# Supported functions of .math()

## Construction functions

Function Description
bignumber(x) Create a BigNumber, which can store numbers with arbitrary precision.
boolean(x) Create a boolean or convert a string or number to a boolean.
chain(value) Wrap any value in a chain, allowing to perform chained operations on the value.
complex(re, im) Create a complex value or convert a value to a complex value.
createUnit(units) Create a user-defined unit and register it with the Unit type.
fraction(numerator, denominator) Create a fraction convert a value to a fraction.
matrix(x) Create a Matrix.
number(value) Create a number or convert a string, boolean, or unit to a number.
sparse(x) Create a Sparse Matrix.
splitUnit(unit, parts) Returns an array of units whose sum is equal to this unit.
string(value) Create a string or convert any object into a string.
unit(x) Create a unit.

## Algebra functions

Function Description
lsolve(L, b) Solves the linear equation system by forwards substitution.
lup(A) Calculate the Matrix LU decomposition with partial pivoting.
lusolve(A, b) Solves the linear system `A * x = b` where `A` is an [n x n] matrix and `b` is a [n] column vector.
slu(A, order, threshold) Calculate the Sparse Matrix LU decomposition with full pivoting.
usolve(U, b) Solves the linear equation system by backward substitution.

## Arithmetic functions

Function Description
abs(x) Calculate the absolute value of a number.
add(x, y) Add two values, `x + y`.
cbrt(x [, allRoots]) Calculate the cubic root of a value.
ceil(x) Round a value towards plus infinity If `x` is complex, both real and imaginary part are rounded towards plus infinity.
cube(x) Compute the cube of a value, `x * x * x`.
divide(x, y) Divide two values, `x / y`.
dotDivide(x, y) Divide two matrices element wise.
dotMultiply(x, y) Multiply two matrices element wise.
dotPow(x, y) Calculates the power of x to y element wise.
exp(x) Calculate the exponent of a value.
fix(x) Round a value towards zero.
floor(x) Round a value towards minus infinity.
gcd(a, b) Calculate the greatest common divisor for two or more values or arrays.
hypot(a, b, ...) Calculate the hypotenusa of a list with values.
lcm(a, b) Calculate the least common multiple for two or more values or arrays.
log(x [, base]) Calculate the logarithm of a value.
log10(x) Calculate the 10-base logarithm of a value.
mod(x, y) Calculates the modulus, the remainder of an integer division.
multiply(x, y) Multiply two values, `x * y`.
norm(x [, p]) Calculate the norm of a number, vector or matrix.
nthRoot(a) Calculate the nth root of a value.
pow(x, y) Calculates the power of x to y, `x ^ y`.
round(x [, n]) Round a value towards the nearest integer.
sign(x) Compute the sign of a value.
sqrt(x) Calculate the square root of a value.
square(x) Compute the square of a value, `x * x`.
subtract(x, y) Subtract two values, `x - y`.
unaryMinus(x) Inverse the sign of a value, apply a unary minus operation.
unaryPlus(x) Unary plus operation.
xgcd(a, b) Calculate the extended greatest common divisor for two values.

## Bitwise functions

Function Description
bitAnd(x, y) Bitwise AND two values, `x & y`.
bitNot(x) Bitwise NOT value, `~x`.
bitOr(x, y) Bitwise OR two values, `x | y`.
bitXor(x, y) Bitwise XOR two values, `x ^ y`.
leftShift(x, y) Bitwise left logical shift of a value x by y number of bits, `x << y`.
rightArithShift(x, y) Bitwise right arithmetic shift of a value x by y number of bits, `x >> y`.
rightLogShift(x, y) Bitwise right logical shift of value x by y number of bits, `x >>> y`.

## Combinatorics functions

Function Description
bellNumbers(n) The Bell Numbers count the number of partitions of a set.
catalan(n) The Catalan Numbers enumerate combinatorial structures of many different types.
composition(n, k) The composition counts of n into k parts.
stirlingS2(n, k) The Stirling numbers of the second kind, counts the number of ways to partition a set of n labelled objects into k nonempty unlabelled subsets.

## Complex functions

Function Description
arg(x) Compute the argument of a complex value.
conj(x) Compute the complex conjugate of a complex value.
im(x) Get the imaginary part of a complex number.
re(x) Get the real part of a complex number.

## Geometry functions

Function Description
[distance([x1, y1], [x2, y2])](functions/distance.md) Calculates: The eucledian distance between two points in 2 and 3 dimensional spaces.
intersect(endPoint1Line1, endPoint2Line1, endPoint1Line2, endPoint2Line2) Calculates the point of intersection of two lines in two or three dimensions and of a line and a plane in three dimensions.

## Logical functions

Function Description
and(x, y) Logical `and`.
not(x) Logical `not`.
or(x, y) Logical `or`.
xor(x, y) Logical `xor`.

## Matrix functions

Function Description
concat(a, b, c, ... [, dim]) Concatenate two or more matrices.
cross(x, y) Calculate the cross product for two vectors in three dimensional space.
det(x) Calculate the determinant of a matrix.
diag(X) Create a diagonal matrix or retrieve the diagonal of a matrix When `x` is a vector, a matrix with vector `x` on the diagonal will be returned.
dot(x, y) Calculate the dot product of two vectors.
eye(n) Create a 2-dimensional identity matrix with size m x n or n x n.
filter(x, test) Filter the items in an array or one dimensional matrix.
flatten(x) Flatten a multi dimensional matrix into a single dimensional matrix.
inv(x) Calculate the inverse of a square matrix.
ones(m, n, p, ...) Create a matrix filled with ones.
partitionSelect(x, k) Partition-based selection of an array or 1D matrix.
range(start, end [, step]) Create an array from a range.
resize(x, size [, defaultValue]) Resize a matrix.
size(x) Calculate the size of a matrix or scalar.
sort(x) Sort the items in a matrix.
squeeze(x) Squeeze a matrix, remove inner and outer singleton dimensions from a matrix.
subset(x, index [, replacement]) Get or set a subset of a matrix or string.
trace(x) Calculate the trace of a matrix: the sum of the elements on the main diagonal of a square matrix.
transpose(x) Transpose a matrix.
zeros(m, n, p, ...) Create a matrix filled with zeros.

