [<<](https://code.jsoftware.com/wiki/Vocabulary/ampv "Vocabulary/ampv") [Back to: Vocabulary](https://code.jsoftware.com/wiki/NuVoc "NuVoc") [Thru to: Dictionary](https://www.jsoftware.com/help/dictionary/d631.htm... | ampdot.md | [
{
"role": "user",
"content": "What is u&.v equivalent to?\n\nEvidence:\nu&.v is equivalent to (u&.:v)"mv , where mv is the monadic rank of v."
},
{
"role": "assistant",
"content": "(u&.:v)"mv , where mv is the monadic rank of v"
}
] |
"Vocabulary/RankInfoIsImportant")
---
u&.v is equivalent to (u&.:v)"mv , where mv is the monadic rank of v. That is,
```
u&.v y <--> {{v^:\_1 u (v y)}}"mv y
x u&.v y <--> x {{v^:\_1 (v x) u (v y)}}"mv y
```
You should understand [Rank (")](https://code.jsoftware.com/wiki/Vocabulary/quote "Vocabulary/... | ampdot.md | [
{
"role": "user",
"content": "What is u&.v equivalent to?\n\nEvidence:\nu&.v is equivalent to (u&.:v)"mv , where mv is the monadic rank of v. That is,"
},
{
"role": "assistant",
"content": "(u&.:v)"mv , where mv is the monadic rank of v"
}
] |
ps://code.jsoftware.com/wiki/Vocabulary/ampdotco "Vocabulary/ampdotco") before trying to understand Under (Dual) (&.).
Executes u on the [argument](https://code.jsoftware.com/wiki/Vocabulary/AET#Argument "Vocabulary/AET")(s) with a temporary change of viewpoint, indicated by v. First v is executed, to move to the new ... | ampdot.md | [
{
"role": "user",
"content": "What are examples given for the temporary change of viewpoint operation?\n\nEvidence:\nlike Daylight Saving Time, or buying online in a different currency."
},
{
"role": "assistant",
"content": "like Daylight Saving Time, or buying online in a different currency."
... |
ssary") as defined by the [rank](https://code.jsoftware.com/wiki/Vocabulary/Glossary#Rank "Vocabulary/Glossary") of v:
- For each cell, u is applied to the [result](https://code.jsoftware.com/wiki/Vocabulary/Glossary#Result "Vocabulary/Glossary")(s) of v
- Then v^:\_1 (i.e. the [obverse](https://code.jsoftware.com... | ampdot.md | [
{
"role": "user",
"content": "What is applied to the result of u to give the result for that cell?\n\nEvidence:\nThen v^:\_1 (i.e. the [obverse](https://code.jsoftware.com/wiki/Vocabulary/Glossary#Obverse "Vocabulary/Glossary") of v) is applied to the [result](https://code.jsoftware.com/wiki/Vocabulary/Glos... |
ll "Vocabulary/Glossary")
Some v's can be undone even though as functions they may have no mathematical inverse.
Finally the [results](https://code.jsoftware.com/wiki/Vocabulary/Glossary#Result "Vocabulary/Glossary") for all [mv\-cells](https://code.jsoftware.com/wiki/Vocabulary/Glossary#Cell "Vocabulary/Glossar... | ampdot.md | [
{
"role": "user",
"content": "Can some v's be undone even though as functions they may have no mathematical inverse?\n\nEvidence:\nSome v's can be undone even though as functions they may have no mathematical inverse."
},
{
"role": "assistant",
"content": "Yes"
}
] |
tware.com/wiki/Vocabulary/FramingFill "Vocabulary/FramingFill") result(s) of v .
We say that u _is applied under_ v .
**Example:** Apply (i.) to the [contents](https://code.jsoftware.com/wiki/Vocabulary/Glossary#Contents "Vocabulary/Glossary") of each [box](https://code.jsoftware.com/wiki/Vocabulary/AET#Box "Vocabula... | ampdot.md | [
{
"role": "user",
"content": "What is the most common use of &.?\n\nEvidence:\n1\. The most common use of &. is \[x\] u&.> y which applies the verb u inside each box of the arguments. This follows the rules above: u&.> has rank 0 regardless of u, so each box is opened separately, operated on, and then rebox... |
es above: u&.> has rank 0 regardless of u, so each box is opened separately, operated on, and then reboxed.
Examples:
Convert a [list](https://code.jsoftware.com/wiki/Vocabulary/AET#List "Vocabulary/AET") of [boxed](https://code.jsoftware.com/wiki/Vocabulary/Glossary#Boxed "Vocabulary/Glossary") [strings](https://cod... | ampdot.md | [
{
"role": "user",
"content": "What does toupper&.> produce when applied to the boxed list z =: ;:'alpha bravo charlie'?\n\nEvidence:\n toupper&.> z
+-----+-----+-------+
|ALPHA|BRAVO|CHARLIE|
+-----+-----+-------+"
},
{
"role": "assistant",
"content": "+-----+-----+-------+
|ALPHA|BRAVO|CHARLI... |
r&.> z
+-----+-----+-------+
|ALPHA|BRAVO|CHARLIE|
+-----+-----+-------+
```
Add the contents of corresponding boxes
```
\]l =. 1;2 3;4 5 6
+-+---+-----+
|1|2 3|4 5 6|
+-+---+-----+
\]r =. 3 1 4;1 5;9
+-----+---+-+
|3 1 4|1 5|9|
+-----+---+-+
l +&.> r
+-----+---+--------+
|4 2 5|3 8|13 14 15|
+-----+---+---... | ampdot.md | [
{
"role": "user",
"content": "What does the standard library define the name each as?\n\nEvidence:\nThe standard library defines the name each as &.>"
},
{
"role": "assistant",
"content": "&.>"
}
] |
ed in ~system/main/stdlib.ijs- View the definition(s) in a JQt session by entering: open '~system/main/stdlib.ijs'
2\. A useful trick is to use each when one or more arguments are not boxed. Since \> y leaves y unchanged if it is not boxed, an unboxed argument will be processed as individual unboxed atoms:
```
... | ampdot.md | [
{
"role": "user",
"content": "\n\nEvidence:\n"
},
{
"role": "assistant",
"content": ""
}
] |
-------+
|103|101 104|101 105 109|
+---+-------+-----------+
```
---
### Semiduals x u&.(a:\`v) y and x u&.(v\`a:) y
The operation encapsulated by u&.v is used often and is important as a notation to aid thought. When the operation is dyadic, sometimes the sequence of transforming/operating/transforming back should ... | ampdot.md | [
{
"role": "user",
"content": "What does the gerund form with a: represent in the context of semiduals for dyadic operations?\n\nEvidence:\nThis can be represented by a gerund form where a: indicates which argument is to be used unmodified."
