Vyxapedia

Elements

Click an element's link to see some examples (if any) as well as any additional information that isn't part of the official documentation.

Symbol Name Arity Description
λ Lambda * Open a lambda - λ...;
ƛ Lambda Map 1 Open a mapping lambda - ƛ
¬ Logical Not 1 Return the inverse (negation) of the truthiness of an item.
Logical And 2 Returns the first truthy argument if both are truthy, otherwise returns the first falsy argument.
Apply Lambda 1 Like a mapping lambda, but the results are evaluated immediately, instead of being lazily evaluated
Logical Or 2 Returns the first truthy argument, otherwise the first falsy argument.
Remove at Index 2 Returns every item in a list except the item at the given index.
÷ Item Split 1 Pushes each item of the top of the stack onto the stack.
× Asterisk Literal 0 the string "*" (asterisk)
« Base Compressed String 0 Open/close a bijective base-255 compressed string - «...«
Newline NA NOP
» Base Compressed Number 0 Open/close a bijective base-255 compressed number - »...»
° Complex Number Separator NA Separates the real and imaginary parts of a complex number
MultiCommand 2 Logarithm / Repeat Character / Capitalisation transfer
ß Conditional Execute 1 + * Executes element A if the top of the stack is truthy
Function Call 1 Calls a function / executes as python / number of distinct prime factors / vectorised not
Split On / Fill By Coordinates 2 Split a on b (works on lists and numbers as well) / Fill a matrix by calling a function with the lists of coordinates in the matrix.
½ Halve 1 Halves an item
Mathematical Digraph NA Used for mathematical digraphs
ø String Digraph NA Used for string-based digraphs
Combinations/Remove/Fixed Point Collection 2 Does either combinations_with_replacement, removes items from a not in b, or applies a on b until the result stops changing (including the initial value).
¢ Infinite Replacement / Apply at Indices 3 Replace b in a with c until a does not change / Call a function on all elements at specified indices together and put that back in the list
Complement / Comma Split 1 1 - a if number, split by commas if string.
æ Is Prime / Case Check 1 (a is prime) if a is a number, else check which case a is
ʀ Inclusive Zero Range 1 Inclusive range or whether each character is alphabetical
ʁ Exclusive Zero Range 1 Exclusive range or palindromise
ɾ Inclusive One Range 1 Inclusive range or uppercase
ɽ Exclusive One Range / Lowercase 1 Exclusive range or lowercase
Þ List Digraph NA Used for list-related digraphs
ƈ Choose / random choice / set same / drop while 2 Binomial coefficient / choose a random items from b / same except duplicates / drop while
Palindromise 1 Palindromise a
¨ Other Digraphs NA Used for various random digraphs
Space NA NOP
! Stack Length 0 Push the length of the stack
" Pair 2 Place the top two items into a single list
# Comment NA The characters until the next newline are commented out
#{ Multiline Comment NA The characters until the next `}#` are commented out. Nestable.
$ Swap 2 Swap the top two items
% Modulo / Format 2 Modulo two numbers / format two strings
& Apply To Register * Apply the next element to the register
' Lambda Filter 1 Open a filter lambda - '...;
( Open For Loop 1 Start a for loop, iterating over the popped top of stack.
) Close For loop NA Close a for loop
* Multiplication / Arity Change 2 Multiply two numbers or strings / Change the arity of a function
+ Addition 2 Adds the top two items on the stack
, Print 1 Print a with trailing newline
- Subtract 2 Subtracts the top two items on the stack
. Decimal Separator NA Decimal separator
/ Divide / Split 2 Divide two numbers or split strings
0 Literal digit 0 0 Literal digit 0
1 Literal digit 1 0 Literal digit 1
2 Literal digit 2 0 Literal digit 2
3 Literal digit 3 0 Literal digit 3
4 Literal digit 4 0 Literal digit 4
5 Literal digit 5 0 Literal digit 5
6 Literal digit 6 0 Literal digit 6
7 Literal digit 7 0 Literal digit 7
8 Literal digit 8 0 Literal digit 8
9 Literal digit 9 0 Literal digit 9
: Duplicate 1 Push a twice
; Close Structure NA Close a lambda / map lambda / sort lambda / function
< Less Than 2 Basic comparison - less than
= Equals 2 Basic comparison - equals
> Greater Than 2 Basic comparison - greater than
? Input 0 Get the next input from the input source
@ Function Call / Declaration * / NA Call / declare function (@name; / @name|code;)
A All 1 Check if all items in a list are truthy / check if a character is a vowel
B Binary To Decimal 1 Convert a binary string or list to base 10
C Chr / Ord 1 Convert between characters and ordinals
D Triplicate 1 Push three copies of a to stack
E Two Power / Python Eval 1 2 ** a, or eval(a)
F Filter 2 Filter a list by another list or function.
