Atoms

Atoms

Atoms are Jelly's built-in links. z will denote the only argument of a monadic function, x and y the left and right argument of a dyadic one.

Jump to:
 Single-byte nilads
 Single-byte monads
 Single-byte dyads
 Ø atoms (assorted nilads)
 Æ atoms (arithmetic monads)
 æ atoms (arithmetic dyads)
 Œ atoms (other monads)
 œ atoms (other dyads)

Single-byte nilads

Symbol	Function
®	Restore; retrieve the value of the register. Initially 0.
³	Return the third command line argument (first input) or 100.
⁴	Return the fourth command line argument (second input) or 16.
⁵	Return the fifth command line argument (third input) or 10.
⁶	Return the sixth command line argument (fourth input) or ' '.
⁷	Return the seventh command line argument (fifth input) or '\n'.
⁸	Return the link's left argument or [].
⁹	Return the link's right argument or 256.
Ɠ	Read and evaluate a single line from STDIN.
ƈ	Read a single character from STDIN.
ɠ	Read a single line from STDIN.

Single-byte monads

Symbol	Function
¬	Logical NOT: if z is zero or empty, then 1, else 0.
½	Square root.
!	Factorial or Pi function.
A	Absolute value.
B	Convert from integer to binary.
C	Complement; compute 1 − z.
D	Convert from integer to decimal.
E	Check if all elements of z are equal.
F	Flatten list.
G	Attempt to format z as a grid.
H	Halve; compute z ÷ 2.
I	Increments; compute the differences of consecutive elements of z.
J	Returns [1 … len(z)].
K	Join z, separating by spaces.
L	Length.
M	Return all indices of z that correspond to maximal elements.
N	Negative; compute −z.
O	Ord; cast to number.
P	Product of a list.
Q	Return the unique elements of z, sorted by first appearance.
R	Inclusive range [1 … z].
S	Sum of a list.
T	Return all indices of z that correspond to truthy elements.
U	Upend; reverse an array.
V	Eval z as Jelly code, with no arguments. If z is a list, it maps Python's str function to all of z's elements, concatenates them and then eval's the result. Vectorizes at depth 1.
W	Wrap; return [z].
X	Random; choose a random item from z if z is a list, or from 1 to z inclusive if z is a positive integer. If z = 0, return z. Error if z is negative or a decimal.
Y	Join z, separating by linefeeds.
Z	Zip; push the array of all columns of z.
~	Bitwise NOT.
°	Convert z from degrees to radians.
¹	Identity; return z.
²	Square.
Ạ	All; return 0 if z contains a falsey value, else 1.
Ḅ	Convert from binary to integer.
Ḍ	Convert from decimal to integer.
Ẹ	Any; return 1 if z contains a truthy value, else 0.
Ḥ	Double; compute 2z.
Ị	Insignificant; return abs(z) ≤ 1.
Ḳ	Split z at spaces.
Ḷ	Lowered range; return [0 … z−1].
Ṃ	Minimum.
Ṇ	Logical NOT. Does not vectorize.
Ọ	Chr; cast to character.
Ṛ	Reverse z. Does not vectorize.
Ṣ	Sort the list z.
Ṭ	Return a Boolean array with 1s at the indices in z.
Ụ	Grade the list z up, i.e., sort its indices by their corresponding values.
Ṿ	Uneval; right inverse of V.
Ẉ	Get the length of each element of z.
Ỵ	Split z at linefeeds.
Ẓ	If z is a prime, then 1, else 0 (alias for ÆP).
Ȧ	Any and all; return 0 if z is empty, or contains a falsey value when flattened, else 1.
Ḃ	Bit; return z % 2.
Ċ	Ceil; round z up to the nearest integer. Imag. part for complex z.
Ḋ	Dequeue; return z[1:].
Ė	Enumerate; return [ [1,y[1]] , [2,y[2]], ... ].
Ḟ	Floor; round z down to the nearest integer. Real part for complex z.
Ġ	Group the indices of z by their corresponding values.
Ḣ	Head; pop and return the first element of z. Modifies z.
İ	Inverse;Reciprocal; compute 1 ÷ z.
Ṁ	Maximum.
Ṅ	Print z and a linefeed. Returns z.
Ȯ	Print z. Returns z.
Ṗ	Pop; return z[:-1].
Ṙ	Print a string representation of z, without a linefeed. Returns z.
Ṡ	Sign of z. Conjugate for complex z.
Ṫ	Tail; pop and return the last element of z. Modifies z.
Ẇ	Sublists; all non-empty contiguous slices of z.
Ẋ	Shuffle; return a random permutation of z.
Ẏ	Tighten; dump all lists inside z.
Ż	Prepend 0 to z. For integers, return [0 … z].
§	Sum. Vectorizes at depth 1.
Ä	Cumulative sum. Vectorizes at depth 1.
‘	Increment; compute z + 1.
’	Decrement; compute z − 1.