},
{
"role": "assistant",
"content": "It indicates whic... |
cates which argument is to be used unmodified. The form using &. is defined in terms of the infinite-rank version &.::
- x u&.(a:\`v) y is x u&.:(a:\`v)"(_lu,mv_) where _lu_ is the left rank of u and _mv_ is the monadic rank of v
- x u&.(v\`a:) y is x u&.:(v\`a:)"(_mv,ru_) where _ru_ is the right rank of u and _mv... | ampdot.md | [
{
"role": "user",
"content": "What does the NB. comment in the example say about the behavior of 100 200 +"_&.(a:`>) <"2 i. 3 2 4?\n\nEvidence:\n100 200 +"_&.(a:`>) <"2 i. 3 2 4 NB. open y (but not x), add x to each contents, rebox"
},
{
"role": "assistant",
"content": "open y (but not x), add ... |
--+---------------+
|100 101 102 103|108 109 110 111|116 117 118 119|
|204 205 206 207|212 213 214 215|220 221 222 223|
+---------------+---------------+---------------+
+"\_&.(a:\`>) b. 0 NB. This works because the left rank of u&.(a:\`v) comes from u
0 \_ 0
```
---
### Structural Under - u&.v y when v has no in... | ampdot.md | [
{
"role": "user",
"content": "Even when v has no inverse, under what condition may it be possible to define a notional inverse for u&.v y?\n\nEvidence:\nEven when v has no inverse, when v _rearranges_ or _selects from_ y, it may be possible to define a notional inverse that, referring to the value of y, rev... |
, reverses the effect of the rearrangement/selection. This surrogate inverse is defined for the following values of v:
<table class="wikitable"><tbody><tr><td><b><tt>v</tt></b></td><td><b>Inverse used<br></b></td><td><b>Description of operation<br></b></td></tr><tr><td><tt>,</tt></td><td><tt>($y)&($,)</tt></td><td... | ampdot.md | [
{
"role": "user",
"content": "What inverse is used when v is a comma (,)?\n\nEvidence:\n<tt>,</tt></td><td><tt>($y)&($,)</tt></td><td>Execute <tt>u</tt> on (<tt>,y</tt>), then put result into original shape of <tt>y</tt></td>"
},
{
"role": "assistant",
"content": "($y)&($,)"
}
] |
t>((+ i.)/@, m)}&y</tt></td><td>Execute <tt>u</tt> on selected cells of <tt>y</tt>, then put result back into those cells</td></tr></tbody></table>
- u&.(m&(\];.0)) y is the preferred idiom for applying u to a continuous subarray of y. The update may be performed in 0lace.
- If m&{ selects a contiguous section... | ampdot.md | [
{
"role": "user",
"content": "What is the preferred idiom for applying u to a continuous subarray of y?\n\nEvidence:\nu&.(m&(\];.0)) y is the preferred idiom for applying u to a continuous subarray of y. The update may be performed in 0lace."
},
{
"role": "assistant",
"content": "u&.(m&(\];.0)) ... |
-
[Under](https://code.jsoftware.com/wiki/Vocabulary/ampdotco "Vocabulary/ampdotco") (&.:)
---
### More Information
1\. Under (Dual) (&.) differs from [Under](https://code.jsoftware.com/wiki/Vocabulary/ampdotco "Vocabulary/ampdotco") (&.:) in that u&.v applies u under v [cell-by-cell](https://code.jsoftware.com/wi... | ampdot.md | [
{
"role": "user",
"content": "How does Under (Dual) (&.) differ from Under (&.:)?\n\nEvidence:\nUnder (Dual) (&.) differs from Under (&.:) in that u&.v applies u under v cell-by-cell, whereas u&.:v applies u under v to the entire argument(s) (x and) y ."