G Max 1 Maximum value or a
H Hex To Decimal 1 Convert hexadecimal to decimal
I Into Two Pieces 1 Push n spaces / quine cheese / into two pieces
J Merge 2 Join two lists or items
K Factors / Substrings / Prefixes 1 Get either the factors of a, substrings that occur more than once, or prefixes
L Length 1 Get length of a
M Map Function 2 Map function object b over a
N Negate / Swap Case / First Integer Where Truthy 1 Negate a number / swap case of a string / first integer where a function truthy
O Count / Maximums-by 2 Count number of times b occurs in a / Maximums-by
P Strip / Minimums-by 2 Remove the set of elements in b from both ends of a / Minimums-by
Q Quit NA Quit the program
R Reduce 2 Reduce a by b, or reverse each item of b
S Stringify 1 Stringify a list or number
T Truthy Indices / Triple / Triadify 1 Get indices of truthy elements, triple, or make the arity of a function 3
U Uniquify 1 Remove duplicates
V Replace / Map to Indices 3 Replace b with c in a / Map a function at elements of a list whose indices are in another list
W Wrap 0 Stack wrapped into a list
X Break NA Break out of the current loop or return early from a function.
Y Interleave 2 Interleave two lists
Z Zip 2 Zip two lists or Zip a with b mapped over a. Fills with 0s if needed.
[ Open If Statement 1 Open an if Statement
\ Single char Literal 0 Pushes a single character
] Close If Statement NA Close an if Statement
` String Literal 0 A string literal - `...`
^ Reverse Stack NA Reverse the stack.
_ Pop 1 Pop the top item of the stack
a Any 1 Check if any items of a list are truthy / Check if a character is an uppercase letter
b Binary 1 Convert a number or string to binary
c Contains / First Truthy Item Under Function Application 2 Check if one thing contains another / returns the first truthy item in a list after applying a function
d Double / Dyadify 1 Double a number or repeat a string twice / make a function dyadic
e Exponentiation 2 Exponentiate two numbers / extend string / get length of a regex match
f Flatten 1 Turn a number into a list of digits, split a string into a list of characters, or flatten a list.
g Minimum 1 Take the minimum of a list
h Head 1 First item of something
i Index 2 Index into a list
j Join 2 Join a by b.
k Constant Digraph 0 Used for constant digraphs.
l Cumulative Groups / First Non-Negative Truthy Integers 2 Cumulative groups (overlapping groups, aperture) / Equal length
m Mirror 1 Append input reversed to itself.
n Context 0 Context variable, value of the current loop or function.
o Remove 2 Remove instances of b in a
p Prepend 2 Prepend b to a
q Uneval 1 Enclose in backticks, escape backslashes and backticks.
r Range 2 Range between two numbers, or cumulative reduce, or regex match
s sort 1 Sort a list or string
t Tail 1 Last item
u Minus One 0 Push -1
v Vectorise * Vectorise an element
¨v Simple vectorise * Simple vectorise an element. Well, you'll have to look at the code to know what that means.
¨V Right vectorize * Right vectorize an element. Like `v`, but vectorizes on the rightmost list instead of the leftmost list.
w Listify 1 a wrapped in a singleton list
x Recurse / Continue / Print Stack Call current function (Functions/Lambdas) / Continue (For Loops) / Print the entire stack (otherwise)
y Uninterleave 1 Push every other item of a, and the rest.
z Zip-self 1 Zip a with itself
{ Open While Loop NA Open a while loop - `{...}`
| Branch In Structure Branch the structure - means various things depending on context
} Close While Loop Close a while loop
~ Filter / Execute Without Pop For monads, filter a list by that. For dyads, execute without popping from the stack.
Max by Tail 1 Maximum by last item
Min by Tail 1 Minimum by last item
Dyadic Maximum 2 Maximum of two values / Maximum of a list by a function
Dyadic Minimum 2 Minimum of two values / Minimum of a list by a function
Increment / Space Replace With 0 1 Add 1 to a number / replace all spaces in a string with "0"
Decrement 1 Subtract 1 from a number
Parity 1 A number modulo 2
¤ Empty String 0 The empty string
ð Space 0 A Space
Variable Set 1 Set variable (→name)
Variable Get 0 Get the value of a variable (←name)
β To Base Ten / From Custom Base 2 Convert a number from a custom base to base 10
τ From Base Ten / To Custom Base 2 Convert a number to a different base from base 10.
ȧ Absolute value 1 Take the absolute value of a number, or remove whitespace from a string
Boolify 1 Convert an arbitrary value into a truthy or falsy value, vectorises with flag t
ċ Not One 1 Check if something is not equal to 1
Divmod 2 Divmod / combinations / trim / chunk-while
ė Enumerate 1 Zip with a range of the same length
Find 2 Find a value in another
ġ Gcd / Group by Function * Greatest Common Denominator of a list or some numbers
Head Extract 1 Separate the first item of something and push both to stack
Floor Division 2 Floor divide a by b
ŀ Left Justify / Gridify / Infinite Replace / Collect until false 3 Find one value inside another, starting from a certain index.
Mean 1 Average of a list - sum / length
Join By Nothing 1 Join a list by the empty string. Vectorises if the list contains lists.
ȯ Slice 2 Slice from an index to the end
Powerset 1 All possible combinations of a
Round 1 Round a number to the nearest integer / real and imaginary part of complex number
Sort by Function 2 Sort a list by a function / create a range / split on a regex
Tail Extract 1 Remove the last item and push both onto the stack
Chunk Wrap 2 Wrap a list in chunks of a certain length / apply a function to every second item of a list
Repeat * Repeat a value several times
Exclusive Range Length 1 Range from 0 to length of a
ż Inclusive Range Length 1 Range from 1 to length of a inclusive
Square Root 1 Square root a number / every second character of a
Open List 0 Open a list - ⟨...⟩
Close list 1 Close a list - ⟨...⟩
Two Character String 0 Collect the next two characters as a string - ‛..
