Math

Math is a package of functions for PapajScript. This package contains advanced mathematical functions. It was released on May 14, 2020.

List of current Math functions

Notes:

• If you do not want to type Math. every time, just type @use(Math) before. However, if you want to stop using the package, type @unuse(Math).
• The version 0.5.1.1 is the last version where you can use Math. functions without running @use(Math). Starting from April 16, 2021, all Math functions require to be activated by @use(Math)

Constants

Package Function	Syntax	Output type	Purpose	Since
Math.PI	(no args) function	Number	π (pi) number, π ≈ 3.1415926535897	0.4.3
Math.EU	(no args) function	Number	Euler's number, e ≈ 2.7182818284590	0.4.3
Math.FI	(no args) function	Number	Golden ratio, φ ≈ 1.6180339887498	0.4.3
Math.EM	(no args) function	Number	Euler-Mascheroni constant γ ≈ 0.5772156649015	0.4.3

General purpose

Package Function	Syntax	Output type	Purpose	Since
Math.choose	NUM1 NUM2 function	Number	Binomial coefficient; N1 = n, N2 = k	0.4.3
Math.gcd	NUM1 NUM2 function	Number	Greatest Common Divisor	0.4.3
Math.lcm	NUM1 NUM2 function	Number	Least Common Multiplier	0.4.3
Math.fibonacci	NUM1 function	Number	Fibonacci number	0.4.3
Math.divides	NUM1 NUM2 function	Boolean	Returns TRUE if NUM1 divides NUM2 (i.e. NUM1 mod NUM2 = 0), and returns FALSE otherwise	0.5.1.1
Math.gamma	NUM1 function	Number	Returns a Gamma function value	0.5.1
Math.gammaln	NUM1 function	Number	Returns a natural logarithm of Gamma function value	0.5.1
Math.erf	NUM1 function	Number	error function	0.5.2
Math.erfc	NUM1 function	Number	complementary error function	0.5.2
Math.randomIntRange	NUM1 NUM2 function	Number	Get a random integer from the range of [a, b]	0.5.2
Math.randomRealRange	NUM1 NUM2 function	Number	Get a random real number from the range of [a, b)	0.5.2

Trigonometric and hyperbolic functions

Package Function	Syntax	Output type	Purpose	Since
Math.sin	NUM1 function	Number	sine	0.4.3
Math.cos	NUM1 function	Number	cosine	0.4.3
Math.tan	NUM1 function	Number	tangent	0.4.3
Math.cot	NUM1 function	Number	cotangent	0.4.3
Math.sec	NUM1 function	Number	secant	0.4.3
Math.csc	NUM1 function	Number	cosecant	0.4.3
Math.arcsin	NUM1 function	Number	arcsine	0.5.0
Math.arccos	NUM1 function	Number	arccosine	0.5.0
Math.arctan	NUM1 function	Number	arctangent	0.5.0
Math.arccot	NUM1 function	Number	arccotangent	0.5.0
Math.arcsec	NUM1 function	Number	arcsecant	0.5.2
Math.arccsc	NUM1 function	Number	arccosecant	0.5.2
Math.sinh	NUM1 function	Number	hyperbolic sine	0.5.0
Math.cosh	NUM1 function	Number	hyperbolic cosine	0.5.0
Math.tanh	NUM1 function	Number	hyperbolic tangent	0.5.0
Math.coth	NUM1 function	Number	hyperbolic cotangent	0.5.0
Math.sech	NUM1 function	Number	hyperbolic secant	0.5.0
Math.csch	NUM1 function	Number	hyperbolic cosecant	0.5.0
Math.arsinh	NUM1 function	Number	hyperbolic area sine	0.5.2
Math.arcosh	NUM1 function	Number	hyperbolic area cosine	0.5.2
Math.artanh	NUM1 function	Number	hyperbolic area tangent	0.5.2
Math.arcoth	NUM1 function	Number	hyperbolic area cotangent	0.5.2
Math.arsech	NUM1 function	Number	hyperbolic area secant	0.5.2
Math.arcsch	NUM1 function	Number	hyperbolic area cosecant	0.5.2
Math.toDegrees	NUM1 function	Number	convert radians to degrees	0.5.0
Math.toRadians	NUM1 function	Number	convert degrees to radians	0.5.0