},
{
"role": "assistant",
"content": "u... |
performance](https://code.jsoftware.com/wiki/Vocabulary/SpecialCombinations "Vocabulary/SpecialCombinations") include:
<table class="wikitable"><tbody><tr><td><b>What it does</b></td><td><b>Type;<br></b><p><b>Precisions;<br>Ranks</b></p></td><td><b><a title="Vocabulary/SpecialCombinations" href="/wiki/Vocabulary/Speci... | ampdot.md | [
{
"role": "user",
"content": "What bug warning is given for using ,&.&>/ y to join contents of boxed items along the first axis?\n\nEvidence:\nBug warning: Atomic replication is inaccurate. OK if contents of same rank. Better to use <@; y"
},
{
"role": "assistant",
"content": "Atomic replication... |
use <tt><@; y</tt></td></tr><tr><td>Join contents of boxed items along last axis</td><td></td><td><tt>,.&.>/ y</tt></td><td></td><td></td></tr><tr><td rowspan="2">Bitwise operations on bytes</td><td rowspan="2">byte</td><td><tt>u&.(a.&i.) y</tt></td><td><tt>(u y) -: u"0 y</tt></td><td rowspan="2">avoi... | ampdot.md | [
{
"role": "user",
"content": "What J expression joins contents of boxed items along last axis?\n\nEvidence:\nJoin contents of boxed items along last axis</td><td></td><tt>,.&.>/ y</tt>"
},
{
"role": "assistant",
"content": ",.&.>/ y"
}
] |
# Vocabulary/ampm - J Wiki
[\>>](https://code.jsoftware.com/wiki/Vocabulary/ampv "Vocabulary/ampv") [<<](https://code.jsoftware.com/wiki/Vocabulary/atco "Vocabulary/atco") [Down to: Dyad](#dyadic) [Back to: Vocabulary](https://code.jsoftware.com/wiki/NuVoc "NuVoc") [Thru to: Dictionary](https://www.jsoftware.com/h... | ampm.md | [
{
"role": "user",
"content": "What is the rank of the Bond conjunction m&v y or u&n y?\n\nEvidence:\n[Rank Infinity](https://code.jsoftware.com/wiki/Vocabulary/RankInfo#rank "Vocabulary/RankInfo") _\-- operates on x and y as a whole --_"
},
{
"role": "assistant",
"content": "inf"
}
] |
Y IS THIS IMPORTANT?](https://code.jsoftware.com/wiki/Vocabulary/RankInfoIsImportant "Vocabulary/RankInfoIsImportant")
(m&v) makes a monad out of a dyad v by supplying the (noun) value m as the _left_ argument of v
(m&v y) is the same as (m v y)
```
triple =: 3&\*
i: 3
\_3 \_2 \_1 0 1 2 3
triple i: 3 NB. ... | ampm.md | [
{
"role": "user",
"content": "What does (m&v) do?\n\nEvidence:\n(m&v) makes a monad out of a dyad v by supplying the (noun) value m as the _left_ argument of v"
},
{
"role": "assistant",
"content": "It makes a monad out of a dyad v by supplying the (noun) value m as the left argument of v."
}
... |
a noun to a verb, creating a unit that bypasses processing by other modifiers. To prefix 'Mr. ' to each boxed string:
```
'Mr. '&, each 'Jones';'Smith';'Williams'
+---------+---------+------------+
|Mr. Jones|Mr. Smith|Mr. Williams|
+---------+---------+------------+
```
2\. Create a monad out of a dyad when one ... | ampm.md | [
{
"role": "user",
"content": "What rank does the Bond conjunction have, and what does it operate on?\n\nEvidence:\n[Rank 0 _](https://code.jsoftware.com/wiki/Vocabulary/RankInfo#rank0 "Vocabulary/RankInfo") _-- operates on atoms of x, and the entirety of y --_"
},
{
"role": "assistant",
"content... |
Y IS THIS IMPORTANT?](https://code.jsoftware.com/wiki/Vocabulary/RankInfoIsImportant "Vocabulary/RankInfoIsImportant")
> [](https://code.jsoftware.com/wiki/File:Warning.png) **This form has been removed from J Version 9.6 and later**
The dyad form appli... | ampm.md | [
{
"role": "user",
"content": "What is x m&v y equivalent to?\n\nEvidence:\nPhrase: x m&v y applies m&v to y repeatedly x times, and is equivalent to: x (m&v @ \] ^: \[) y"
},
{
"role": "assistant",
"content": "x (m&v @ \] ^: \[) y"
}
] |
# Vocabulary/ampv - J Wiki
[\>>](https://code.jsoftware.com/wiki/Vocabulary/ampdot "Vocabulary/ampdot") [<<](https://code.jsoftware.com/wiki/Vocabulary/ampm "Vocabulary/ampm") [Back to: Vocabulary](https://code.jsoftware.com/wiki/NuVoc "NuVoc") [Thru to: Dictionary](https://www.jsoftware.com/help/dictionary/d630n.ht... | ampv.md | [
{
"role": "user",
"content": "What is u&v equivalent to?\n\nEvidence:\nu&v is equivalent to (u&:v)"mv , where mv is the monadic rank of v."
},
{
"role": "assistant",
"content": "(u&:v)"mv , where mv is the monadic rank of v"
}
] |
t "Vocabulary/RankInfoIsImportant")
---
u&v is equivalent to (u&:v)"mv , where mv is the monadic rank of v. That is,
```
u&v y <--> {{u (v y)}}"mv y
x u&v y <--> x {{(v x) u (v y)}}"mv y
```
You should understand [Rank (")](https://code.jsoftware.com/wiki/Vocabulary/quote "Vocabulary/quote") and [App... | ampv.md | [
{
"role": "user",
"content": "What is u&v equivalent to?\n\nEvidence:\nu&v is equivalent to (u&:v)"mv , where mv is the monadic rank of v. That is,"
},
{
"role": "assistant",
"content": "(u&:v)"mv , where mv is the monadic rank of v."
}
] |
ll independently**.
```
('Ike';'James') >&#&> ('Newton';'Bond') NB. Is first name longer than last name?
0 1
```
This contrasts with u&:v which applies v to the entire argument(s) and then applies u on the entire [filled and assembled](https://code.jsoftware.com/wiki/Vocabulary/FramingFill "Vocabulary/FramingFil... | ampv.md | [
{
"role": "user",
"content": "How is operand v executed in the context of u&v?\n\nEvidence:\n- Operand v is executed monadically."
},
{
"role": "assistant",
"content": "monadically"
}
] |
erand u is executed either monadically or dyadically depending whether u&v has been called monadically or dyadically.