Ten 0 Push 10 to the stack
Hundred 0 Push 100 to the stack
Is Even 1 Check if a value is even
Divisible By Three 1 Check if a is divisible by 3
Twenty Six 0 Push 26 to the stack
Divisible By Five 1 Check if a is divisible by 5
Sixty Four 0 Push 64 to the stack
One Twenty Eight 0 Push 128 to the stack
Two Fifty Six 0 Push 256 to the stack
Newline 0 Push a newline to the stack
Join On Newlines 1 Join the top of the stack on newlines (insert "\n" between items)
§ Vertical Join 1 Transpose (filling with spaces) and then join on newlines
ε Absolute Difference / Repeat / Regex match 2 Returns the absolute difference / Fills an array of a certain length / Does a regex match
¡ Factorial 1 Returns the factorial of the top of the stack
Summate 1 Returns the sum of the top of the stack (reduce by addition)
¦ Cumulative Sum 1 Returns the sums of the prefixes of the top of the stack (cumulatively reduce by addition)
All Equal 1 Returns whether all items are equal
µ Sorting Lambda NA Sort the top of the stack by the function µ...;
Ȧ Assign 3 The equivalent of a[b] = c
Bifurcate 1 Pushes the top of the stack then its reverse. Literally duplicate and reverse
Ċ Counts 1 Returns a list of [item, count of item in the top of stack]
Is Divisible / Arbitrary Duplicate / Ordered Group By 2 Returns whether two items are divisible / numerous copies of the top of the stack / groups by results of function preserving order (adjacent group-by)
Ė Vyxal Exec / Reciprocal 1 Executes as Vyxal / Reciprocal of number
Generator / Modulo Index / Format 2 Make a generator from function a with initial vector b, or get every nth item or format numbers as decimals.
Ġ Group consecutive 1 Group consecutive identical items
Head Remove / Behead 1 All but the first item of a list / Drop 1
İ Index into / Collect while unique / Complex Number 1 Index into list at indices / Collect values while values are unique (not including the initial value)
Ŀ Transliterate 3 Replace each item of one value in another value with the corresponding element from a third value
Insert 3 Insert a value at a specified index / Map a function over every nth item of a list
Integer partitions / First Truthy Non-Negative Integer 1 Integer partitions / join by space
Ȯ Over 0 Push the second-last item of stack to the top
Permutations 1 Get all permutations of a value
Reverse 1 Reverse a value
Vectorised sums / Strip whitespace from both sides / Is positive 1 Sum of each item in a list
Tail Remove / Truthy Under 1 Cut off the last item of a list / push 1 under the top of the stack
Split And Keep Delimiter 2 Split a value and keep the delimiter
Cartesian Product / Fixpoint 2 Take the Cartesian Product of two values, or apply a function until there is no change. If arguments are numbers, turns them into ranges.
Slice Until 2 Slice a list until a certain index / find all results for a regex match
Ż Slice From One Until 2 Slice from index 1 until a number / get groups of a regex match
Parallel Apply Parallel apply two elements to the top of the stack
Parallel Apply Wrap Parallel apply two elements and wrap the results in a list
Very Last Input 0 Push the very last input (input[::-1][0]) to the stack
¹ Second Last Input 0 Push the very last input (input[::-1][1]) to the stack
² Square 1 Square a number / Format a string into a square
Shift 3 Shift the top of stack two values down
Ceiling 1 Take the ceiling of a number / Imaginary part of complex number / split a string on spaces
Floor 1 Floor a number / real part of complex number / extract the integer part of a string
¯ Deltas 1 Deltas (consecutive differences)
± Sign 1 Get the sign of a number
Print Without Newline 1 Print a value without a trailing newline
Print Without Popping 0 Print a value without popping the stack
Input List 0 All inputs wrapped in a list
Right Bit Shift 2 Right-bitshift a value / right-justify a string
Left Bit Shift 2 Left-bitshift a value / left-justify a string
Bitwise And 2 Performs bitwise and between two numbers / centre a string
Bitwise Or 2 Performs bitwise or between two numbers / Removes a character at nth index / Merges strings on longest common prefix and suffix
Bitwise Xor 2 Performs bitwise xor between two numbers / appends n spaces to a string / prepends n characters to a string / Levenshtein Distance
Bitwise Not 1 Performs bitwise not on a number / check if any letters are uppercase / keep only truthy elements of a list
Random Choice 1 Random choice of single item from array
Lesser Than or Equal To 2 a is lesser than or equal to b?
Greater Than or Equal To 2 a is greater than or equal to b?
Not Equal To 2 a is not equal to b?
