otisberg/qwen3.6-27b-jdocs-cpt-gguf
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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... |
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 [list](https://code.jsoftware.com/wiki/Vocabulary/AET#List "Vocabulary/AET") of length _n_ is a _permutation_ if it cont... |
on: p
12
A. i NB. The AI of permutation: i (identity)
0
```
---
### Common uses
1\. Work conveniently with permutations, using 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,... |
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 bracketed in any order
```
\] 'a b c'=: 3 ? #S... |
jsoftware.com/wiki/Vocabulary/AET#Item "Vocabulary/AET") of S
```
S mul/ S NB. the Cayley Table of subgroup S
0 9 16 18
9 16 18 0
16 18 0 9
18 0 9 16
```
---
### More Information
1\. The permutation y can be expressed in either [cycle or direct form](https://code.jsoftware.com/wiki/Vocabulary/ccapd... |
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.jsoftware.com/wiki/Vocabulary/RankInfo#rank0 "Vocabulary/RankInfo") _\-- operates on atoms of x,... |
anagram index (AI) x.
```
N =: 6 NB. length of permutation
26 A. i. N NB. What is permutation having AI of 26?
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... |
3\. Build a [table](https://code.jsoftware.com/wiki/Vocabulary/AET#Table "Vocabulary/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... |
# 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.... |
tware.com/wiki/Vocabulary/Glossary#Precision "Vocabulary/Glossary").
```
$ a.
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... |
e ASCII codes are control characters that mess up the display. See [Screen Output 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/V... |
tring](https://code.jsoftware.com/wiki/Vocabulary/Glossary#String "Vocabulary/Glossary")). This **converts from characters to numbers**
```
a. i. 'A'
65
a. i. 'AZaz09'
65 90 97 122 48 57
```
2\. Find the letter for a given _ASCII code_
```
65 { a.
A
```
3\. Make lists of the _ASCII roman alphabet_, upper... |
Use These Combinations
Combinations using a. y that have [exceptionally good 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></t... |
# 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... |
nk_~ "Vocabulary/RankInfo") _\-- operates on \[x and\] y as a whole --_ [WHY IS 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... |
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 "Vocabulary/ampdot") (&.) happens to give the same answer as (... |
*Note:** [Under (Dual)](https://code.jsoftware.com/wiki/Vocabulary/ampdot "Vocabulary/ampdot") (&.) **does not give the same answer** as (&.:)
```
mean&.:^. y
5.65685
mean&.^. y
2 4 8 16
```
Contrast this with the above Example of addition under logarithm.
This is because mean does not have [rank](https://cod... |
NB. square of y
stddev =: u&.:v NB. square root of mean of sum 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 ... |
s v^:\_1 (v x) u y
```
1 +&.:(a:\`^.) 2 3
5.43656 8.15485
^ 1 + ^. 2 3
5.43656 8.15485
```
---
[Under (Dual)](https://code.jsoftware.com/wiki/Vocabulary/ampdot "Vocabulary/ampdot") (&.)
---
### More Information
1\. [Under (Dual)](https://code.jsoftware.com/wiki/Vocabulary/ampdot "Vocabulary/ampdot") (&.) dif... |
# 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... |
``
u =: < NB. x is smaller than y
v =: | NB. magnitude
csm =: +/ @: u &: v NB. Count how many x's are smaller than y in magnitude
\_1 2 0 csm 2 \_3 0
2
```
- Verb v is executed monadically.
- Verb u is executed either monadically or dyadically depending whether u&:v ... |
l 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 0 +/@:<&:| 2 \_3 0 NB. "csm" example as an anonymous verb in a 1-liner
2
\_1 2 0 +/@:<&| 2 \_3 0 ... |
ulary/fork") ((f g h))
---
### More Information
1\. Contrast **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
An illustration of the process follows, extracted from the series of diagrams referenced below:
[
2\. So what's the difference between [Atop](https://code.jsoftware.com/wiki/Vocabulary/at "Vocabulary/at") (@) and [Compo... |
# 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... |
/Vocabulary/quote "Vocabulary/quote") and [the rankless form of Under (&.:)](https://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 tempora... |
[cell](https://code.jsoftware.com/wiki/Vocabulary/Glossary#Cell "Vocabulary/Glossary") 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/Gl... |
de.jsoftware.com/wiki/Vocabulary/Glossary#Cell "Vocabulary/Glossary") are [collected](https://code.jsoftware.com/wiki/Vocabulary/FramingFill#Collection "Vocabulary/FramingFill") into the end result.