See: **More Information** for a visual comparison of [At](https://code.jsoftware.com/wiki/Vocabulary/atco "Vocabulary/atco") (@:), [Atop](https://code.jsoftware.com/wiki/Vocabulary/at "Vocabulary/at")... | ampv.md | [
{
"role": "user",
"content": "What is recommended as a replacement for the monadic use of &?\n\nEvidence:\nThe monadic use of & is deprecated. Use @ instead."
},
{
"role": "assistant",
"content": "Use @ instead."
}
] |
l code in places where f@g is recognized, if only the monadic form of the compounds is eligible for special treatment.
```
\*:&+: 3 4 5 NB. double, then square. Applied to each atom
36 64 100
\*: +: 3 4 5 NB. Same result if applied to entire list
36 64 100
+/&+: 3 4 5 NB. Double, then "total". Applied... | ampv.md | [
{
"role": "user",
"content": "What is the result of \*:&+: 3 4 5?\n\nEvidence:\n \*:&+: 3 4 5 NB. double, then square. Applied to each atom
36 64 100"
},
{
"role": "assistant",
"content": "36 64 100"
}
] |
--+
firstname ,&> lastname NB. Join each first name to last, individually
DennisRitchie
RichardStallman
KenIverson
(>firstname) , (>lastname) NB. very different applied to entire array
Dennis
Richard
Ken
Ritchie
Stallman
Iverson
firstname (>@\[ , >@\])"0 lastname NB. equivalent form
DennisRitchie
RichardS... | ampv.md | [
{
"role": "user",
"content": "In the J programming language, what is the output of firstname (>@\[ , >@\])"0 lastname when firstname contains Dennis Richard Ken and lastname contains Ritchie Stallman Iverson?\n\nEvidence:\n firstname (>@\[ , >@\])"0 lastname NB. equivalent form
DennisRitchie
RichardStall... |
(u v)), [Fork](https://code.jsoftware.com/wiki/Vocabulary/fork "Vocabulary/fork") ((f g h))
---
### More Information
1\. (\[x\] u&v y) is the same as (\[x\] u&:v"mv y) (where mv is the monadic rank of v).
The second phrase uses [Appose](https://code.jsoftware.com/wiki/Vocabulary/ampco "Vocabulary/ampco") (&:) inste... | ampv.md | [
{
"role": "user",
"content": "How is ([x] u&v y) equivalently expressed using Appose (&:)?\n\nEvidence:\n([x] u&v y) is the same as ([x] u&:v"mv y) (where mv is the monadic rank of v)."
},
{
"role": "assistant",
"content": "([x] u&:v"mv y) (where mv is the monadic rank of v)"
}
] |
ware.com/wiki/File:ComposeFlow.png "flow diagram of the compose conjunction")
flow diagram of the compose conjunction
**Compose** (u&v) , [Appose](https://code.jsoftware.com/wiki/Vocabulary/ampco "Vocabulary/ampco") (u&:v) , [Atop](https://code.jsoftware.com/wiki/Vocabulary/at "Vocabulary/at") (@) , and [At](https://... | ampv.md | [
{
"role": "user",
"content": "What's the difference between Atop (@) and Compose (&) for the monads?\n\nEvidence:\nNone at all, for the _monads_ (u@v) and (u&v)"
},
{
"role": "assistant",
"content": "None at all"
}
] |
ry/at") (@) and Compose (&) ?
None at all, for the _monads_ (u@v) and (u&v)
```
u&v y ↔ u v y
u@v y ↔ u v y
```
But the _dyads_ are different:
```
x u&v y ↔ (v x) u (v y)
x u@v y ↔ u x v y
```
According to the [J Dictionary](https://www.jsoftware.com/help/dictionary/d632.htm "jdic:d632") -- &: _is equiva... | ampv.md | [
{
"role": "user",
"content": "According to the chunk, what are the equivalences for the monads u&v y and u@v y?\n\nEvidence:\nNone at all, for the _monads_ (u@v) and (u&v)
```
u&v y ↔ u v y
u@v y ↔ u v y
```"
},
{
"role": "assistant",
"content": "None at all, for the _monads_ (u@v) and (u&... |
tements assume that u&v is applied at the rank mv as defined above.
The correct equivalences for u&v are given above.
2\. Note also that in u&f&v, f will be applied monadically. If the whole expression is called dyadically, then v is applied to each argument, f applied monadically to each result of v, and then u appl... | ampv.md | [
{
"role": "user",
"content": "In u&f&v called dyadically, how is f applied and what is the equivalent fork expression?\n\nEvidence:\nNote also that in u&f&v, f will be applied monadically. If the whole expression is called dyadically, then v is applied to each argument, f applied monadically to each result ... |
# Vocabulary/assertdot - J Wiki
[\>>](https://code.jsoftware.com/wiki/Vocabulary/breakdot "Vocabulary/breakdot") [<<](https://code.jsoftware.com/wiki/Vocabulary/zeroco "Vocabulary/zeroco") [Back to: Vocabulary](https://code.jsoftware.com/wiki/NuVoc "NuVoc") [Thru to: Dictionary](https://www.jsoftware.com/help/dictio... | assertdot.md | [
{
"role": "user",
"content": "According to the provided J Wiki chunk, inside what is the assert. control valid?\n\nEvidence:\nValid only inside an explicit definition."
},
{
"role": "assistant",
"content": "an explicit definition"
}
] |
plicit definition](https://code.jsoftware.com/wiki/Vocabulary/Glossary#ExplicitDefinition "Vocabulary/Glossary").