Exactly Equal To 2 a equal to b? (non-vectorizing)
ƒ Reduce by 2 Reduce by an element
ɖ Scan by 2 Cumulatively reduce by an element
Set Union 2 Merge two arrays without duplicates
Transpose 1 Transpose an array
Symmetric Set difference 2 Uncommon elements of two arrays
£ Set Register 1 Set the register to argument value
¥ Push Register 0 Push the current register value
Grade Up 1 Indices of elements to sort in ascending order / uppercase / increment number twice
Grade Down 1 Indices of elements to sort in descending order / lowercase / decrement number twice
Ǎ Remove non-alphabets 1 Remove non-alphabetical characters / power with base 2
ǎ Nth prime 1 nth prime / all substrings
Ǐ Prime factorization 1 prime factorization / append first element
ǐ Prime factors 1 all prime factors / Title Case string
Ǒ Multiplicity / Remove Fixpoint / First Truthy Index Under Function 2 Order, Multiplicity, Valuation / remove till fixpoint / First truthy index under function application
ǒ Modulo 3 1 Modulo 3 / Split into Length 2
Ǔ Rotate Left 2 Rotate Left / Rotate Left Once
ǔ Rotate Right 2 Rotate Right / Rotate Right Once
One Element Lambda 0 One Element lambda function (prefix)
Two Element Lambda 0 Two Element lambda function (prefix)
Three Element Lambda 0 Three Element lambda function (prefix)
Index of next character in codepage 0 Return the index of the next character in the vyxal code page + 101
Split On newlines 1 Split on newlines / Power with base 10
Push To Global Array 1 Push to global array (no popping)
¼ Pop From Global Array 0 Pop from global array, push to stack
¾ Push Global Array 0 Push global array, no modification of global array
Π Product of Array / Cartesian product over list 1 Product of Array / Cartesian product over a list of lists
Rotate Stack Left 0 Rotate Stack Left
Rotate Stack Right 0 Rotate Stack Right
🍪 Cookie 0 print "cookie" forever
sus 0 print "sus"
kA Uppercase alphabet 0 "ABCDEFGHIJKLMNOPQRSTUVWXYZ" (uppercase alphabet)
ke e, Euler's number 0 2.718281828459045 (math.e, Euler's number)
kf Fizz 0 Fizz
kb Buzz 0 Buzz
kF FizzBuzz 0 FizzBuzz
kH Hello, World! 0 Hello, World!
kh Hello World (No Punctuation) 0 Hello World
k1 1000 0 10^3 / 1000
k2 10000 0 10^4 / 10000
k3 100000 0 10^5 / 100000
k4 1000000 0 10^6 / 1000000
ka Lowercase alphabet 0 "abcdefghijklmnopqrstuvwxyz" (lowercase alphabet)
kL Lowercase and uppercase alphabet 0 "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ" (uppercase+lowercase alphabet)
kd Digits 0 "0123456789" (Digits 0-9)
k6 Hex digits (lowercase) 0 "0123456789abcdef" (Hex digits)
k^ Hex digits (uppercase) 0 "0123456789ABCDEF" (Hex digits uppercase)
ko Octal digits 0 "01234567" (Octal digits)
kp Punctuation 0 string.punctuation (Punctuations)
kP Printable ASCII Without Space 0 printable ascii exluding space
kQ Printable ASCII With Space 0 printable ascii with space
kw ASCII Whitespace 0 All ASCII whitespace
kr Digits, lowercase alphabet, and uppercase alphabet 0 "0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ" (0-9A-Za-z)
kB Uppercase and lowercase alphabet 0 "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz" (A-Za-z)
kZ Uppercase alphabet reversed 0 "ZYXWVUTSRQPONMLKJIHGFEDCBA" (uppercase alphabet reversed)
kz Lowercase alphabet reversed 0 "zyxwvutsrqponmlkjihgfedcba" (lowercase alphabet reversed)
kl Uppercase and lowercase alphabet, reversed 0 "ZYXWVUTSRQPONMLKJIHGFEDCBAzyxwvutsrqponmlkjihgfedcba" (Z-Az-a)
ki Pi 0 3.141592653589793 (Pi)
kg Golden ratio/phi 0 1.618033988749895 (golden ratio/phi)
kD Current day in the format YYYY-MM-DD 0 Current day in the format YYYY-MM-DD
kN Current time as a list of ⟨hh|mm|ss⟩ 0 Current time as a list of ⟨hh|mm|ss⟩
kḋ Current day in the format DD/MM/YYYY 0 Current day in the format DD/MM/YYYY
kḊ Current day in the format MM/DD/YYYY 0 Current day in the format MM/DD/YYYY
Current day in the format ⟨DD|MM|YYYY⟩ 0 Current day in the format ⟨DD|MM|YYYY⟩
Braces, square brackets, angle brackets, and parentheses 0 {}[]<>()
kḂ Parentheses, square brackets, and braces 0 "()[]{}" (Brackets)
Parentheses and square brackets 0 ()[]
kḃ Opening brackets 0 "([{" (Open brackets)
k≥ Closing brackets 0 ")]}" (Close brackets)
k≤ Opening brackets (with <) 0 "([{<" (Fish bones :P)
Closing brackets (with >) 0 ")]}>" (Closing brackets)
kv Lowercase vowels 0 "aeiou" (Vowels lowercase)
kV Upercase vowels 0 "AEIOU" (Vowels uppercase)
k∨ Lowercase and uppercase vowels 0 "aeiouAEIOU" (vowelsVOWELS)
k⟇ Vyxal codepage 0 Yields the Vyxal codepage
[1, 2] 0 [1, 2]
kḭ 4294967296 0 2 ** 32, 2^32, 4294967296
k+ [1, -1] 0 [1, -1]
k- [-1, 1] 0 [-1, 1]
k≈ [0, 1] 0 [0, 1]
k/ Slashes 0 "/\\" (Forwardslash, backslash)
kR 360 0 360
kW https:// 0 https://
k℅ http:// 0 http://
k↳ https://www. 0 https://www.
http://www. 0 http://www.
