Arithmetic Functions

You can check out the available functions and required parameters in the table below. Please use the links provided to review the original documentation on mathjs.org.

You can check out this diagram for Useful Functions & Syntax used in Machinations:
https://my.machinations.io/d/framework-useful-functions–syntax/a51907aeb67b4ca8b03add11829841c6

Function	What it does
abs(x)	Calculate the absolute value of a number `abs(-4.2) = 4.2`
add(x, y)	Add two or more values `add(2,3,4) = 9`
cbrt(x , allRoots)	Calculates the cubic root of a value `cbrt(27) = 3`
ceil(x)	Round a value towards plus infinity `ceil(3.2) = 4`
cube(x)	Compute the cube of a value `cube(2) = 8`
divide(x, y)	Divide two values, x / y `divide(2,3) = 0.6666...`
dotPow(x, y)	Calculates the power of x to y element-wise `dotPow(2,3) = 8`
exp(x)	Calculate the exponent of a value `exp(2) = 7.38905..`
expm1(x)	Calculate the value of subtracting one from the exponential value `expm1(2) = 6.38905..`
fix(x)	Round a value towards zero `fix(3.2) = 3`
floor(x)	Round a value towards minus infinity `floor(-3.2) = -4`
gcd(a, b, …)	Calculate the greatest common divisor for two or more values or arrays `gcd(8,12) = 4`
hypot(a, b, …)	Calculate the hypotenuse of a list with values `hypot(3,4) = 5`
lcm(a, b, …)	Calculate the least common multiple for two or more values or arrays `lcm(6,21,5) = 210`
log(x, base)	Calculate the logarithm of a value `log(1024, 2) = 10`
log10(x)	Calculate the 10-base logarithm of a value `log10(10000) = 4`
log1p(x)	Calculate the logarithm of a value+1 `log1p(2.5) = 1.25276...`
log2(x)	Calculate the 2-base of a value `log2(16) = 4`
mod(x, y)	Calculates the modulus, the remainder of an integer division `mod(8, 3) = 2`
multiply(x, y)	Multiply two or more values `multiply(2.5*10) = 25`
norm(x, p)	Calculate the norm of a number, vector or matrix `log(1024, 2) = 10`
nthRoot(a, root)	Calculate the nth root of a value. The default value of root is 2 if left empty `nthRoot(9, 2) = 3`
nthRoots(x, root)	Calculate the nth roots of a value. Root is optional and has a value of 2 by default. The output is a complex value `nthRoots(1) = {re: 1, im: 0}, {re: -1, im: 0}`
pow(x, y)	Calculates the power of x to y `pow(4, 2) = 16`
round(x, n)	Round a value towards the nearest integer. n represents the number of rounded decimals `round(3.333, 2) = 3.3`
sign(x)	Compute the sign of a value `sign(-10) = -1`
sqrt(x)	Calculate the square root of a value `sqrt(25) = 5`
square(x)	Compute the square of a value `square(5) = 25`
subtract(x, y)	Subtract two values `subtract(5.3, 2) = 3.3`
unaryMinus(x)	Inverse the sign of a value, apply a unary minus operation `unaryMinus(3.3) = -3.3`
unaryPlus(x)	Unary plus operation `unaryPlus(3.5) = 3.5`
xgcd(a, b)	Calculate the extended greatest common divisor for two values `xgcd(8, 12) = [4, -1, 1]`

Logical Functions

Function	What it does
and(x, y)	Logical and `and(2, 5) = true`
not(x)	Logical not `not(2) = false`
or(x, y)	Logical or `or(5, 0) = true`
xor(x, y)	Logical xor `xor(5, 0) = true`

Set & Array Functions

Function	What it does
setCartesian(X, Y)	Create the cartesian product of two arrays. `setCartesian([1, 2], [3, 4]) = [[1, 3], [1, 4], [2, 3], [2, 4]]`
setDifference(X, Y)	Create the difference between two arrays: every element of X, that is not the element of Y. `setDifference([1, 2, 3, 4], [3, 4, 5, 6]) = [1, 2]`
setDistinct(X)	Collect the distinct elements of an array. `setDistinct([1, 1, 1, 2, 2, 3]) = [1, 2, 3]`
setIntersect(X, Y)	Create the intersection of two arrays. `setIntersect([1, 2, 3, 4], [3, 4, 5, 6]) = [3, 4]`
setIsSubset(X, Y)	Check whether array X is a subset of array Y. `setIsSubset([3, 4], [3, 4, 5, 6]) = true`
setMultiplicity(element, X)	Count the number of occurrences of an element in an array. `setMultiplicity(2, [1, 2, 2, 4]) = 2`
setPowerset(X)	Create the powerset of an array. `setPowerset([1, 2]) = [[], [1], [2], [1, 2]]`
setSize(X)	Count the number of elements of an array. `setSize([1, 2, 2, 4]) = 4`
setSymDifference(X, Y)	Create the symmetric difference of two arrays. `setSymDifference([1, 2, 3, 4], [3, 4, 5, 6]) = [1, 2, 5, 6]`
setUnion(X, Y)	Create the union of two arrays. `setUnion([1, 2, 3, 4], [4, 5]) = [1, 2, 3, 4, 5]`