---
Signals [assertion failure](https://code.jsoftware.com/wiki/Vocabulary/ErrorMessages#assert "Vocabulary/ErrorMessages") if followed by a noun which is neither Boolean (1) nor an array: (1 1 1 …) of al... | assertdot.md | [
{
"role": "user",
"content": "What does assert. signal if followed by a noun which is neither Boolean nor an array of all 1's?\n\nEvidence:\nSignals assertion failure if followed by a noun which is neither Boolean (1) nor an array: (1 1 1 …) of all 1's."
},
{
"role": "assistant",
"content": "ass... |
or selected J phrases.
NB. The assertions must appear inside an explicit definition
NB. in this case an anonymous one.
3 : 0''
assert. (3j5) -: 3 j. 5
assert. (3j5 3j6) -: 3 j. 5 6
assert. (3j5 4j5) -: 3 4 j. 5
assert. 1 -: 2
assert. (3j5 4j6) -: 3 4 j. 5 6
)
```
The script will stop loading wi... | assertdot.md | [
{
"role": "user",
"content": "What error is shown and what happens when loading a J script that contains a failing assert. statement?\n\nEvidence:\nThe script will stop loading with an [assertion failure](https://code.jsoftware.com/wiki/Vocabulary/ErrorMessages#assert "Vocabulary/ErrorMessages") at the firs... |
-
### Details
Note that assert. is followed by a single sentence and is not paired with end. .
### More Information
Use the [Foreign](https://code.jsoftware.com/wiki/Vocabulary/Foreigns "Vocabulary/Foreigns") (9!:35) to disable _all_ assert.\-statements. Once disabled, the noun phrase following assert. is never eva... | assertdot.md | [
{
"role": "user",
"content": "How do you disable all assert.-statements?\n\nEvidence:\nUse the [Foreign](https://code.jsoftware.com/wiki/Vocabulary/Foreigns "Vocabulary/Foreigns") (9!:35) to disable _all_ assert.\-statements. Once disabled, the noun phrase following assert. is never evaluated."
},
{
... |
ON?│0│ y=│1│
└─┴──────────┴─┴───┴─┘
1 trial 0
┌─┬──────────┬─┬───┬─┐
│1│trial: ON?│0│ y=│0│
└─┴──────────┴─┴───┴─┘
(9!:35) 1 NB. switch asserts back ON
2 trial 1
┌─┬──────────┬─┬───┬─┐
│2│trial: ON?│1│ y=│1│
└─┴──────────┴─┴───┴─┘
3 trial 0
┌─┬──────────┬─┬───┬─┐
│3│trial: ON?│1│ y=│0│
└─┴──────────┴─┴─... | assertdot.md | [
{
"role": "user",
"content": "What command switches asserts back ON?\n\nEvidence:\n (9!:35) 1 NB. switch asserts back ON"
},
{
"role": "assistant",
"content": "(9!:35) 1"
}
] |
# Vocabulary/at - J Wiki
[\>>](https://code.jsoftware.com/wiki/Vocabulary/atdot "Vocabulary/atdot") [<<](https://code.jsoftware.com/wiki/Vocabulary/graveco "Vocabulary/graveco") [Back to: Vocabulary](https://code.jsoftware.com/wiki/NuVoc "NuVoc") [Thru to: Dictionary](https://www.jsoftware.com/help/dictionary/d620.h... | at.md | [
{
"role": "user",
"content": "What is u@v equivalent to?\n\nEvidence:\nu@v is equivalent to (u@:v)"v."
},
{
"role": "assistant",
"content": "(u@:v)"v"
}
] |
om/wiki/Vocabulary/RankInfoIsImportant "Vocabulary/RankInfoIsImportant")
---
u@v is equivalent to (u@:v)"v. That is,
```
u@v y <--> {{u (v y)}}"mv y
x u@v y <--> x {{u (x v y)}}"(lv,rv) y
```
where mv, lv, and rv are the monadic, left, and right ranks of v, respectively. You should understand [Rank (")](... | at.md | [
{
"role": "user",
"content": "What is u@v equivalent to?\n\nEvidence:\nu@v is equivalent to (u@:v)"v. That is,"
},
{
"role": "assistant",
"content": "(u@:v)"v"
}
] |
he _composition_ of verbs u and v; the resulting verb is applied **independently to each v\-cell of the argument(s)**.
This contrasts with u@:v which applies v to the entire argument(s) and then applies u on the entire [filled and assembled](https://code.jsoftware.com/wiki/Vocabulary/FramingFill "Vocabulary/FramingFil... | at.md | [
{
"role": "user",
"content": "How does the composition u@v apply the resulting verb compared to u@:v?\n\nEvidence:\nhe _composition_ of verbs u and v; the resulting verb is applied **independently to each v\-cell of the argument(s)**.
This contrasts with u@:v which applies v to the entire argument(s) and t... |
alled monadically or dyadically.
```
#@> 'Newton';'Einstein'
6 8
2 3 <@, 4 5
+-------+
|2 3 4 5|
+-------+
```
See: **More Information** for a visual comparison of [At](https://code.jsoftware.com/wiki/Vocabulary/atco "Vocabulary/atco") (@:), Atop (@), [Compose](https://code.jsoftware.com/wiki/Vocabulary/ampv "... | at.md | [
{
"role": "user",
"content": "What is the resulting verb u@n equivalent to when the right operand of @ is a noun n?\n\nEvidence:\nIf the right operand of @ is a noun n, the resulting verb u@n is equivalent to u@(n"\_") , where the constant verb (n"\_") ignores its argument(s) and produces the result n , whi... |
ent to u.
The resulting verb ignores its argument(s) and is customarily called with an empty array argument, e.g. ''.
```
greet=: echo@'hello'
greet''
hello
100 i.@4 'apple'
0 1 2 3
```
".@'name' is a good way to take the value of the noun name at the point of execution rather than the point of parsing.
