> For the complete documentation index, see [llms.txt](https://machinations.gitbook.io/docs/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://machinations.gitbook.io/docs/registers/math.js-functions.md). # Math.js Functions All Math.js functions supported ## Arithmetic functions | Function | What it does | | ------------------------------------------------------------------------------- | -------------------------------------------------------------------------------------------------------------------- | | [abs(x)](https://mathjs.org/docs/reference/functions/abs.html) | Calculate the absolute value of a number | | [add(x, y)](https://mathjs.org/docs/reference/functions/add.html) | Add two or more values, x + y | | [cbrt(x \[, allRoots\])](https://mathjs.org/docs/reference/functions/cbrt.html) | Calculates the cubic root of a value | | [ceil(x)](https://mathjs.org/docs/reference/functions/ceil.html) | Round a value towards plus infinity If x is complex, both real and imaginary parts are rounded towards plus infinity | | [cube(x)](https://mathjs.org/docs/reference/functions/cube.html) | Compute the cube of a value, x \* x \* x | | [divide(x, y)](https://mathjs.org/docs/reference/functions/divide.html) | Divide two values, x / y | | [dotPow(x, y)](https://mathjs.org/docs/reference/functions/dotPow.html) | Calculates the power of x to y element-wise | | [exp(x)](https://mathjs.org/docs/reference/functions/exp.html) | Calculate the exponent of a value | | [expm1(x)](https://mathjs.org/docs/reference/functions/expm1.html) | Calculate the value of subtracting 1 from the exponential value | | [fix(x)](https://mathjs.org/docs/reference/functions/fix.html) | Round a value towards zero | | [floor(x)](https://mathjs.org/docs/reference/functions/floor.html) | Round a value towards minus infinity | | [gcd(a, b)](https://mathjs.org/docs/reference/functions/gcd.html) | Calculate the greatest common divisor for two or more values or arrays | | [hypot(a, b, …)](https://mathjs.org/docs/reference/functions/hypot.html) | Calculate the hypotenusa of a list with values | | [lcm(a, b)](https://mathjs.org/docs/reference/functions/lcm.html) | Calculate the least common multiple for two or more values or arrays | | [log(x \[, base\])](https://mathjs.org/docs/reference/functions/log.html) | Calculate the logarithm of a value | | [log10(x)](https://mathjs.org/docs/reference/functions/log10.html) | Calculate the 10-base logarithm of a value | | [log1p(x)](https://mathjs.org/docs/reference/functions/log1p.html) | Calculate the logarithm of a value+1 | | [log2(x)](https://mathjs.org/docs/reference/functions/log2.html) | Calculate the 2-base of a value | | [mod(x, y)](https://mathjs.org/docs/reference/functions/mod.html) | Calculates the modulus, the remainder of an integer division | | [multiply(x, y)](https://mathjs.org/docs/reference/functions/multiply.html) | Multiply two or more values, x \* y | | [norm(x \[, p\])](https://mathjs.org/docs/reference/functions/norm.html) | Calculate the norm of a number, vector or matrix | | [nthRoot(a)](https://mathjs.org/docs/reference/functions/nthRoot.html) | Calculate the nth root of a value | | [nthRoots(x)](https://mathjs.org/docs/reference/functions/nthRoots.html) | Calculate the nth roots of a value | | [pow(x, y)](https://mathjs.org/docs/reference/functions/pow.html) | Calculates the power of x to y, x ^ y | | [round(x \[, n\])](https://mathjs.org/docs/reference/functions/round.html) | Round a value towards the nearest integer | | [sign(x)](https://mathjs.org/docs/reference/functions/sign.html) | Compute the sign of a value | | [sqrt(x)](https://mathjs.org/docs/reference/functions/sqrt.html) | Calculate the square root of a value | | [square(x)](https://mathjs.org/docs/reference/functions/square.html) | Compute the square of a value, x \* x | | [subtract(x, y)](https://mathjs.org/docs/reference/functions/subtract.html) | Subtract two values, x - y | | [unaryMinus(x)](https://mathjs.org/docs/reference/functions/unaryMinus.html) | Inverse the sign of a value, apply a unary minus operation | | [unaryPlus(x)](https://mathjs.org/docs/reference/functions/unaryPlus.html) | Unary plus operation | | [xgcd(a, b)](https://mathjs.org/docs/reference/functions/xgcd.html) | Calculate the extended greatest common divisor for two values | ## Bitwise Functions | Functions | What it does | | ----------------------------------------------------------------------------------------- | ----------------------------------------------------------------------- | | [bitAnd(x, y)](https://mathjs.org/docs/reference/functions/bitAnd.html) | Bitwise AND two values, x & y | | [bitNot(x)](https://mathjs.org/docs/reference/functions/bitNot.html) | Bitwise NOT value, \~x | | [bitOr(x, y)](https://mathjs.org/docs/reference/functions/bitOr.html) | Bitwise OR two values, x \| y | | [bitXor(x, y)](https://mathjs.org/docs/reference/functions/bitXor.html) | Bitwise XOR two values, x ^ y | | [leftShift(x, y)](https://mathjs.org/docs/reference/functions/leftShift.html) | Bitwise