Statistics – general functions

Package Function	Syntax	Output type	Purpose	Since
Math.moment	ARR1 NUM1 function	Number	N-th moment of the elements of A1	0.5.2
Math.quantile	ARR1 NUM1 function	Number	a (1/N)-quantile of A1 (i.e. if N1 = 0.25 = 1/4, then the first 4-quantile, and if N1 = 0.5 = 2/4 then the second 4-quantile etc.)	0.5.2
Math.tertile	ARR1 NUM1 function	Number	the N1-th tertile (3-quantile)	0.5.2
Math.quartile	ARR1 NUM1 function	Number	the N1-th quartile (4-quantile)	0.5.2
Math.octile	ARR1 NUM1 function	Number	the N1-th octile (8-quantile)	0.5.2
Math.decile	ARR1 NUM1 function	Number	the N1-th decile (10-quantile)	0.5.2
Math.hexadecile	ARR1 NUM1 function	Number	the N1-th hexadecile (16-quantile)	0.5.2
Math.percentile	ARR1 NUM1 function	Number	the N1-th percentile (100-quantile)	0.5.2
Math.skewness	ARR1 function	Number	skewness coefficient of A1	0.5.3
Math.kurtosis	ARR1 function	Number	kurtosis coefficient of A1	0.5.3
Math.kurtosis3	ARR1 function	Number	excess kurtosis coefficient of A1 (kurtosis - 3)	0.5.3
Math.excessKurtosis	ARR1 function	Number	same as Math.kurtosis3	0.5.3