... | at.md | [
{
"role": "user",
"content": "What is a good way to take the value of the noun name at the point of execution rather than the point of parsing?\n\nEvidence:\n.@'name' is a good way to take the value of the noun name at the point of execution rather than the point of parsing."
},
{
"role": "assistant... |
4 5 1
mean@cat z NB. mean of the ROWS of cat z
1 3.25
mean@cat b.0 NB. rank of (mean@cat)
1 1 1
```
You can also implement: _f(g(x))_ with: [Compose](https://code.jsoftware.com/wiki/Vocabulary/ampv "Vocabulary/ampv") (&) or [Cap](https://code.jsoftware.com/wiki/Vocabulary/squarelfco "Vocabulary/squa... | at.md | [
{
"role": "user",
"content": "What issue can arise when choosing between @ and @: (or similar methods) to implement f(g(x)) like mean@cat?\n\nEvidence:\nBut see [Rank in a hurry: an insidious rank problem] for how and when these different methods give different results."
},
{
"role": "assistant",
... |
"Vocabulary/EZRank") for how and when these different methods give different results.
---
### Should I use @ or @:?
Suppose your y is a list of boxes and you want to create a list of the number of items in the contents of each box. You want to apply # individually on the contents of each box, so you use @ to get
``... | at.md | [
{
"role": "user",
"content": "What is the result of #@> 4 5 6 7;1 2;3 ?\n\nEvidence:\n #@> 4 5 6 7;1 2;3
4 2 1"
},
{
"role": "assistant",
"content": "4 2 1"
}
] |
quares of all the numbers. You want to apply +/ to all the squares, so you use @: to get
```
+/@:\*: 3 4 5
50
```
If you used @, +/ would be applied on each result item of \*: - and because the rank of \*: is 0, you would be applying +/ on individual atoms:
```
+/@\* 3 4 5
9 16 25
```
---
[At](https://code.... | at.md | [
{
"role": "user",
"content": "What is the result of applying +/@:\*: to the list 3 4 5?\n\nEvidence:\n +/@:\*: 3 4 5
50"
},
{
"role": "assistant",
"content": "50"
}
] |
(u v)), [Fork](https://code.jsoftware.com/wiki/Vocabulary/fork "Vocabulary/fork") ((f g h))
---
### More Information
1\. Phrase (u@:v)"v means "apply v followed by u on each cell of the operand(s) independently". The rank of a cell is given by the rank of the verb v . The results from the cells are collected to pro... | at.md | [
{
"role": "user",
"content": "What does the phrase (u@:v)"v mean?\n\nEvidence:\nPhrase (u@:v)"v means "apply v followed by u on each cell of the operand(s) independently""
},
{
"role": "assistant",
"content": "apply v followed by u on each cell of the operand(s) independently"
}
] |
ode.jsoftware.com/wiki/File:AtopFlow.png "flow diagram of the atop conjunction")
flow diagram of the atop conjunction
**Atop** (u@v) , [At](https://code.jsoftware.com/wiki/Vocabulary/atco "Vocabulary/atco") (u@:v) , [Appose](https://code.jsoftware.com/wiki/Vocabulary/ampco "Vocabulary/ampco") (&:) , and [Compose](htt... | at.md | [
{
"role": "user",
"content": "What's the difference between Atop (@) and Compose (&) for the monads (u@v) and (u&v)?\n\nEvidence:\nNone at all, for the _monads_ (u@v) and (u&v)"
},
{
"role": "assistant",
"content": "None at all"
}
] |
lary/ampv "Vocabulary/ampv") (&) ?
None at all, for the _monads_ (u@v) and (u&v)
```
u&v y ↔ u v y
u@v y ↔ u v y
```
But the _dyads_ are different:
```
x u&v y ↔ (v x) u (v y)
x u@v y ↔ u x v y
```
According to the [J Dictionary](https://www.jsoftware.com/help/dictionary/d632.htm "jdic:d632") -- &: _is e... | at.md | [
{
"role": "user",
"content": "What is the definition of the dyad x u&v y?\n\nEvidence:\n x u&v y ↔ (v x) u (v y)"
},
{
"role": "assistant",
"content": "(v x) u (v y)"
}
] |
# Vocabulary/atco - J Wiki
[\>>](https://code.jsoftware.com/wiki/Vocabulary/ampm "Vocabulary/ampm") [<<](https://code.jsoftware.com/wiki/Vocabulary/atdot "Vocabulary/atdot") [Back to: Vocabulary](https://code.jsoftware.com/wiki/NuVoc "NuVoc") [Thru to: Dictionary](https://www.jsoftware.com/help/dictionary/d622.htm "... | atco.md | [
{
"role": "user",
"content": "What does the At conjunction form?\n\nEvidence:\nForms the _composition_ of two verbs u and v ."
},
{
"role": "assistant",
"content": "the composition of two verbs u and v"
}
] |
/Vocabulary/RankInfoIsImportant "Vocabulary/RankInfoIsImportant")
---
Forms the _composition_ of two verbs u and v .