left logical shift of a value x by y number of bits, x << y | | [rightArithShift(x, y)](https://mathjs.org/docs/reference/functions/rightArithShift.html) | Bitwise right arithmetic shift of a value x by y number of bits, x >> y | | [rightLogShift(x, y)](https://mathjs.org/docs/reference/functions/rightLogShift.html) | Bitwise right logical shift of value x by y number of bits, x >>> y | ## Logical Functions | Function | What it does | | ----------------------------------------------------------------- | ------------ | | [and(x, y)](https://mathjs.org/docs/reference/functions/and.html) | Logical and | | [not(x)](https://mathjs.org/docs/reference/functions/not.html) | Logical not | | [or(x, y)](https://mathjs.org/docs/reference/functions/or.html) | Logical or | | [xor(x, y)](https://mathjs.org/docs/reference/functions/xor.html) | Logical xor | ## Matrix Functions | Function | What it does | | ---------------------------------------------------------------- | ---------------------------------------- | | [size(x)](https://mathjs.org/docs/reference/functions/size.html) | Calculate the size of a matrix or scalar | | [sort(x)](https://mathjs.org/docs/reference/functions/sort.html) | Sort the items in a matrix | ## Probability Functions | Function | What it does | | ------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------- | | [factorial(n)](https://mathjs.org/docs/reference/functions/factorial.html) | Compute the factorial of a value Factorial only supports an integer value as argument | | [gamma(n)](https://mathjs.org/docs/reference/functions/gamma.html) | Compute the gamma function of a value using Lanczos approximation for small values, and an extended Stirling approximation for large values | | [pickRandom(array)](https://mathjs.org/docs/reference/functions/pickRandom.html) | Random pick one or more values from a one dimensional array | | [random(\[min, max\])](https://mathjs.org/docs/reference/functions/random.html) | Return a random number larger or equal to min and smaller than max using a uniform distribution | | [randomInt(\[min, max\])](https://mathjs.org/docs/reference/functions/randomInt.html) | Return a random integer number larger or equal to min and smaller than max using a uniform distribution | ## Relational Functions | Function | Whate it does | | --------------------------------------------------------------------------------------- | -------------------------------------------------------------- | | [compare(x, y)](https://mathjs.org/docs/reference/functions/compare.html) | Compare two values | | [compareNatural(x, y)](https://mathjs.org/docs/reference/functions/compareNatural.html) | Compare two values of any type in a deterministic, natural way | | [equal(x, y)](https://mathjs.org/docs/reference/functions/equal.html) | Test whether two values are equal | | [larger(x, y)](https://mathjs.org/docs/reference/functions/larger.html) | Test whether value x is larger than y | | [largerEq(x, y)](https://mathjs.org/docs/reference/functions/largerEq.html) | Test whether value x is larger or equal to y | | [smaller(x, y)](https://mathjs.org/docs/reference/functions/smaller.html) | Test whether value x is smaller than y | | [smallerEq(x, y)](https://mathjs.org/docs/reference/functions/smallerEq.html) | Test whether value x is smaller or equal to y | | [unequal(x, y)](https://mathjs.org/docs/reference/functions/unequal.html) | Test whether two values are unequal | ## Statistics Functions | Function | What it does | | --------------------------------------------------------------------------------- | ---------------------------------------------------------------------------------- | | [mad(a, b, c, …)](https://mathjs.org/docs/reference/functions/mad.html) | Compute the median absolute deviation of a matrix or a list with values | | [max(a, b, c, …)](https://mathjs.org/docs/reference/functions/max.html) | Compute the maximum value of a matrix or a list with values | | [mean(a, b, c, …)](https://mathjs.org/docs/reference/functions/mean.html) | Compute the mean value of matrix or a list with values | | [median(a, b, c, …)](https://mathjs.org/docs/reference/functions/median.html) | Compute the median of a matrix or a list with values | | [min(a, b, c, …)](https://mathjs.org/docs/reference/functions/min.html) | Compute the minimum value of a matrix or a list of values | | [mode(a, b, c, …)](https://mathjs.org/docs/reference/functions/mode.html) | Computes the mode of a set of numbers or a list with values(numbers or characters) | | [prod(a, b, c, …)](https://mathjs.org/docs/reference/functions/prod.html) | Compute the product of a matrix or a list with values | | [std(a, b, c, …)](https://mathjs.org/docs/reference/functions/std.html) | Compute the standard deviation of a matrix or a list with values | | [sum(a, b, c, …)](https://mathjs.org/docs/reference/functions/sum.html) | Compute the sum of a matrix or a list with values | | [variance(a, b, c, …)](https://mathjs.org/docs/reference/functions/variance.html) | Compute the variance