This contrasts with u&.:v which applies v to the entire argument(s) and then applies v^:\_1@:u on the entire [filled and... |
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 reboxed.
Examples:
Convert a [list](https://code.jsoftware.com/wiki/Vocabulary/AET#List "Vocabulary/AET") of [boxed](https://code.jsoftware.... |
-----+---+--------+
```
The standard library defines the name each as &.>
```
(<'Mr. ') , each 'Smith';'Jones'
+---------+---------+
|Mr. Smith|Mr. Jones|
+---------+---------+
```
each is a
- [Standard Library](http://www.jsoftware.com/help/user/library.htm) word(s) residing in the 'z'-locale
- Defined in... |
+----+
100 + each 3;1 4;1 5 9 NB. Add 100 inside each box
+---+-------+-----------+
|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 dy... |
---+
|0 1 2 3| 8 9 10 11|16 17 18 19|
|4 5 6 7|12 13 14 15|20 21 22 23|
+-------+-----------+-----------+
100 200 +"\_&.(a:\`>) <"2 i. 3 2 4 NB. open y (but not x), add x to each contents, rebox
+---------------+---------------+---------------+
|100 101 102 103|108 109 110 111|116 117 118 119|
|204 205 206 207|212... |
t may be possible to define a notional inverse that, referring to the value of y, 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 oper... |
) 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 of y, the update may be performed in place.
---
[Under](https://code.jsoftware.com/wiki/Vocabulary/ampdotco "Vocabulary/ampdotco") (&.:)
---
### More Information
1\.... |
Use These Combinations
Combinations using &. y that have [exceptionally good 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></t... |
<td><tt>u&.(a.&i.) y</tt></td><td><tt>(u y) -: u"0 y</tt></td><td rowspan="2">avoids conversion to integer</td></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>
--- |
# 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... |
\_6 \_3 0 3 6 9
```
Conversely...
(u&n) makes a monad out of a dyad u by supplying the (noun) value n as the _right_ argument of u
(u&n y) is the same as (y u n)
```
i:3
\_3 \_2 \_1 0 1 2 3
gt0=: >&0
gt0 i:3 NB. Same as (i:3) > 0
0 0 0 0 1 1 1
```
---
### Common Uses
1\. Weld a noun to a verb, creati... |
Vocabulary/RankInfo") _\-- operates on atoms of x, and the entirety of y --_ [WHY IS THIS IMPORTANT?](https://code.jsoftware.com/wiki/Vocabulary/RankInfoIsImportant "Vocabulary/RankInfoIsImportant")
> [](https://code.jsoftware.com/wiki/File:Warning.png) ... |
# 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... |
(https://code.jsoftware.com/wiki/Vocabulary/quote "Vocabulary/quote") and [Appose (&:)](https://code.jsoftware.com/wiki/Vocabulary/ampco "Vocabulary/ampco") before trying to understand Compose (&) .
Applies v to each **mv\-cell** of each argument, and then applies u to the result(s) of v **for each mv\-cell independen... |
https://code.jsoftware.com/wiki/Vocabulary/at "Vocabulary/at") (@), Compose (&) and [Appose](https://code.jsoftware.com/wiki/Vocabulary/ampco "Vocabulary/ampco") (&:).
---
### Common Uses
Monadic
**The monadic use of & is deprecated. Use @ instead.** Some compounds of the form f&g are not recognized for special cod... |
Same result if applied to entire list
36 64 100
+/&+: 3 4 5 NB. Double, then "total". Applied to each atom.
6 8 10
+/ +: 3 4 5 NB. Not the same if applied to entire list!
24
```
Dyadic
```
\]firstname =: 'Dennis';'Richard';'Ken'
+------+-------+---+
|Dennis|Richard|Ken|
+------+-------+---+
\]lastna... |
"Vocabulary/ampco") (&:), [Hook](https://code.jsoftware.com/wiki/Vocabulary/hook "Vocabulary/hook") ((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... |
iki/images/thumb/f/f1/ComposeFlow.png/900px-ComposeFlow.png)](https://code.jsoftware.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:... |
(@) 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 equivalent to_... |
# 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... |
lean (1) or an array: (1 1 1 …) of all 1's.