512 0 512
k⁋ 1024 0 1024
2048 0 2048
kṄ 4096 0 4096
kṅ 8192 0 8192
16384 0 16384
32768 0 32768
k₴ 65536 0 65536
2147483648 0 2147483648
k⁰ Lowercase consonants with y 0 bcdfghjklmnpqrstvwxyz
Lowercase consonants without y 0 bcdfghjklmnpqrstvwxz
kT BF command set 0 BF command set ("[]<>-+.,")
kṗ Bracket pair list 0 List of bracket pairs ("[(),[],{},<>]")
kṖ Nested brackets 0 String of all brackets nested ("([{<>}])")
kS Amogus 0 Amogus ("ඞ")
k₁ [1, 1] 0 The list [1, 1]
k₂ 2 ** 20 0 2 to the power of 20, 1048576
k₃ 2 ** 30 0 2 to the power of 30, 1073741824
k∪ Lowercase Vowels With Y 0 Lowercase vowels with y, "aeiouy"
k⊍ Uppercase Vowels With Y 0 Uppercase vowels with y, "AEIOUY"
k∩ Vowels With Y 0 Vowels with y, "aeiouyAEIOUY"
k□ Directions 0 Cardinal directions, [[0,1],[1,0],[0,-1],[-1,0]]
kṘ Roman Numerals 0 IVXLCDM
k• Qwerty Keyboard 0 The list ["qwertyuiop","asdfghjkl","zxcvbnm"]
∆b Binary String 1 Get a binary string of a number
∆c Cosine 1 Get the cosine of an angle in radians
∆C Arc Cosine 1 Get the arccosine of an angle in radians
∆q Quadratic Solver 2 Solve a quadratic equation of the form ax^2 + bx = 0
∆Q General Quadratic Solver 2 Solve a quadratic equation of the form x^2 + ax + b = 0
∆s Sine 1 Get the sine of an angle in radians
∆S Arc Sine 1 Get the arcsine of an angle in radians
∆t Tangent 1 Get the tangent of an angle in radians
∆T Arc Tangent 1 Get the arctangent of an angle in radians
∆Ṫ Arc Tangent 2 2 Get the arctangent of an angle in radians
∆P Polynomial Solver 1 Solve a polynomial of the form a[0]x^len(a) + a[1]x^len(a)-1 ... = 0
∆ƈ n Pick r (npr) 2 Get the number of combinations of r items from a set of n items
∆± Copy Sign 2 Copy the sign of one number to the other
∆K Sum of Proper Divisors / Stationary Points 1 Get the sum of all proper divisors of a number / get the stationary points of a function
∆² Perfect Square? / Square Expression 1 Is the number a perfect square? (1, 4, 9, 16, 25, 36) / Raise an algebraic expression to the power of 2
∆e Euler's Number (e) raised to power a 1 Get the value of Euler's number (e) raised to the power of a
∆E (Euler's Number (e) Raised to Power a) - 1 1 Get the value of Euler's number (e) raised to the power of a minus 1
∆L Natural Logarithm 1 Get the natural logarithm of a number
∆l Logarithm (log_2) 1 Get the logarithm of a number to base 2
∆τ Common Logarithm 1 Get the common logarithm of a number
∆d Straight Line Distance 2 Get the straight line distance between two points (x1, x2, ..., xn) and (y1, y2, ..., yn)
∆D To Degrees 1 Convert an angle from radians to degrees
∆R To Radians 1 Convert an angle from degrees to radians
∆Ṗ Next Prime After a Number / Discriminant of Polynomial 1 Get the next prime number after a given number / the discriminant of a polynomial
∆ṗ First Prime Before a Number / Factor Expression 1 Get the first prime number before a given number / factor a mathematical expression
∆p Nearest Prime to a Number / Python equivalent of an expression 1 Get the prime number closest to a given number, get the greater to break ties / return the python equivalent of a mathematical expression - sympy's .pycode() function
∆ṙ Polynomial from Roots 1 Get the polynomial with coefficients from the roots of a polynomial
∆W Round to n Decimal Places 2 Round a number to n decimal places
∆% Modular Exponentiation 3 Get the modular exponentiation a**b mod c
∆Ŀ Least Common Multiple 1 or 2 Get the least common multiple of two numbers
∆i nth Digit of Pi / Integrate 1 Get the nth digit of pi
∆I First N Digits of Pi 1 Generate the first n digits of pi
∆Ė N Digits of Euler's Number (e) / Sympy Evaluate 1 Get the first n digits of Euler's number (e) / evaluate an expression as sympy
∆ė Nth Digit of Euler's Number (e) / Differentiate 1 Get the nth digit of Euler's number (e)
∆f nth Fibonacci Number 1 Get the nth fibonacci number, 1-indexed
∆F nth Fibonacci Number, 0-indexed 1 Get the nth fibonacci number, 0-indexed
∆Ṙ Random Float 0 Get a random float in the range [0, 1), pseudo random number
∆ṫ Totient Function / Local Minima 1 Get the totient function of a number / local minima of a function
∆n Next Power 2 Get the next power of b after a.