Matrix Functions

Function	What it does
row(value, index)	Return a row from a Matrix. The returned value will be an array `row([[1, 2], [3, 4]], 1) = [[1, 2]]`
column(value, index)	Return a column from a Matrix. The returned value will be an array `column([[1, 2], [3, 4]], 1) = [[1, 3]]`
concat(a, b, c, … )	Concatenate two or more matrices. `concat([[1, 2], [5, 6]], [[3, 4], [7, 8]]) = [[1, 2, 3, 4], [5, 6, 7, 8]]`
count(x)	Count the number of elements of a matrix, array, or string. `count([[1, 2, 3], [4, 5, 6]]) = 6`
filter(x, test)	Filter the items in an array or one-dimensional matrix. `filter([6, -2, -1, 4, 3], isPositive) = [6, 4, 3]`
resize(x, size)	Resize a matrix based on a given size `resize([1, 2, 3, 4, 5], [3]) = [1, 2, 3]`
subset(value, index)	Get or set a subset of a matrix or string `subset([[1, 2], [3, 4]], index(1, 0)) = 3`
size(x)	Calculate the size of a matrix or scalar `size([[1, 2, 3], [4, 5, 6]]) = [2, 3]`
sort(x)	Sort the items in a matrix `sort([5, 10, 1]) = [1, 5, 10]`
`squeeze(x)`	Remove inner and outer singleton dimensions from a matrix `squeeze([[0, 0, 0]]) = [0, 0, 0]`

Probability Functions

Function	What it does
combinations(n, k)	Compute the number of ways of picking `k` unordered outcomes from `n` possibilities. `combinations(7, 5) = 21`
factorial(n)	Compute the factorial of a value Factorial only supports an integer value as an argument `factorial(5) = 120`
gamma(n)	Compute the gamma function of a value using Lanczos approximation for small values, and an extended Stirling approximation for large values `gamma(5) = 24`
permutations(n k)	Compute the number of ways of obtaining an ordered subset of `k` elements from a set of `n` elements. `permutations(5, 3) = 60`
pickRandom(array)	Random pick one or more values from a one-dimensional array `pickRandom([3, 6, 12, 2]) = one random value in the array`
random(min, max)	Return a random number larger or equal to min and smaller than max using a uniform distribution `random(30, 40) = returns a random number between 30 and 39`
randomInt(min, max)	Return a random integer number larger or equal to min and smaller than max using a uniform distribution `randomInt(30, 40) = returns a random integer between 30 and 39`

Relational Functions

Function	What it does
compare(x, y)	Compare two values `compare(2, [1, 2, 3]) = [1, 0, -1]`
compareNatural(x, y)	Compare two values of any type in a deterministic, natural way `compareNatural(6, 1) = 1`
equal(x, y)	Test whether two values are equal `equal(5, 5) = true`
larger(x, y)	Test whether value x is larger than y `larger(2, 5) = false`
largerEq(x, y)	Test whether value x is larger or equal to y `largerEq(5, 5) = true`
smaller(x, y)	Test whether value x is smaller than y `smaller(5, 0) = false`
smallerEq(x, y)	Test whether value x is smaller or equal to y `smallerEq(5, 5) = true`
unequal(x, y)	Test whether two values are unequal `unequal(5, 0) = true`

Statistics Functions

Function	What it does
corr(A, B)	Compute the correlation coefficient of two lists with values, For matrices, the matrix correlation coefficient is calculated `corr([1, 2, 3, 4, 5], [4, 5, 6, 7, 8]) = 1`
cumsum(a, b, c, …)	Compute the cumulative sum of a matrix or a list with values. `cumsum(2, 1, 4, 3) = [2, 3, 7, 10]`
mad(a, b, c, …)	Compute the median absolute deviation of a matrix or a list with values `mad([[1, 2, 3], [4, 5, 6]]) = 1.5`
max(a, b, c, …)	Compute the maximum value of a matrix or a list with values `max(2, 1, 4, 3) = 4`
mean(a, b, c, …)	Compute the mean value of matrix or a list with values `mean(2, 1, 4, 3) = 2.5`
median(a, b, c, …)	Compute the median of a matrix or a list with values `median(5, 2, 7) = 5`
min(a, b, c, …)	Compute the minimum value of a matrix or a list of values `min(2, 1, 4, 3) = 1`
mode(a, b, c, …)	Computes the mode of a set of numbers or a list with values(numbers or characters) `mode(2, 1, 4, 3, 1) = [1]`
prod(a, b, c, …)	Compute the product of a matrix or a list with values `prod(2, 3, 4) = 24`
std(a, b, c, …)	Compute the standard deviation of a matrix or a list with values `std([2, 4, 6, 8]) = 2.5819...`
sum(a, b, c, …)	Compute the sum of a matrix or a list with values `sum([2, 1, 4, 3]) = 10`
variance(a, b, c, …)	Compute the variance of a matrix or a list with values `variance([2, 4, 6, 8]) = 6.666...`