---
### Common Uses
1\. Check that the argument y is Boolean, else signal an error
```
assert. y e. 0 1
```
2\. Write a test-script for an addon.
```
NB. Test script for selected J phrases.
NB. The assertions must appear inside an explicit definition
NB. in this cas... |
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.
Use the [Foreign](https://code.jsoftware.com/wiki/Vocabulary/Foreigns "Vocabulary/Foreigns") (9!:34) to discover if asse... |
# 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... |
Rank (")](https://code.jsoftware.com/wiki/Vocabulary/quote "Vocabulary/quote") and [At (@:)](https://code.jsoftware.com/wiki/Vocabulary/atco "Vocabulary/atco") before trying to understand Atop (@) .
Forms the _composition_ of verbs u and v; the resulting verb is applied **independently to each v\-cell of the argument(... |
ose](https://code.jsoftware.com/wiki/Vocabulary/ampv "Vocabulary/ampv") (&) and [Appose](https://code.jsoftware.com/wiki/Vocabulary/ampco "Vocabulary/ampco") (&:).
---
### Noun right operand (u@n)
If the right operand of @ is a noun n, the resulting verb u@n is equivalent to u@(n"\_) , where the constant verb (n"\_)... |
e noun
0 1 2
3 4 5
cat z NB. appends 1 to each row of z
0 1 2 1
3 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") (&)... |
#@> 4 5 6 7;1 2;3
4 2 1
```
If you used @:, the interpreter would open all the boxes and join them together, then applying # just once on the assembled result:
```
#@:> 4 5 6 7;1 2;3
3
```
Suppose your y is a list of numbers and you want to total of the squares of all the numbers. You want to apply +/ to all th... |
&:), [Hook](https://code.jsoftware.com/wiki/Vocabulary/hook "Vocabulary/hook") ((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 g... |
ware.com/mediawiki/images/thumb/e/ec/AtopFlow.png/900px-AtopFlow.png)](https://code.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.... |
cabulary/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 equivalent to_... |
# 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 "... |
. a sample list (the contents don't matter)
<: # y NB. count the items in y and subtract 1
5
compo =: <:@:# NB. Make a new verb: the "composition" of (<:) and (#)
compo y
5
```
You can safely chain verbs using (@:) with minimal need for parentheses
```
1 2 3 +/@:\*:@:- 2 2 2 NB. sum of squa... |
4 5
cat z 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_... |
ach box, so you use @ to get
```
#@> 4 5 6 7;1 2;3
4 2 1
```
If you used @:, the interpreter would open all the 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") (@), [Compos... |
ed](https://code.jsoftware.com/wiki/Vocabulary/FramingFill#Collection "Vocabulary/FramingFill").
An illustration of this explanation follows, extracted from the series of diagrams referenced below:
[![flow diagram of the at conjunction](https://code.jsoftware.com/mediawiki/images/thumb/4/44/AtFlow.png/900px-AtFlow.pn... |
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 squared-differences" example in the introduction, we needed (@:) not (@)
```
1 2 3 +/@:\*:@:- 2 2 2
2
1 2 3 +/@\*:@- 2 2 2 NB. different result using (@) in place of (@:)
1 0 1
```
... |
# 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... |
# 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:... |
able sample verbs
n=: 1
m@.n NB. m@.n produces a verb
1:
(m@.n) '' 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@.... |
RankInfo#rankv "Vocabulary/RankInfo") _\-- depends on the rank of v --_ [WHY IS THIS IMPORTANT?](https://code.jsoftware.com/wiki/Vocabulary/RankInfoIsImportant "Vocabulary/RankInfoIsImportant")
---
For each cell, \[x\] m@.v y uses the result of executing \[x-cell\] v y-cell to select an atom of the _**agenda**_ m, wh... |
each cell of the arguments. Give v the appropriate rank.
```
(%&2)\`(1+3&\*)@.(2&|)"0\] 1 2 3 4 NB. Divide by 2 if even, triple and add one if odd - checking each atom separately
4 1 10 2
```
2\. To select and apply a verb according to the first test that the argument passes, akin to a series of if./else. statem... |
test2.
3\. To select and apply a verb according to the argument's value, akin to the select./case. control words.
```
'b' (1+\])\`(3$\])\`(2\*\])\`('default'"\_)@.('abc' i. \[) 10
10 10 10
```
4\. To select and apply a verb according to the interval which contains the argument.