∆ḟ Previous Power 2 Get the previous power of b before a.
∆Z ZFill 2 Pad a string with zeros to a given length
∆ċ Nth Cardinal 1 Get the nth cardinal / convert number to words
∆o Nth Ordinal 1 Get the nth ordinal / convert number to wordth ordinal
∆M Mode 1 Get the mode of a list
∆ṁ Median 1 Get the median of a list - returns a list of the two middle items if even length list (use ṁ to average them)
∆Ċ Polynomial Expression From Coefficients 1 Get the polynomial expression from a list of coefficients
∆¢ Carmichael Function 1 Get the Carmichael function of a number / Local Maxima
∆› Increment until false 2 Increment a until b(a) is false (deprecated, use `>` instead)
∆‹ Decrement until false 2 Decrement a until b(a) is false (deprecated, use `<` instead)
∆ǐ Prime Exponents 1 Get the exponents of prime factors of a number
∆Ǐ All Prime Exponents 1 Get all exponents of prime factors less than the maximum prime factor
∆* Next Multiple 2 Get the next multiple of a number greater than another number
∆ȯ Hyperbolic Cosine 1 Get the hyperbolic cosine of a number in radians
∆Ȯ Hyperbolic Arccosine 1 Get the hyperbolic arccosine of a number in radians
∆ṡ Hyperbolic Sine 1 Get the hyperbolic sine of a number in radians
∆Ṡ Hyperbolic Arcsine 1 Get the hyperbolic arcsine of a number in radians
∆ṅ Hyperbolic Tangent 1 Get the hyperbolic tangent of a number in radians
∆Ṅ Hyperbolic Arctangent 1 Get the hyperbolic arctangent of a number in radians
∆/ Hypotenuse 1 Get the hypotenuse of a right-angled triangle - equivalent to `²∑√`
∆r Reduced Echelon Form 1 Get the reduced echelon form of a matrix
øb Parenthesise 1 Parenthesise a string
øB Bracketify 1 Enclose a string in brackets
øḃ Curly Bracketify 1 Enclose a string in curly brackets
øḂ Angle Bracketify 1 Enclose a string in angle brackets
øβ Balanced Brackets 1 Check if brackets in a string ("{}()[]<>") are balanced
ø↳ Custom Pad Left 3 Pad a string to the left with a certain character
ø↲ Custom Pad Right 3 Pad a string to the right with a certain character
øM Flip Brackets Vertical Palindromise 1 Vertically palindromise and reverse brackets and slashes, without duplicating center
øA Letter to Number 1 Convert a letter to a number, or vice versa (1-indexed)
øṗ Flip Brackets Vertical Palindromise, Center, Join on Newlines 1 Vertically palindromise each and reverse brackets and slashes, without duplicating center, then center and join by newlines. Equivalent to `øMøĊ⁋`
øm Flip Brackets Vertical Mirror, Center, Join on Newlines 1 Vertically mirror each and reverse brackets and slashes, then center and join by newlines. Equivalent to `øṀøĊ⁋`
øo Remove Until No change 2 Remove b from a until a does not change
øO Count Overlapping 2 Count the number of overlapping occurances of b in a
øV Replace Until No Change 3 Replace b with c in a until a does not change
øc String Compress 1 Compress a string of lowercase letters and spaces in base 255
øC Number Compress 1 Compress a positive integer in base 255
øĊ Center 1 Center a list of strings
øe Run Length Encoding 1 Run length encoding, convert from string/list to list of items and amount repeated.
øĖ Separated Run Length Encoding 1 Run length encoding, convert from string/list to list of items and list of amounts. Equivalent to `øe∩÷`
ød Run Length Decoding 1 Run length decoding, convert from list of characters and lengths to a string/list
øḊ Dyadic Run Length Decode 2 Run length decoding, convert list of characters and list of lengths to a string/list
øD Dictionary Compression 1 Optimally compress a string of English using words from the Vyxal dictionary
øW Group on words 1 Group a string on words
øċ Semi Optimal number compress 1 Semi-optimally compress a number
øṙ Regex replace 3 Replace matches of a with c in b
øp Starts With 2 Check if one value starts with another
øE Ends With 2 Check if one value ends with another
øf Ends With Set 2 Check if a value ends with others
øs Starts With Set 2 Check if a value starts with others
øP Pluralise Count 2 Create a sentence of the form 'a bs'
øṁ Vertical Mirror 1 Vertical Mirror - Split by newlines, mirror each line, join by newlines
øṀ Flip Brackets Vertical Mirror 1 Vertical mirror, and swap brackets and slashes in the second half.
øṖ String Partitions 1 All partitions of a string/list
øḋ To Decimal 1 Convert a rational to its decimal representation.
ø⟇ Get Codepage Character / Get Codepage Index 1 Get the character at a certain index in the vyxal codepage / Get the index of a character in the vyxal codepage
øṘ Roman Numeral 1 Convert a decimal to its roman numeral representation / Convert a roman numeral to its decimal representation.
øJ Parse JSON 1 Parse a JSON string into a Vyxal object
øḞ Replace First Occurrence 3 Replace the first instance of an item with another item
øṄ Replace Nth Occurrence 4 Replace the nth instance of an item with another item. If n is negative, then replaces the last nth instance.
