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)
ƒ atoms (custom)

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.
`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 array Does not vectorize.
`Ṣ`	Sort the list z.
`Ṭ`	Return a Boolean array with 1's at the indices in z.
`Ụ`	Grade the list z up, i.e., sort its indices by their values.
`Ṿ`	Uneval; right inverse of `V`.
`Ỵ`	Split z at linefeeds.
`Ȧ`	Any and all; return 0 if z is empty or contains a falsey value, 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; 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.
`‘`	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.
`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.
`ị`	Return the element of y at index 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.
`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:]`.
`ẋ`	Repeat list x y times.
`ẇ`	Sublist exists; return 1 if x is a contiguous sublist of y, else 0.
`ż`	Zip; interleave x and y.
`«`	Minimum of x and y.
`»`	Maximum of x and y.

`Ø` atoms (assorted nilads)

Symbol	Function
`ØA`	Alphabet; yield `'ABCDEFGHIJKLMNOPQRSTUVWXYZ'`.
`ØB`	Base digits; yield `'0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz'`.
`ØC`	Consonants; yield `'BCDFGHJKLMNPQRSTVWXYZbcdfghjklmnpqrstvwxyz'`.
`ØD`	Digits; yield `'0123456789'`.
`ØH`	Hexadecimal digits; yield `'0123456789ABCDEF'`.
`ØJ`	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'`.
`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'`.

`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.
`Æ½`	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 z^th prime.
`ÆP`	If z is a prime, then 1, else 0.
`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.
`Æl`	Natural logarithm.
`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.
`ÆḌ`	Proper divisors.
`ÆẸ`	Inverse of `ÆE`.
`ÆṢ`	Arcsine.
`ÆṬ`	Arctangent.
`ÆḊ`	Determinant. For non-square z, computes det(zz^T)^½; if z is a row vector, this is its norm.
`ÆḞ`	Returns the zth item in the Fibonacci sequence.
`ÆṪ`	Totient function.
`Æḍ`	Proper divisor count.
`Æṣ`	Proper divisor sum.
`Æṛ`	Construct the polynomial with roots z. Returns list of coefficients.
`Æ°`	Convert z from radians to degrees.
`Æ²`	If z is a square, then 1, else 0.

`æ` atoms (arithmetic dyads)

Symbol	Function
`æ.`	Dot product of two vectors (real/complex).
`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()`.
`æR`	Inclusive prime range, from x to y.
`æi`	Modular inverse of x, modulo y, or if none exists, 0.
`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 × 2^y.
`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$`.
`ŒD`	Diagonals of a matrix. Starts with the main diagonal.
`ŒG`	GET request z. `http://` is prepended by default.
`Œc`	Unordered pairs (`œc2`).
`Œċ`	Unordered pairs with replacement (`œċ2`).
`Œg`	Group runs of equal elements.
`Œl`	Lower case.
`Œr`	Run-length encode. `“aab”Œr` is `[['a', 2], ['b', 1]]`.
`Œṙ`	Run-length decode. Right inverse of `Œr`.
`Œs`	Swap case.
`Œt`	Title case.
`Œu`	Upper case.
`ŒP`	Powerset of z. May contain duplicates.
`Œp`	Cartesian product of z's items.
`ŒṖ`	Partition of z (z must be a list).
`ŒḌ`	Reconstruct matrix from its diagonals.
`ŒḊ`	Depth.
`ŒR`	List from −abs(z) to abs(z) inclusive (shorthand for `Ar@N$`).
`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.
`ŒV`	Evaluate Python code z.

`œ` atoms (other dyads)

Symbol	Function
`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.
`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 all truthy indices of x.
`œp`	Partition y at all truthy indices of x, without keeping the borders.
`œṡ`	Split x at the first occurrence of y.

`ƒ` atoms (custom)

Symbol	Function
`ƒB`	Check if z is a palindrome.
`ƒR`	Range; generate all primes between x and y.

Atoms - GolfingSuccess/jelly GitHub Wiki

Atoms

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)

`ƒ` atoms (custom)

⚠️ GitHub.com Fallback ⚠️

Atoms - GolfingSuccess/jelly GitHub Wiki

Atoms

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)

ƒ atoms (custom)

⚠️ **GitHub.com Fallback** ⚠️

`Ø` atoms (assorted nilads)

`Æ` atoms (arithmetic monads)

`æ` atoms (arithmetic dyads)

`Œ` atoms (other monads)

`œ` atoms (other dyads)

`ƒ` atoms (custom)

⚠️ GitHub.com Fallback ⚠️