```
u@:v y <--> u (v y)
x u@:v y <--> u (x v y)
```
The result is a tacit verb equivalent to u \[x\] v y (where \[x\] represents an optional x\-argument)
```
y =: i. 6 NB. a sample... | atco.md | [
{
"role": "user",
"content": "What does the composition of two verbs u and v using @: produce?\n\nEvidence:\nThe result is a tacit verb equivalent to u [x] v y (where [x] represents an optional x-argument)"
},
{
"role": "assistant",
"content": "A tacit verb equivalent to u [x] v y (where [x] re... |
:\*:@:- 2 2 2 NB. sum of squared differences
2
+/ \*: 1 2 3 - 2 2 2 NB. same thing, without using (@:)
2
```
See: **More Information** for a visual comparison of At (@:), [Atop](https://code.jsoftware.com/wiki/Vocabulary/at "Vocabulary/at") (@), [Compose](https://code.jsoftware.com/wiki/Vocabulary/ampv "Voca... | atco.md | [
{
"role": "user",
"content": "What is the result of evaluating mean@:cat z, where z is i.2 3, mean is defined as +/ % #, and cat is defined as ,&1"1?\n\nEvidence:\n mean@:cat z NB. mean of the COLUMNS of cat z
1.5 2.5 3.5 1"
},
{
"role": "assistant",
"content": "1.5 2.5 3.5 1"
}
] |
NB. appends 1 to each row of z
0 1 2 1
3 4 5 1
mean@:cat z NB. mean of the COLUMNS of cat z
1.5 2.5 3.5 1
mean@:cat b.0 NB. rank of (mean@:cat)
\_ \_ \_
```
But see [Rank in a hurry: an insidious rank problem](https://code.jsoftware.com/wiki/Vocabulary/EZRank#An_insidious_rank_problem "Vocabulary/EZRa... | atco.md | [
{
"role": "user",
"content": "What is the result of +/@:\*: 3 4 5?\n\nEvidence:\n +/@:\*: 3 4 5
50"
},
{
"role": "assistant",
"content": "50"
}
] |
\*: - and because the rank of \*: is 0, you would be applying +/ on individual atoms:
```
+/@\* 3 4 5
9 16 25
```
Suppose your y is a list of boxes and you want to create a list of the number of items in the contents of each box. You want to apply # individually on the contents of each box, so you use @ to get
`... | atco.md | [
{
"role": "user",
"content": "What is the result of #@> 4 5 6 7;1 2;3 and why?\n\nEvidence:\n #@> 4 5 6 7;1 2;3
4 2 1"
},
{
"role": "assistant",
"content": "4 2 1 because @ applies # individually on the contents of each box"
}
] |
boxes and join them together, then applying # just once on the assembled result:
```
#@:> 4 5 6 7;1 2;3
3
```
---
[Atop](https://code.jsoftware.com/wiki/Vocabulary/at "Vocabulary/at") (@), [Compose](https://code.jsoftware.com/wiki/Vocabulary/ampv "Vocabulary/ampv") (&), [Appose](https://code.jsoftware.com/wiki/Vo... | atco.md | [
{
"role": "user",
"content": "What is the result of evaluating the J expression #@:> 4 5 6 7;1 2;3 ?\n\nEvidence:\n #@:> 4 5 6 7;1 2;3
3"
},
{
"role": "assistant",
"content": "3"
}
] |
(u v)), [Fork](https://code.jsoftware.com/wiki/Vocabulary/fork "Vocabulary/fork") ((f g h))
---
### More Information
1\. Unlike [Atop](https://code.jsoftware.com/wiki/Vocabulary/at "Vocabulary/at") (@), the _rank_ of (u@:v) is infinite, irrespective of the ranks of v. This means that u will be executed on the entire... | atco.md | [
{
"role": "user",
"content": "How does the rank of (u@:v) compare to Atop (@)?\n\nEvidence:\nUnlike [Atop](https://code.jsoftware.com/wiki/Vocabulary/at "Vocabulary/at") (@), the _rank_ of (u@:v) is infinite, irrespective of the ranks of v."
},
{
"role": "assistant",
"content": "The rank of (u@:... |
y/FramingFill").
An illustration of this explanation follows, extracted from the series of diagrams referenced below:
[](https://code.jsoftware.com/wiki/File:AtFlow.png "flow diagram of the at conj... | atco.md | [
{
"role": "user",
"content": "What conjunction's flow diagram is extracted and shown from the series of diagrams?\n\nEvidence:\nflow diagram of the at conjunction"
},
{
"role": "assistant",
"content": "the at conjunction"
}
] |
application and rank here: [a series of flow diagrams](https://code.jsoftware.com/wiki/File:CompositionConjunctions.png "File:CompositionConjunctions.png")
2\. u@:v is called for when the rank of v is less than the ranks of an argument, but you want to apply u to the **entire result** of v.
Thus, in the "sum of squar... | atco.md | [
{
"role": "user",
"content": "Why is u@:v needed instead of u@v when the rank of v is less than the ranks of an argument?\n\nEvidence:\n2\. u@:v is called for when the rank of v is less than the ranks of an argument, but you want to apply u to the **entire result** of v."
},
{
"role": "assistant",
... |
pplied to each atom of x and y individually, making +/ useless because it is now applied to each number independently.
2\. So what's the difference between [Atop](https://code.jsoftware.com/wiki/Vocabulary/at "Vocabulary/at") (@) and [Compose](https://code.jsoftware.com/wiki/Vocabulary/ampv "Vocabulary/ampv") (&) ?
N... | atco.md | [
{
"role": "user",
"content": "What is the difference between the dyads x u&v y and x u@v y?\n\nEvidence:\n x u&v y ↔ (v x) u (v y)
x u@v y ↔ u x v y"
},
{
"role": "assistant",
"content": "x u&v y ↔ (v x) u (v y) while x u@v y ↔ u x v y"
}
] |
# Vocabulary/atdiff - J Wiki
2\. So what's the difference between [Atop](https://code.jsoftware.com/wiki/Vocabulary/at "Vocabulary/at") (@) and [Compose](https://code.jsoftware.com/wiki/Vocabulary/ampv "Vocabulary/ampv") (&) ?