øS Strip whitespace from both sides 1 Strip whitespace from both sides of a string / Remove trailing zeros from a number
øL Strip whitespace from the left side 1 Strip whitespace from the left side of a string
øR Strip whitespace from the right side 1 Strip whitespace from the right side of a string
øl Strip from the left side 2 Strip from the left side of a string
ør Strip from the right side 2 Strip from the right side of a string
ø^ Canvas Draw 3 Draw on a canvas (see knowledge/spec/canvas.md for more details) and return it as a string
ø∧ Global Canvas Draw 3 Draw on the global canvas (see knowledge/spec/canvas.md for more details), which is implicitly printed.
ø. Surround 2 Surround a value with another
øŀ Left Align 1 Left align a string/string list
øɽ Right Align 1 Right align a string/string list
Þ* Cartesian product over list 1 Cartesian product over a list of lists
Þa Adjacency matrix (Directed) 1 Adjacency matrix of directed graph (nonzero A_ij denotes edge from i to j)
Þn Infinite list of all integers 0 All integers in an infinite list (0, 1, -1, 2, -2, ...)
Þż Lift 1 Multiply a numeric list by a range from 1 to its length
ÞŻ Sort Every Level 1 Sort every level of a multidimensional list
ÞA Adjacency matrix (Undirected) 1 Adjacency matrix of undirected graph
Þo Ordinals 0 An infinite list of first, second, third, fourth etc
Þc Cardinals 0 An infinite list of one, two, three, four etc
Þp Primes 0 An infinite list of primes
Þu All Unique 1 Are all elements of a list/string unique?
Þj Depth 1 Depth of ragged list
ÞẊ Cartesian Power 2 Cartesian power, cartesian product with self n times. If both arguments are numbers, turns the left into a range.
Þf Flatten By depth 2 Flatten a list by a certain depth (default 1)
ÞB Random Bits 1 Fill a list with random bits
Þ< All Less Than Increasing 2 Find all numbers less than a certain value in a (potentially infinite) list assumed to be (non-strictly) increasing
Þǔ Untruth 1 Return a list with 1s at the (0-indexed) indices in a, and 0s elsewhere
ÞǓ Connected Uniquify 1 Remove occurences of adjacent duplicates in a list
Þk 2-dimensional Convolution 2 Return two-dimensional convolution of matrices
Þi Multidimensional Indexing 2 Index a list of coordinates into a value.
ÞI All Indices (Multidimensional) 2 All multidimensional indices of element in list
Þḟ Multidimensional Search 2 Find the first multidimensional index of a value in another
ÞḞ Fill to make rectangular 2 Fill a 2-D list to make it rectangular
Þm Zero Matrix 1 Given a list of dimensions, create a matrix with those dimensions, filled with zeroes
ÞṄ Infinite Integer Partitions 0 Infinite list of sets of positive integers (equivalent to Þ∞vṄÞf)
Þ÷ Divide List Into N Equal Length Parts 2 Divide a list into n equal length parts
ÞZ Fill By Coordinates 2 Fill a matrix by calling a function with the lists of coordinates in the matrix.
Þ… Evenly Distribute 2 Evenly distribute a number over elements of a list
Þ↓ Minimum By Function 2 Find the minimum value of a list by applying a function to each element
Þ↑ Maximum By Function 2 Find the maximum value of a list by applying a function to each element
Þ× All Combinations 1 All combinations of a list / string, of all lengths, with replacement
Þx All Combinations Without Replacement 1 All combinations of a list / string, of all lengths, without replacement
ÞF All Fibonacci 0 All Fibonacci numbers as a LazyList.
Þ! All Factorials 0 All factorials as a LazyList.
ÞU Uniquify Mask 1 A list of booleans describing which elements of a will remain after uniquifying.
ÞD Diagonals 1 Diagonals of a matrix, starting with the main diagonal.
Þ√ Diagonals Ordered 1 Diagonals of a matrix, starting with the shortest top diagonal
Þḋ Anti-diagonals 1 Anti-diagonals of a matrix, starting with the main anti-diagonal.
Þ` Anti-diagonals Ordered 1 Anti-diagonals of a matrix, starting with the shortest top anti-diagonal
ÞS Sublists 1 Sublists of a list.
ÞṪ Transpose With Filler 2 Transpose a matrix, with a filler value for empty cells.
Þ℅ Random Permutation 1 Random permutation of a list / string
ÞṀ Matrix Multiplication 2 Multiply two matrices together.
ÞḊ Matrix Determinant 1 Calculate the determinant of a matrix.
Þ\ Anti-diagonal 1 Anti-diagonal of a matrix
Þ/ Main Diagonal 1 Diagonal of a matrix
ÞC Matrix Column Reduce 2 Reduce columns of a matrix by a function.
ÞĠ Gridify 1 Gridify a 2-D list by padding each element with space to make columns aligned, joining each row on spaces, then joining by newlines.
Þ∨ Multiset Difference 2 Similar to set difference, but with duplicates allowed.
Þ∩ Multiset Intersection 2 Similar to set intersection, but with duplicates allowed.
Þ∪ Multiset Union 2 Similar to set union, but with duplicates allowed.
Þ⊍ Multiset Symmetric Difference 2 Similar to set symmetric difference, but with duplicates allowed.