Single-byte dyads

Symbol	Function
×	Multiplication.
÷	Floating point division.
%	Modulus.
&	Bitwise AND.
*	Exponentiation with base x.
+	Addition.
,	Pair; return [x, y].
:	Integer division.
;	Concatenate.
<	If x is less than y, then 1, else 0.
=	If x equals y, then 1, else 0. Vectorizes.
>	If x is greater than y, then 1, else 0.
^	Bitwise XOR.
_	Subtraction.
a	Logical AND. Vectorizes with depth 0.
b	Convert from integer to base y.
c	Combinations; compute xCy.
d	Divmod.
e	If x occurs in y, then 1, else 0.
f	Filter; remove the elements from x that are not in y.
g	Greatest common divisor (GCD, HCF).
i	Find the first index of element y in list x, or 0.
j	Join list x with separator y.
k	Partition y after truthy indices of x.
l	Logarithm with base y.
m	Modular; return every y th element of x. If y is zero, mirror: prepend x to its reverse.
n	Not equals. If x equals y, then 0, else 1. Vectorizes.
o	Logical OR. Vectorizes with depth 0.
p	Cartesian product.
r	Inclusive range. Descending if x > y.
s	Split x into slices of length y.
t	Trim all elements of y from both sides of x.
v	Eval x as Jelly code, with argument y.
w	Find the first index of sublist y within list x, or 0.
x	Times; repeat the elements of x y times.
y	Translate the elements of y according to the mapping in x.
z	Zip; transpose x with filler y.
|	Bitwise OR.
⁼	Equals. Does not vectorize.
⁻	Not equals. Does not vectorize.
ạ	Absolute difference.
ḅ	Convert from base y to integer.
ḍ	If x divides y, then 1, else 0.
ẹ	Return the indices of all occurrences of y in x.
ḥ	Jelly hash function. x contains a magic number (akin to a salt, can also be a base-250 compressed integer as a string) concatenated with a collection of values. If there are more than two items in x, all but the first are concatenated into a single collection. If there are two items and the second is a number N, the range [1,N] is used as the collection. y is the input to the hash function. Depending on the resulting hash, an item from the collection is returned.
ị	Return the element of y at index x % len(y). If floor(x) and ceil(x) aren't equal, return the elements of y at indices floor(x) % len(y) and ceil(x) % len(y).
ḷ	Left argument; return x.
ṃ	Base decompression; convert x to base length(y) then index into y.
ọ	Order, multiplicity, valuation; how many times is x divisible by y?
ṛ	Right argument; return y.
ṣ	Split list x at occurrences of y.
ṭ	Tack; append x to y.
ȧ	Logical AND. Does not vectorize.
ḃ	Convert from integer to bijective base y.
ċ	Count the occurrences of y in x.
ḋ	Dot product of two vectors (real/complex). Right pads the shorter argument with 0.
ḟ	Filter; remove the elements from x that are in y.
ḣ	Head; return x[:y].
ṁ	Mold; reshape the content of x like the content of y. Reuses the content of x if necessary.
ȯ	Logical OR. Does not vectorize.
ṗ	Cartesian power.
ṙ	Rotate x y units to the left.
ṡ	Return all (overlapping) slices of length y of x.
ṫ	Tail; return x[y - 1:].
ẇ	Sublist exists; return 1 if x is a contiguous sublist of y, else 0.
ẋ	Repeat list x y times.
ż	Zip; interleave x and y.
«	Minimum of x and y.
»	Maximum of x and y.

Ø atoms (assorted nilads)