```
%:\`-:\`+:\`%@.(10 50 90&I... |
t list of cells. This single application of the gerund must produce one result for each implied cell. The results are assembled, using the original order of the implied cells, into the final result.
The implied rank is \-#$ \[x\] v y, in other words the rank of \[x\]/y minus the rank of v y. Each gerund of m needs to ... |
8
1600 1681 1764 1849 1936 2025 2116 2209 2304 2401
```
v y produces a list of 5 numbers, making the implied rank 1. The verbs in m were applied on lists or tables, and the results were assembled.
```
(+/"1)\`(<./"1)\`(>./"1)@.((3&|)@:(+/)"1) i. 10 10
45 10 29 345 40 59 645 70 89 945
((3&|)@:(+/)"1) i. 10 10
0... |
m.
4\. If (\[x\] v y) has few atoms, the interpreter may choose to execute the gerunds of m on individual cells of the arguments instead of on lists of those cells.
---
### Use These Combinations
Combinations using \[x\] u@.v y that have [exceptionally good performance](https://code.jsoftware.com/wiki/Vocabulary/Sp... |
# Vocabulary/bang - J Wiki
[\>>](https://code.jsoftware.com/wiki/Vocabulary/bangdot "Vocabulary/bangdot") [<<](https://code.jsoftware.com/wiki/Vocabulary/numberco "Vocabulary/numberco") [Down to: Dyad](#dyadic) [Back to: Vocabulary](https://code.jsoftware.com/wiki/NuVoc "NuVoc") [Thru to: Dictionary](https://www.j... |
ps and step size \_1: n ^!.\_1 n .
```
\*/ 5 4 3 2 1 NB. product (5th 'falling power' of 5)
120
! 5 NB. gets abbreviated
120
! i.6 NB. 0! = 1
1 1 2 6 24 120
```
More generally, it computes the _[Gamma function](https://en.wikipedia.org/wiki/Gamma_function "wikipedia:Gamma function... |
ential function, monad
NB. calculating the (positive) intersections of exp(y)and ga(y) by
NB. solving exp(y)- ga(y)= 0 numerically, using Newton-Raphson
NB. with seed values 1 and 10, resp
(exp-ga) VN^:\_ (1) NB. IP4=~ (0.52;1.69)
0.524922
ga (exp-ga) VN^:\_ (1)
1.69033
(exp-ga) VN^:\_ (10) ... |
``
10!10 NB. There is only 1 way of picking all 10 balls
1
1!10 NB. There are 10 ways of choosing 1 ball from 10
10
2!10 NB. 45 ways to pick 2 out of 10
45
5!10
252
```
This example was found in K.E. Iverson, Computers and Mathematical Notation, [E. Ambivalence](http://www.jsoftware.com/p... |
In general x ! y is defined as (!y) % (!x) \* (!(y-x)) .
[Stope Function](https://code.jsoftware.com/wiki/Vocabulary/hat#stope "Vocabulary/hat") (^!.\_1 y) to count permutations.
---
### See Also
[John D. Cook, Binomial Coefficients](http://www.johndcook.com/blog/binomial_coefficients/) discusses the domain of this... |
# Vocabulary/bangco - J Wiki
[\>>](https://code.jsoftware.com/wiki/Vocabulary/slash "Vocabulary/slash") [<<](https://code.jsoftware.com/wiki/Vocabulary/bangdot "Vocabulary/bangdot") [Back to: Vocabulary](https://code.jsoftware.com/wiki/NuVoc "NuVoc") [Thru to: Dictionary](https://www.jsoftware.com/help/dictionary/d4... |
ode.jsoftware.com/wiki/Vocabulary/AET#Box "Vocabulary/AET") or displaying the definitions of verbs and [modifiers](https://code.jsoftware.com/wiki/Vocabulary/Glossary#Modifier "Vocabulary/Glossary")
- managing [locales](https://code.jsoftware.com/wiki/Vocabulary/AET#Locale "Vocabulary/AET") and reporting on their st... |
code.jsoftware.com/wiki/File:Important.png) **For a detailed catalog of m and n in table form, see [Vocabulary/Foreigns](https://code.jsoftware.com/wiki/Vocabulary/Foreigns "Vocabulary/Foreigns").**
To execute any [verb](https://code.jsoftware.com/wiki/Vocabulary/AET#Verb "Vocabulary/AET") at all in J, you need to cal... |
e names, [noun](https://code.jsoftware.com/wiki/Vocabulary/AET#Noun "Vocabulary/AET") [phrases](https://code.jsoftware.com/wiki/Vocabulary/Glossary#Phrase "Vocabulary/Glossary") to be analysed, etc.