Þ• Dot Product 2 Dot product of two lists.
Þṁ Mold without repeat 2 Mold a list without repeating elements.
ÞM Maximal Indices 1 Indices of the maximal elements of a list.
Þ∴ Elementwise Vectorised Dyadic Maximum 2 Elementwise vectorised dyadic maximum.
Þ∵ Elementwise Vectorised Dyadic Minimum 2 Elementwise vectorised dyadic minimum.
Þs All Slices of a List 2 Get all slices of a list, skipping a certain number of items
Þ¾ Empty the Global Array 0 Empty the global array.
Þr Remove Last Item and Prepend 0 1 Remove the last item of a list and prepend 0. A shortcut for Ṫ0p
Þ∞ Infinite List of Positive Integers 0 An infinite list of positive integers
Þ: Infinite List of Non-Negative Integers 0 An infinite list of non-negative integers
ÞR Remove Last Item From Cumulative Sums and Prepend 0 1 Remove the last item of the cumulative sums of a list and prepend 0. A shortcut for ¦Ṫ0p
Þẇ Unwrap 1 Take a and push a[0]+a[-1] and a[1:-1]
Þg Shortest By Length 1 Return the shortest item in a list.
ÞG Longest By Length 1 Return the longest item in a list.
Þṡ Sort By Length 1 Sort a list by length.
ÞṠ Is Sorted? 1 Returns true if an item is sorted in ascending order using default sorting rules.
ÞṘ Is Sorted in Reverse? 1 Returns true if an item is sorted in descending order using default sorting rules.
ÞȮ Is Ordered? 1 Returns true if the item is sorted in either descending or ascending order.
ÞĊ Is Unordered? 1 Returns true if the item is not sorted in either descending or ascending order.
Þ⇧ Is Strictly Ascending? 1 Returns true if the list is in strictly ascending order.
Þ⇩ Is Strictly Descending? 1 Returns true if the list is in strictly descending order.
Þċ Cycle 1 Form an infinite list from a vector.
ÞK Suffixes 1 Suffixes of a list.
ÞT Multi-dimensional truthy indices 1 Multi-dimensional indices of truthy elements
Þİ First n Items and Rest 2 Push the first n items of a, then the rest of a
ÞN Alternating Negation 1 An infinite list of an item, then that item negated, then that item, and so on. Uses the negation element for negation.
Þ□ Identity Matrix of Size n 1 A matrix with 1s on the main diagonal and zeroes elsewhere
Þe Matrix Exponentiation 2 A matrix multiplied by itself n times
Þd Distance matrix (Directed) 1 Distance matrix of directed graph
Þw Distance matrix (Undirected) 1 Distance matrix of undirected graph
ÞṖ Split Before Indices 2 Split a list before indices in another list
Þṗ Split on Truthy Indices 2 Split a list on truthy indices / Partition a list on truthy items
Þẏ Multidimensonal Indices 1 A list of indices for a multidimensional list
Þė Multidimensonal Enumeration 1 Enumerate a list and all its sublists
¨□ Parse direction arrow to integer 1 Map characters in `>^<v` to integers (0, 1, 2, 3 respectively)
¨^ Parse direction arrow to vector 1 Map characters in `>^<v` to direction vectors
¨U Get Request 1 Send a GET request to a URL
¨= Invariant After Application 1 Push whether the result of applying an element to an item is the same as the original item
¨M Map At Indices 3 Map a function at elements of a list whose indices are in another list
¨, Print With Space 1 Print a value with a space after it
¨… Print With Space Without Popping 1 Print a value with a space after it, without popping it
¨> Strict Greater Than 2 Non-vectorising greater than - useful for lists. Note that all corresponding elements should be of the same type.
¨< Strict Less Than 2 Non-vectorising greater than - useful for lists. Note that all corresponding elements should be of the same type.
¨* All Multiples 1 Return all multiples of a
¨e All Powers 1 Return all powers of a
¨² All Powers of 2 0 Return all powers of 2
¨₀ All Powers of 10 0 Return all powers of 10
¨£ Star Map Reduce each pair of two lists zipped together by a function. Equivalent to Zvƒ
¨ẇ Wrap Last n Items 1 Wrap the last n items on the stack into a list
¨2 Dyadic Map Lambda 2 Open a dyadic mapping lambda - ¨2...; Receives item and index.
¨3 Triadic Map Lambda 3 Open a triadic mapping lambda - ¨3...; Receives item, index, and vector.
¨₂ Dyadic Filter Lambda 2 Open a dyadic filter lambda - ¨₂...; Receives item and index.
¨₃ Triadic Filter Lambda 3 Open a triadic filter lambda - ¨₃...; Receives item, index, and vector.
¨Z Zip lambda 3 Open a zip lambda - ¨Z...; Pops top two items off stack, zips them, and loops over them, pushing each item to the stack. Equivalent to `Zƛ÷...;`.
¨p For Each Overlapping Pair Run element for each overlapping pair. Equivalent to `2lvƒ`
¨? Explicit STDIN 0 Read from STDIN, even if there are arguments
¨S Override Inputs 1 Overrides the list of inputs
¨R Reset Inputs 0 Resets the list of inputs to what they were before overriding with `¨S`
¨i If/Else If the top of the stack is truthy, run the first element, otherwise the second.