None at all, for the _monads_ (u@v) and (u&v)
```
u&v y ↔ u v y
u@v y ↔ u v y
```
Bu... | atdiff.md | [
{
"role": "user",
"content": "What is the difference between the dyads of u&v and u@v?\n\nEvidence:\nBut the _dyads_ are different:
x u&v y ↔ (v x) u (v y)
x u@v y ↔ u x v y"
},
{
"role": "assistant",
"content": "x u&v y ↔ (v x) u (v y) while x u@v y ↔ u x v y"
}
] |
# Vocabulary/atdot - J Wiki
[\>>](https://code.jsoftware.com/wiki/Vocabulary/atco "Vocabulary/atco") [<<](https://code.jsoftware.com/wiki/Vocabulary/at "Vocabulary/at") [Back to: Vocabulary](https://code.jsoftware.com/wiki/NuVoc "NuVoc") [Thru to: Dictionary](https://www.jsoftware.com/help/dictionary/d621.htm "jdic:... | atdot.md | [
{
"role": "user",
"content": "What does the chunk say about the rank of m@.n?\n\nEvidence:\nNo rank - the result is a verb"
},
{
"role": "assistant",
"content": "No rank - the result is a verb"
}
] |
@.n</tt></td><td>Select From Agenda</td><td>Conjunction</td></tr></tbody></table>
No rank - the result is a verb
---
(m@.n) creates the entity defined by the n\-th atom from the _**agenda**_ m, which is a list of [atomic representations](https://code.jsoftware.com/wiki/Vocabulary/Glossary#AtomicRep "Vocabulary/Gloss... | atdot.md | [
{
"role": "user",
"content": "What does m@.n produce when m is a gerund and n=1?\n\nEvidence:\nm@.n NB. m@.n produces a verb
1:"
},
{
"role": "assistant",
"content": "1:"
}
] |
NB. The verb can be executed
1
```
---
### More Information
1\. n may be negative to count back from the end of m.
2\. If n is a list, a train of entities is created from the selected items of m.
```
m=: 0: \` 1: \` 2: \` 3:
m@.0 1
0: 1:
```
3\. If n is boxed, each level of boxing indicates a level of pare... | atdot.md | [
{
"role": "user",
"content": "If n is boxed in m@.n, what does each level of boxing indicate?\n\nEvidence:\n3\. If n is boxed, each level of boxing indicates a level of parentheses in the verb train"
},
{
"role": "assistant",
"content": "a level of parentheses in the verb train"
}
] |
table class="wikitable"><tbody><tr><td><tt>[x] m@.v y</tt></td><td>Agent</td><td>Conjunction</td></tr></tbody></table>
[Rank](https://code.jsoftware.com/wiki/Vocabulary/RankInfo#rankv "Vocabulary/RankInfo") _\-- depends on the rank of v --_ [WHY IS THIS IMPORTANT?](https://code.jsoftware.com/wiki/Vocabulary/RankInfoIs... | atdot.md | [
{
"role": "user",
"content": "What does [x] m@.v y use the result of executing [x-cell] v y-cell to select?\n\nEvidence:\nFor each cell, [x] m@.v y uses the result of executing [x-cell] v y-cell to select an atom of the _**agenda**_ m, which it then converts to a verb w and executes as [x-cell] w y-cell to ... |
**agenda**_ m, which it then converts to a verb w and executes as \[x-cell\] w y-cell to produce a cell of the result.
```
NB. 3 different verbs
soso =: {{
echo 'Your score was ', ": y
}}
good =: {{
echo 'Your score was ', ": y
echo 'Keep it up!'
}}
great =: {{
echo 'Your score was ', ": y
echo 'That''s fa... | atdot.md | [
{
"role": "user",
"content": "What is the output produced when the rate verb is applied to a score of 10?\n\nEvidence:\n rate 10
Your score was 10
That's fantastic!
Would you like to try again?"
},
{
"role": "assistant",
"content": "Your score was 10
That's fantastic!
Would you like to try aga... |
End of preview. Expand in Data Studio
My-J-Dataset-Msg
Made with ❤️ using 🦥 Unsloth Studiomy-j-dataset-chatml-v2 was generated with Unsloth Recipe Studio. It contains 4,998 generated records.
🚀 Quick Start
from datasets import load_dataset
# Load the main dataset
dataset = load_dataset("otisberg/my-j-dataset-msg", "data", split="train")
df = dataset.to_pandas()
📊 Dataset Summary
📈 Records: 4,998
📋 Columns: 3
✅ Completion: 100.0% (5,000 requested)
📋 Schema & Statistics
| Column | Type | Column Type | Unique (%) | Null (%) | Details |
|---|---|---|---|---|---|
messages |
string |
expression | 4856 (97.2%) | 0 (0.0%) | - |
⚙️ Generation Details
Generated with 4 column configuration(s):
expression: 1 column(s)
llm-structured: 1 column(s)
seed-dataset: 2 column(s)
📄 Full configuration available in builder_config.json and detailed metadata in metadata.json.
📚 Citation
If you use Data Designer in your work, please cite the project as follows:
@misc{nemo-data-designer,
author = {The NeMo Data Designer Team, NVIDIA},
title = {NeMo Data Designer: A framework for generating synthetic data from scratch or based on your own seed data},
howpublished = {\url{https://github.com/NVIDIA-NeMo/DataDesigner}},
year = 2026,
note = {GitHub Repository},
}
💡 About NeMo Data Designer
NeMo Data Designer is a general framework for generating high-quality synthetic data that goes beyond simple LLM prompting. It provides:
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- Relationship control between fields with dependency-aware generation
- Quality validation with built-in Python, SQL, and custom local and remote validators
- LLM-as-a-judge scoring for quality assessment
- Fast iteration with preview mode before full-scale generation
For more information, visit: https://github.com/NVIDIA-NeMo/DataDesigner (pip install data-designer)
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