## Probability functions

Function Description
combinations(n, k) Compute the number of ways of picking `k` unordered outcomes from `n` possibilities.
factorial(n) Compute the factorial of a value Factorial only supports an integer value as argument.
gamma(n) Compute the gamma function of a value using Lanczos approximation for small values, and an extended Stirling approximation for large values.
kldivergence(x, y) Calculate the Kullback-Leibler (KL) divergence between two distributions.
multinomial(a) Multinomial Coefficients compute the number of ways of picking a1, a2, .
permutations(n [, k]) Compute the number of ways of obtaining an ordered subset of `k` elements from a set of `n` elements.
pickRandom(array) Random pick a value from a one dimensional array.
random([min, max]) Return a random number larger or equal to `min` and smaller than `max` using a uniform distribution.
randomInt([min, max]) Return a random integer number larger or equal to `min` and smaller than `max` using a uniform distribution.

## Relational functions

Function Description
compare(x, y) Compare two values.
deepEqual(x, y) Test element wise whether two matrices are equal.
equal(x, y) Test whether two values are equal.
larger(x, y) Test whether value x is larger than y.
largerEq(x, y) Test whether value x is larger or equal to y.
smaller(x, y) Test whether value x is smaller than y.
smallerEq(x, y) Test whether value x is smaller or equal to y.
unequal(x, y) Test whether two values are unequal.

## Statistics functions

Function Description
max(a, b, c, ...) Compute the maximum value of a matrix or a list with values.
mean(a, b, c, ...) Compute the mean value of matrix or a list with values.
median(a, b, c, ...) Compute the median of a matrix or a list with values.
min(a, b, c, ...) Compute the maximum value of a matrix or a list of values.
mode(a, b, c, ...) Computes the mode of a set of numbers or a list with values(numbers or characters).
prod(a, b, c, ...) Compute the product of a matrix or a list with values.
quantileSeq(A, prob[, sorted]) Compute the prob order quantile of a matrix or a list with values.
std(a, b, c, ...) Compute the standard deviation of a matrix or a list with values.
sum(a, b, c, ...) Compute the sum of a matrix or a list with values.
var(a, b, c, ...) Compute the variance of a matrix or a list with values.

## Trigonometry functions

Function Description
acos(x) Calculate the inverse cosine of a value.
acosh(x) Calculate the hyperbolic arccos of a value, defined as `acosh(x) = ln(sqrt(x^2 - 1) + x)`.
acot(x) Calculate the inverse cotangent of a value, defined as `acot(x) = atan(1/x)`.
acoth(x) 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) Calculate the inverse cosecant of a value, defined as `acsc(x) = asin(1/x)`.
acsch(x) Calculate the hyperbolic arccosecant of a value, defined as `acsch(x) = asinh(1/x) = ln(1/x + sqrt(1/x^2 + 1))`.
asec(x) Calculate the inverse secant of a value.
asech(x) Calculate the hyperbolic arcsecant of a value, defined as `asech(x) = acosh(1/x) = ln(sqrt(1/x^2 - 1) + 1/x)`.
asin(x) Calculate the inverse sine of a value.
asinh(x) Calculate the hyperbolic arcsine of a value, defined as `asinh(x) = ln(x + sqrt(x^2 + 1))`.
atan(x) Calculate the inverse tangent of a value.
atan2(y, x) Calculate the inverse tangent function with two arguments, y/x.
atanh(x) Calculate the hyperbolic arctangent of a value, defined as `atanh(x) = ln((1 + x)/(1 - x)) / 2`.
cos(x) Calculate the cosine of a value.
cosh(x) Calculate the hyperbolic cosine of a value, defined as `cosh(x) = 1/2 * (exp(x) + exp(-x))`.
cot(x) Calculate the cotangent of a value.
coth(x) Calculate the hyperbolic cotangent of a value, defined as `coth(x) = 1 / tanh(x)`.
csc(x) Calculate the cosecant of a value, defined as `csc(x) = 1/sin(x)`.
csch(x) Calculate the hyperbolic cosecant of a value, defined as `csch(x) = 1 / sinh(x)`.
sec(x) Calculate the secant of a value, defined as `sec(x) = 1/cos(x)`.
sech(x) Calculate the hyperbolic secant of a value, defined as `sech(x) = 1 / cosh(x)`.
sin(x) Calculate the sine of a value.
sinh(x) Calculate the hyperbolic sine of a value, defined as `sinh(x) = 1/2 * (exp(x) - exp(-x))`.
tan(x) Calculate the tangent of a value.
tanh(x) Calculate the hyperbolic tangent of a value, defined as `tanh(x) = (exp(2 * x) - 1) / (exp(2 * x) + 1)`.

## Unit functions

Function Description
to(x, unit) Change the unit of a value.

## Utils functions

Function Description
isInteger(x) Test whether a value is an integer number.
isNaN(x) Test whether a value is NaN (not a number).
isNegative(x) Test whether a value is negative: smaller than zero.
isNumeric(x) Test whether a value is an numeric value.
isPositive(x) Test whether a value is positive: larger than zero.
isPrime(x) Test whether a value is prime: has no divisors other than itself and one.
isZero(x) Test whether a value is zero.