- Some **Foreigns** need an x\-[argument](https://code.jsoftware.com/wiki/Vocabulary/AET#Argument "Vocabulary/AET") to... |
949.ijs'
```
3\. Signal your own invented error message with any choice of error number (1 to 255)
See: [13!: Debug](https://code.jsoftware.com/wiki/Vocabulary/Foreigns#m13 "Vocabulary/Foreigns")
```
'my error message' (13!:8) 255
|my error message
| 'my error message' (13!:8)255
```
---
### Use These Com... |
# Vocabulary/bangdot - J Wiki
[\>>](https://code.jsoftware.com/wiki/Vocabulary/bangco "Vocabulary/bangco") [<<](https://code.jsoftware.com/wiki/Vocabulary/bang "Vocabulary/bang") [Back to: Vocabulary](https://code.jsoftware.com/wiki/NuVoc "NuVoc") [Thru to: Dictionary](https://www.jsoftware.com/help/dictionary/d411.... |
wiki/Vocabulary/AET#Noun "Vocabulary/AET")) [operand](https://code.jsoftware.com/wiki/Vocabulary/AET#Operand "Vocabulary/AET") n.
Only when u is one of these primitives can it be customized with !.
<table class="wikitable"><tbody><tr><td>monadic</td><td><tt>*</tt></td><td>Adjust the Absolute Tolerance to (<tt>n</tt>)... |
<tr><td>monadic</td><td><tt>+/</tt></td><td><tt>+/!.0</tt> uses <a title="Vocabulary/AccurateAccumulation" href="/wiki/Vocabulary/AccurateAccumulation"><i><b>compensated summation</b></i></a> for the summation</td></tr><tr><td>dyadic</td><td><tt>+/@:*"1</tt></td><td><tt>+/@:*"1!.0</tt> uses <a title="Vocabulary/Accurat... |
In many cases specifying intolerant comparison causes the interpreter to use faster code.
To guarantee using the faster code v must be specified as 0 or (0), **not** as an equivalent numeric value.
2\. Alter the _comparison tolerance_ of a number primitive, e.g. [Equal](https://code.jsoftware.com/wiki/Vocabulary/eq "... |
NB. Default tolerance is much smaller: 2^\_44
0
2 (=!.n) 2+n NB. But (=!.n) treats 2 and (2+n) as equal
1
2 (=!.n) 2+n+n NB. Still equal! (See below)
1
2 (=!.n) 2+n+n+n
0
```
**_Note:_** J will not accept values of n greater than 2^\_34 . To learn why not, see [Essays/Tolerant Comparison](https://co... |
'a' ,:!.'\*' 'abc'
aaa
abc
```
5\. +/!.0 y uses Kahan's [_compensated summation_](https://en.wikipedia.org/wiki/Kahan_summation_algorithm) algorithm. This gives more accurate totals for long sums.
6\. When a verb operates on an arguments whose rank is higher than the verb's, the verb is executed on each cell separat... |
# Vocabulary/bar - J Wiki
[\>>](https://code.jsoftware.com/wiki/Vocabulary/bardot "Vocabulary/bardot") [<<](https://code.jsoftware.com/wiki/Vocabulary/tildeco "Vocabulary/tildeco") [Down to: Dyad](#dyadic) [Back to: Vocabulary](https://code.jsoftware.com/wiki/NuVoc "NuVoc") [Thru to: Dictionary](https://www.jsoftw... |
oftware.com/wiki/Vocabulary/Glossary#Numeric "Vocabulary/Glossary") y. If y is [complex](https://code.jsoftware.com/wiki/Vocabulary/Glossary#Complex "Vocabulary/Glossary"), |y is the magnitude of y.
```
|5
5
|\_5 NB. absolute value
5
i:3
\_3 \_2 \_1 0 1 2 3
|i:3 NB. absolute ... |
maginary \* Complex](https://code.jsoftware.com/wiki/Vocabulary/jdot "Vocabulary/jdot") (j.), [Circle Functions](https://code.jsoftware.com/wiki/Vocabulary/odot "Vocabulary/odot") (x o. y), [Angle \* Polar](https://code.jsoftware.com/wiki/Vocabulary/rdot "Vocabulary/rdot") (r.)