of a matrix or a list with values | ## Trigonometry Functions | Function | What it does | | --------------------------------------------------------------------- | -------------------------------------------------------------------------------------------------------------------- | | [acos(x)](https://mathjs.org/docs/reference/functions/acos.html) | Calculate the inverse cosine of a value | | [acosh(x)](https://mathjs.org/docs/reference/functions/acosh.html) | Calculate the hyperbolic arccos of a value, defined as acosh(x) = ln(sqrt(x^2 - 1) + x) | | [acot(x)](https://mathjs.org/docs/reference/functions/acot.html) | Calculate the inverse cotangent of a value, defined as acot(x) = atan(1/x) | | [acoth(x)](https://mathjs.org/docs/reference/functions/acoth.html) | Calculate the hyperbolic arccotangent of a value, defined as acoth(x) = atanh(1/x) = (ln((x+1)/x) + ln(x/(x-1))) / 2 | | [acsc(x)](https://mathjs.org/docs/reference/functions/acsc.html) | Calculate the inverse cosecant of a value, defined as acsc(x) = asin(1/x) | | [acsch(x)](https://mathjs.org/docs/reference/functions/acsch.html) | Calculate the hyperbolic arccosecant of a value, defined as acsch(x) = asinh(1/x) = ln(1/x + sqrt(1/x^2 + 1)) | | [asec(x)](https://mathjs.org/docs/reference/functions/asec.html) | Calculate the inverse secant of a value | | [asech(x)](https://mathjs.org/docs/reference/functions/asech.html) | Calculate the hyperbolic arcsecant of a value, defined as asech(x) = acosh(1/x) = ln(sqrt(1/x^2 - 1) + 1/x) | | [asin(x)](https://mathjs.org/docs/reference/functions/asin.html) | Calculate the inverse sine of a value | | [asinh(x)](https://mathjs.org/docs/reference/functions/asinh.html) | Calculate the hyperbolic arcsine of a value, defined as asinh(x) = ln(x + sqrt(x^2 + 1)) | | [atan(x)](https://mathjs.org/docs/reference/functions/atan.html) | Calculate the inverse tangent of a value | | [atan2(y, x)](https://mathjs.org/docs/reference/functions/atan2.html) | Calculate the inverse tangent function with two arguments, y/x | | [atanh(x)](https://mathjs.org/docs/reference/functions/atanh.html) | Calculate the hyperbolic arctangent of a value, defined as atanh(x) = ln((1 + x)/(1 - x)) / 2 | | [cos(x)](https://mathjs.org/docs/reference/functions/cos.html) | Calculate the cosine of a value | | [cosh(x)](https://mathjs.org/docs/reference/functions/cosh.html) | Calculate the hyperbolic cosine of a value, defined as cosh(x) = 1/2 \* (exp(x) + exp(-x)) | | [cot(x)](https://mathjs.org/docs/reference/functions/cot.html) | Calculate the cotangent of a value | | [coth(x)](https://mathjs.org/docs/reference/functions/coth.html) | Calculate the hyperbolic cotangent of a value, defined as coth(x) = 1 / tanh(x) | | [csc(x)](https://mathjs.org/docs/reference/functions/csc.html) | Calculate the cosecant of a value, defined as csc(x) = 1/sin(x) | | [csch(x)](https://mathjs.org/docs/reference/functions/csch.html) | Calculate the hyperbolic cosecant of a value, defined as csch(x) = 1 / sinh(x) | | [sec(x)](https://mathjs.org/docs/reference/functions/sec.html) | Calculate the secant of a value, defined as sec(x) = 1/cos(x) | | [sech(x)](https://mathjs.org/docs/reference/functions/sech.html) | Calculate the hyperbolic secant of a value, defined as sech(x) = 1 / cosh(x) | | [sin(x)](https://mathjs.org/docs/reference/functions/sin.html) | Calculate the sine of a value | | [sinh(x)](https://mathjs.org/docs/reference/functions/sinh.html) | Calculate the hyperbolic sine of a value, defined as sinh(x) = 1/2 \* (exp(x) - exp(-x)) | | [tan(x)](https://mathjs.org/docs/reference/functions/tan.html) | Calculate the tangent of a value | | [tanh(x)](https://mathjs.org/docs/reference/functions/tanh.html) | Calculate the hyperbolic tangent of a value, defined as tanh(x)=(exp(2 \* x) - 1)/(exp(2 \* x)+1) | ## Utils Functions | Function | What it does | | -------------------------------------------------------------------------------------- | ------------------------------------------------------------------------ | | [hasNumericValue(x)](https://mathjs.org/docs/reference/functions/hasNumericValue.html) | Test whether a value is a numeric value | | [isInteger(x)](https://mathjs.org/docs/reference/functions/isInteger.html) | Test whether a value is an integer number | | [isNaN(x)](https://mathjs.org/docs/reference/functions/isNaN.html) | Test whether a value is NaN (not a number) | | [isNegative(x)](https://mathjs.org/docs/reference/functions/isNegative.html) | Test whether a value is negative: smaller than zero | | [isNumeric(x)](https://mathjs.org/docs/reference/functions/isNumeric.html) | Test whether a value is an numeric value | | [isPositive(x)](https://mathjs.org/docs/reference/functions/isPositive.html) | Test whether a value is positive: larger than zero | | [isPrime(x)](https://mathjs.org/docs/reference/functions/isPrime.html) | Test whether a value is prime: has no divisors other than itself and one | | [isZero(x)](https://mathjs.org/docs/reference/functions/isZero.html) | Test whether a value is zero |