Symbol	Function
ؽ	Yield [1, 2].
Ø%	Yield 4294967296 (232).
Ø(	Parentheses; yield '()'.
Ø+	Signs; yield [1, -1].
Ø-	Signs; yield [-1, 1].
Ø.	Bits; yield [0, 1].
Ø0	Zeroes; yield [0, 0].
Ø1	Ones; yield [1, 1].
Ø2	Twos; yield [2, 2].
Ø<	Angle brackets; yield '<>'.
ØA	Alphabet; yield 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'.
ØB	Base digits; yield '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz'.
ØḄ	Consonants; yield 'bcdfghjklmnpqrstvwxyz'.
ØḂ	Consonants; yield 'BCDFGHJKLMNPQRSTVWXYZ'.
ØC	Consonants; yield 'BCDFGHJKLMNPQRSTVWXYZbcdfghjklmnpqrstvwxyz'.
ØD	Digits; yield '0123456789'.
ØH	Hexadecimal digits; yield '0123456789ABCDEF'.
ØJ	Yield Jelly's codepage.
ØP	Pi
ØQ	Qwerty; yield ['QWERTYUIOP', 'ASDFGHJKL', 'ZXCVBNM'].
ØV	Yield 'ṘV' (a cheat for writing a quine.)
ØW	Word; yield 'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789_'
ØY	Consonants; yield 'BCDFGHJKLMNPQRSTVWXZbcdfghjklmnpqrstvwxz'.
Ø[	Square brackets; yield '[]'.
Ø^	Slashes; yield '/\'
Øa	Alphabet; yield 'abcdefghijklmnopqrstuvwxyz'.
Øb	Base64 digits; yield 'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/'
Øc	Vowels; yield 'AEIOUaeiou'.
Øe	Euler's number
Øh	Hexadecimal digits; yield '0123456789abcdef'.
Øp	Phi (golden ratio)
Øq	Qwerty; yield ['qwertyuiop', 'asdfghjkl', 'zxcvbnm'].
Øv	Yield 'Ṙv'.
Øy	Vowels; yield 'AEIOUYaeiouy'.
Ø{	Curly brackets; yield '{}'.
Ø°	Yield 360.
Ø⁵	Yield 250 (Jelly's integer compression base).
Ø⁷	Yield 128 (27).
ØẠ	Alphabet; yield 'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz'.
ØỴ	Consonants; yield 'bcdfghjklmnpqrstvwxz'.
Øẹ	Vowels; yield 'aeiou'.
Øỵ	Vowels; yield 'aeiouy'.
ØṖ	Yield the set of printable ASCII chars.
ØẎ	Consonants; yield 'BCDFGHJKLMNPQRSTVWXZ'.
Øė	Vowels; yield 'AEIOU'.
Øẏ	Vowels; yield 'AEIOUY'.

Æ atoms (arithmetic monads)

Symbol	Function
Æ!	Convert from integer to factorial base.
Æ¡	Convert from factorial base to integer.
Æ?	Convert from integer to primorial base.
Æ¿	Convert from primorial base to integer.
ƽ	Compute the integer square root of z.
ÆA	Arccosine.
ÆC	Count the primes less or equal to z.
ÆD	Compute the array of z's divisors.
ÆE	Compute the array of exponents of z's prime factorization. Includes zero exponents.
ÆF	Compute z's prime factorization as [prime, exponent] pairs.
ÆN	Generate the zth prime.
ÆP	If z is a prime, then 1, else 0 (has the shorter alias Ẓ).
ÆR	Range; generate all primes between 2 and z.
ÆS	Sine.
ÆT	Tangent.
Æc	Carmichael function.
Æd	Divisor count.
Æe	Exponential function.
Æf	Compute the array of primes whose product is z.
Æi	Separate a number z into [real(z), imag(z)].
Æị	Combines the first two elements of a list into a complex number, z[0] + 1j*z[1]. Missing values are replaced with zeroes and extra values are truncated.
Æl	Natural logarithm.
Æm	Arithmetic mean.
Æn	Next; generate the closest prime strictly greater than z.
Æp	Previous; generate the closest prime strictly less than z.
Ær	Find the roots of a polynomial, given a list of coefficients.
Æs	Divisor sum.
Æv	Count distinct prime factors.
ÆẠ	Cosine.
ÆĊ	Returns the zth Catalan number
ÆḌ	Proper divisors.
ÆẸ	Inverse of ÆE.
ÆṢ	Arcsine.
ÆṬ	Arctangent.
ÆḊ	Determinant. For non-square z, computes det(zzT)½; if z is a row vector, this is its norm.
ÆḞ	Returns the zth item in the Fibonacci sequence.
ÆĿ	Returns the zth Lucas number
ÆṪ	Totient function.
Æḍ	Proper divisor count.
Æṃ	Mode. Vectorizes.
Æṛ	Construct the polynomial with roots z. Returns list of coefficients.
Æṣ	Proper divisor sum.
Æṭ	Trace.
Æṁ	Median. Vectorizes.
Æ°	Convert z from radians to degrees.
Ʋ	If z is a square, then 1, else 0.