---
<table class="wikitable"><tbody><tr... |
2\. Detect perfect multiples in a given list of numbers
```
0= 3 | i.7
1 0 0 1 0 0 1
```
---
[Antibase](https://code.jsoftware.com/wiki/Vocabulary/numberco "Vocabulary/numberco") ((0,x) #: y)
---
### More Information
1\. If you want both the quotient and remainder from a division, look at [Antibase](https://co... |
as x, x if y has opposite sign, 0 if y=0.
- if x is [complex](https://code.jsoftware.com/wiki/Vocabulary/Glossary#Complex "Vocabulary/Glossary") it may not have an infinite real or imaginary part.
3\. There is an implied [tolerant comparison](https://code.jsoftware.com/wiki/Vocabulary/Glossary#TolerantComp "Vocabula... |
Use These Combinations
Combinations using x | y that have [exceptionally good 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></t... |
# Vocabulary/barco - J Wiki
[\>>](https://code.jsoftware.com/wiki/Vocabulary/dot "Vocabulary/dot") [<<](https://code.jsoftware.com/wiki/Vocabulary/bardot "Vocabulary/bardot") [Down to: Dyad](#dyadic) [Back to: Vocabulary](https://code.jsoftware.com/wiki/NuVoc "NuVoc") [Thru to: Dictionary](https://www.jsoftware.co... |
xing array
\]y=: ii 2 3 4 NB. sample value of shape: 2 3 4
0 1 2 3
10 11 12 13
20 21 22 23
100 101 102 103
110 111 112 113
120 121 122 123
$ y
2 3 4
$ |:y
4 3 2
|:y
0 100
10 110
20 120
1 101
11 111
21 121
2 102
12 112
22 122
3 103
13 113
23 123
```
---
### Common uses
... |
")
---
Rearranges the [axes](https://code.jsoftware.com/wiki/Vocabulary/Glossary#Axis "Vocabulary/Glossary") of an [array](https://code.jsoftware.com/wiki/Vocabulary/AET#Array "Vocabulary/AET") y.
- (x is an atom) — the axis having index x becomes the new last axis
- (x is a list) — the axes having indices x bec... |
epeat with a higher-rank y
```
$ y=: ii 2 3 4 5 6
2 3 4 5 6
x =: 2 1 NB. axes with sizes 4 and 3 respectively become the last axes
$ x |: y
2 5 6 4 3
```
---
### More Information
1. Use [a special form](https://code.jsoftware.com/wiki/Vocabulary/Idioms#Extract_The_Diagonal_Of_A_Table "Vocabulary/I... |
ering the [axes](https://code.jsoftware.com/wiki/Vocabulary/Glossary#Axis "Vocabulary/Glossary") of an [array](https://code.jsoftware.com/wiki/Vocabulary/AET#Array "Vocabulary/AET") has two effects:
- The [index](https://code.jsoftware.com/wiki/Vocabulary/Glossary#Index "Vocabulary/Glossary") [lists](https://code.js... |
ollowing meanings:
axis 0 - the school
axis 1 - grade level
axis 2 - sex of students
axis 3 - core subject
axis 4 - a list of information for a given combination of school/grade/sex/subject
Each axis has associated with it an interpretation of the [index](https://code.jsoftware.com/wiki/Vocabulary/Glossary#In... |
End of preview. Expand in Data Studio
Jdocs_text_pretrain
Made with ❤️ using 🦥 Unsloth Studiojdocs_dataset was generated with Unsloth Recipe Studio. It contains 191 generated records.
🚀 Quick Start
from datasets import load_dataset
# Load the main dataset
dataset = load_dataset("otisberg/jdocs_text_pretrain", "data", split="train")
df = dataset.to_pandas()
📊 Dataset Summary
- 📈 Records: 191
- 📋 Columns: 1
📋 Schema & Statistics
| Column | Type | Column Type | Unique (%) | Null (%) | Details |
|---|---|---|---|---|---|
text |
string |
expression | 191 (100.0%) | 0 (0.0%) | - |
⚙️ Generation Details
Generated with 3 column configuration(s):
expression: 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:
- Diverse data generation using statistical samplers, LLMs, or existing seed datasets
- 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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