Utils Functions

Function	What it does
hasNumericValue(x)	Test whether a value is a numeric value `hasNumericValue([2.3, ' a ', false]) = [true, false, true]`
isInteger(x)	Test whether a value is an integer number `isInteger(5) = true`
isNaN(x)	Test whether a value is NaN (not a number) `isNaN(NaN) = true`
isNegative(x)	Test whether a value is negative: smaller than zero `isNegative(5) = false`
isNumeric(x)	Test whether a value is an numeric value `isNumeric([2.3, ' a ', false]) = [true, false, true]`
isPositive(x)	Test whether a value is positive: larger than zero `isPositive(-5) = false`
isPrime(x)	Test whether a value is prime: has no divisors other than itself and one `isPrime(23) = true`
isZero(x)	Test whether a value is zero `isZero(0) = true`

Trigonometry Functions

Function	What it does
acos(x)	Calculate the inverse cosine of a value `acos(0.5) = 1.0471...`
acot(x)	Calculate the inverse cotangent of a value, defined as acot(x) = atan(1/x) `acot(0.5) = 1.1071...`
asin(x)	Calculate the inverse sine of a value `asin(0.5) = 0.5235...`
atan(x)	Calculate the inverse tangent of a value `atan(0.5) = 0.4636...`
cos(x)	Calculate the cosine of a value `cos(pi / 4) = 0.7071...`
cosh(x)	Calculate the hyperbolic cosine of a value, defined as cosh(x) = 1/2 * (exp(x) + exp(-x)) `cosh(0.5) = 1.1276...`
cot(x)	Calculate the cotangent of a value `cot(2) = -0.4576...`
coth(x)	Calculate the hyperbolic cotangent of a value, defined as coth(x) = 1 / tanh(x) `coth(2) = 1.03731...`
sec(x)	Calculate the secant of a value, defined as sec(x) = 1/cos(x) `sec(2) = -2.4029...`
sin(x)	Calculate the sine of a value `sin(pi / 4) = 0.7071...`
sinh(x)	Calculate the hyperbolic sine of a value, defined as sinh(x) = 1/2 * (exp(x) – exp(-x)) `sinh(0.5) = 0.52109...`
tan(x)	Calculate the tangent of a value `tan(0.5) = 0.5463...`

Bitwise Functions

Functions	What it does
bitAnd(x, y)	Bitwise AND two values, `bitAnd(6,3) = 2 // and(110, 011) = 010`
bitNot(x)	Bitwise NOT value, `bitNot(5) = -6 // not(1 0101) = 0 1010`
bitOr(x, y)	Bitwise OR two values, `bitOr(6,3) = 7 // or(110, 011) = 111`
bitXor(x, y)	Bitwise XOR two values, `bitXor(6,3) = 5 // xor(110, 011) = 101`
leftShift(x, y)	Bitwise left logical shift of a value x by y number of bits `leftShift(9, 1) = 18`
rightArithShift(x, y)	Bitwise right arithmetic shift of a value x by y number of bits `rightShift(9,1) = 4`
rightLogShift(x, y)	Bitwise right logical shift of value x by y number of bits `rightLogShift(16,1) = 8`

Operators

The following table contains useful operators for working with Registers and/or custom variables. You can find the full list in the Operators section at Mathjs.org.

Name	Syntax	Example	Result
Grouping	`(x)`	`2 * (3 + 4)`	`14`
Matrix, Index	`[...]`	`[[1,2],[3,4]]`	`[[1,2],[3,4]]`
Parameter separator	`x, y`	`max(2, 1, 5)`	`5`
Add	`x + y`	`4 + 5`	`9`
Subtract	`x - y`	`7 - 3`	`4`
Multiply	`x * y`	`2 * 3`	`6`
Divide	`x / y`	`6 / 2`	`3`
Power	`x ^ y`	`2 ^ 3`	`8`
Factorial	`y!`	`5!`	`120`
Logical and	`x and y`	`true and false`	`false`
Logical not	`not y`	`not true`	`false`
Logical or	`x or y`	`true or false`	`true`
Logical xor	`x xor y`	`true xor true`	`false`
Assignment	`x = y`	`a = 5`	`5`
Conditional expression	`x ? y : z`	`15 > 100 ? 1 : -1`	`-1`
Equal	`x == y`	`2 == 4 - 2`	`true`
Unequal	`x != y`	`2 != 3`	`true`
Smaller	`x < y`	`2 < 3`	`true`
Larger	`x > y`	`2 > 3`	`false`
Smallereq	`x <= y`	`4 <= 3`	`false`
Largereq	`x >= y`	`2 + 4 >= 6`	`true`

Yih-Ling Chen

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