æ atoms (arithmetic dyads)

Symbol	Function
æ.	Dot product of two vectors (real/complex). Right pads the shorter argument with 1.
æ×	Matrix multiplication.
æ%	Symmetric modulo 2y; map x in the interval (−y, y]. Try 100Ræ%4 to get the hang of it.
æ*	Matrix power.
æA	Arctangent with two arguments, i.e., atan2().
æC	Convolution power.
æR	Inclusive prime range, from x to y.
æc	Convolution of x and y.
æi	Modular inverse of x, modulo y, or if none exists, 0.
æị	Combines x and y into a complex number as x + 1j*y.
æl	Lowest common multiple (LCM).
ær	Round x to the nearest multiple of 10−y.
æp	Precision; round x to y significant figures.
æċ	Ceil x to the nearest power of y.
æḟ	Floor x to the nearest power of y.
æ«	Bit shift; compute x × 2y.
æ»	Bit shift; compute x × 2−y. Returns an integer.

Œ atoms (other monads)

Symbol	Function
Œ!	All permutations of z. May contain duplicates.
Œ¿	Index of permutation z in a lexicographically sorted list of all permutations of z's items.
Œ?	Shortest permutation of items [1,2,...,N] which would yield z via Œ¿.
ŒB	Bounce; yield z[:-1] + z[::-1]. Vectorizes at depth 1.
ŒḄ	Bounce; yield z[:-1] + z[::-1]. Does not vectorize.
ŒḂ	Check if z is a palindrome. For integers, short for DŒḂ$.
ŒD	Diagonals of a matrix. Starts with the main diagonal.
ŒĖ	Multidimensional enumerate.
ŒG	GET request z. http:// is prepended by default.
ŒĠ	Group multidimensional indices by their corresponding values.
ŒH	Split z into two halves with similar length.
ŒJ	Multidimensional indices of z.
Œb	Like ŒṖ, but returns [[]] for the empty list.
Œc	Unordered pairs (œc2).
Œċ	Unordered pairs with replacement (œċ2).
Œd	Antidiagonals of a matrix. Starts with the main antidiagonal.
Œḍ	Reconstruct matrix from its antidiagonals.
Œg	Group runs of equal elements. Vectorizes at depth 1.
Œɠ	Group run lengths. Does not vectorize.
Œl	Lower case.
ŒM	Return all multidimensional indices of z that correspond to maximal elements.
Œœ	Odd-even. Same as s2Z. [1, 2, 3, 4] gives [[1, 3], [2, 4]].
Œr	Run-length encode. “aab”Œr is [['a', 2], ['b', 1]].
Œṙ	Run-length decode. Right inverse of Œr.
Œs	Swap case.
Œt	Title case.
ŒỤ	Grade the multidimensional array z up, i.e., sort its multidimensional indices by their corresponding values.
Œu	Upper case.
ŒP	Powerset of z. May contain duplicates.
Œp	Cartesian product of z's items.
ŒṖ	Partition of z (z must be a list).
Œṗ	Integer partitions of z (ways to sum positive integers to z)
ŒḌ	Reconstruct matrix from its diagonals.
ŒḊ	Depth.
ŒQ	Distinct sieve. (Replace each first occurrence of a value with 1, and all later occurrences with 0.)
ŒR	List from −abs(z) to abs(z) inclusive (shorthand for Ar@N$).
ŒṘ	Python's string representation.
ŒT	Format time: Let the last three bits of z be abc. If a is 1, include the time; if b is 1, include the minute; if c is 1, include the second.
ŒṪ	Return all multidimensional indices of z that correspond to truthy elements, with depth 0.
ŒṬ	Return a multidimensional rectangular boolean array with 1s at the indices in z.
ŒV	Evaluate Python code z.

œ atoms (other dyads)

Symbol	Function
œ!	Permutations without replacement.
œ&	Multiset intersection.
œ-	Multiset difference.
œ^	Multiset symmetric difference.
œ¿	Index of permutation x in a list of all permutations of x's items sorted by their index in y.
œ?	Permutation at index x of the items in y (where y defines the sort order of those items).
œc	Combinations without replacement.
œẹ	Return the multidimensional indices of all occurrences of y in x.
œi	Find the first multidimensional index of element y in x. Returns empty list if there are no occurrences.
œị	Element of y at multi-dimensional index x. If x is empty, return y. Otherwise, y is replaced by its element at index x[0] (behaves like ị), x is replaced by x[1:], and the procedure is repeated.
œl	Trim all elements of y from the left side of x.
œr	Trim all elements of y from the right side of x.
œs	Split x into y chunks of similar lengths.
œ|	Multiset union.
œS	After sleeping for y seconds, return x.
œṣ	Split x around sublists equal to y.
œċ	Combinations with replacement.
œṖ	Partition y at the indices in x.
œṗ	Partition y before truthy indices of x.
œP	Partition y at the indices in x, without keeping the borders.
œp	Partition y at truthy indices of x, without keeping the borders.
œṡ	Split x at the first occurrence of y.