Statistics – distribution functions

Package Function	Syntax	Output type	Purpose	Since
Math.distNormStd	NUM1 function	Number	Returns a CDF (i.e. P(X ≤ NUM1)) of standard normal distribution (μ = 0, σ = 1)	0.4.3
Math.funcNormStd	NUM1 function	Number	Returns a PDF (i.e. f(NUM1)) of standard normal distribution (μ = 0, σ = 1)	0.5.0
Math.randomNormStd	(no args) function	Number	Generate a random number using standard normal distribution (μ = 0, σ = 1)	0.5.0
Math.genNormStd	NUM1 function	set of Number	Generate N1 random numbers using standard normal distribution (μ = 0, σ = 1)	0.5.0
Math.distNorm	NUM1 NUM2 NUM3 function	Number	Returns a CDF (i.e. P(X ≤ NUM1)) of normal distribution (μ = NUM2, σ = NUM3)	0.4.3
Math.funcNorm	NUM1 NUM2 NUM3 function	Number	Returns a PDF (i.e. f(NUM1)) of normal distribution (μ = NUM2, σ = NUM3)	0.5.0
Math.randomNorm	NUM1 NUM2 function	Number	Generate a random number using normal distribution (μ = NUM1, σ = NUM2)	0.5.0
Math.genNorm	NUM1 NUM2 NUM3 function	set of Number	Generate N1 random numbers using normal distribution (μ = NUM2, σ = NUM3)	0.5.0
Math.distBinom	NUM1 NUM2 NUM3 function	Number	Returns a CDF (i.e. P(X ≤ NUM1)) of binomial distribution (n = NUM2, p = NUM3)	0.5.0
Math.funcBinom	NUM1 NUM2 NUM3 function	Number	Returns a PMF (i.e. P(X = NUM1)) of binomial distribution (n = NUM2, p = NUM3)	0.5.0
Math.randomBinom	NUM1 NUM2 function	Number	Generate a random number using binomial distribution (n = NUM1, p = NUM2)	0.5.0
Math.genBinom	NUM1 NUM2 NUM3 function	set of Number	Generate N1 random numbers using binomial distribution (n = NUM2, p = NUM3)	0.5.0
Math.distGeom	NUM1 NUM2 function	Number	Returns a CDF (i.e. P(X ≤ NUM1)) of geometrical distribution (p = NUM2)	0.5.0
Math.funcGeom	NUM1 NUM2 function	Number	Returns a PMF (i.e. P(X = NUM1)) of geometrical distribution (p = NUM2)	0.5.0
Math.randomGeom	NUM1 function	Number	Generate a random number using geometrical distribution (p = NUM1)	0.5.0
Math.genGeom	NUM1 NUM2 function	set of Number	Generate N1 random numbers using geometrical distribution (p = NUM2)	0.5.0
Math.distExp	NUM1 NUM2 function	Number	Returns a CDF (i.e. P(X ≤ NUM1)) of exponential distribution (λ = NUM2)	0.5.0
Math.funcExp	NUM1 NUM2 function	Number	Returns a PDF (i.e. f(NUM1)) of exponential distribution (λ = NUM2)	0.5.0
Math.randomExp	NUM1 function	Number	Generate a random number using exponential distribution (λ = NUM1)	0.5.0
Math.genExp	NUM1 NUM2 function	set of Number	Generate N1 random numbers using exponential distribution (λ = NUM2)	0.5.0
Math.distPoisson	NUM1 NUM2 function	Number	Returns a CDF (i.e. P(X ≤ NUM1)) of Poisson distribution (λ = NUM2)	0.5.0
Math.funcPoisson	NUM1 NUM2 function	Number	Returns a PMF (i.e. P(X = NUM1)) of Poisson distribution (λ = NUM2)	0.5.0
Math.randomPoisson	NUM1 function	Number	Generate a random number using Poisson distribution (λ = NUM1)	0.5.0
Math.genPoisson	NUM1 NUM2 function	set of Number	Generate N1 random numbers using Poisson distribution (λ = NUM2)	0.5.0
Math.distGamma	NUM1 NUM2 NUM3 function	Number	Returns a CDF (i.e. P(X ≤ NUM1)) of the shape-rate gamma distribution (α = k = NUM2, β = 1/θ = NUM3)	0.5.1
Math.funcGamma	NUM1 NUM2 NUM3 function	Number	Returns a PDF (i.e. f(NUM1)) of the shape-rate gamma distribution (α = k = NUM2, β = 1/θ = NUM3)	0.5.1
Math.randomGamma	NUM1 NUM2 function	Number	Generate a random number using the shape-rate gamma distribution (α = k = NUM1, β = 1/θ = NUM2)	0.5.1
Math.genGamma	NUM1 NUM2 NUM3 function	set of Number	Generate N1 random numbers using the shape-rate gamma distribution (α = k = NUM2, β = 1/θ = NUM3)	0.5.1
Math.distChiSq	NUM1 NUM2 function	Number	Returns a CDF (i.e. P(X ≤ NUM1)) of chi-squared distribution (ν = NUM2)	0.5.1
Math.funcChiSq	NUM1 NUM2 function	Number	Returns a PDF (i.e. f(NUM1)) of chi-squared distribution (ν = NUM2)	0.5.1
Math.randomChiSq	NUM1 function	Number	Generate a random number using chi-squared distribution (ν = NUM1)	0.5.1
Math.genChiSq	NUM1 NUM2 function	set of Number	Generate N1 random numbers using chi-squared distribution (ν = NUM2)	0.5.1
Math.distErlang	NUM1 NUM2 NUM3 function	Number	Returns a CDF (i.e. P(X ≤ NUM1)) of the shape-rate Erlang distribution (α = k = NUM2, β = λ = NUM3)	0.5.1
Math.funcErlang	NUM1 NUM2 NUM3 function	Number	Returns a PDF (i.e. f(NUM1)) of the shape-rate Erlang distribution (α = k = NUM2, β = λ = NUM3)	0.5.1
Math.randomErlang	NUM1 NUM2 function	Number	Generate a random number using the shape-rate Erlang distribution (α = k = NUM1, β = λ = NUM2)	0.5.1
Math.genErlang	NUM1 NUM2 NUM3 function	set of Number	Generate N1 random numbers using the shape-rate Erlang distribution (α = k = NUM2, β = λ = NUM3)	0.5.1
Math.distT	NUM1 NUM2 function	Number	Returns a CDF (i.e. P(X ≤ NUM1)) of Student's t-distribution (ν = NUM2)	0.5.1
Math.funcT	NUM1 NUM2 function	Number	Returns a PDF (i.e. f(NUM1)) of Student's t-distribution (ν = NUM2)	0.5.1
Math.randomT	NUM1 function	Number	Generate a random number using Student's t-distribution (ν = NUM1)	0.5.1
Math.genT	NUM1 NUM2 function	set of Number	Generate N1 random numbers using Student's t-distribution (ν = NUM2)	0.5.1
Math.distBeta	NUM1 NUM2 NUM3 function	Number	Returns a CDF (i.e. P(X ≤ NUM1)) of the beta distribution (α = NUM2, β = NUM3)	0.5.2
Math.funcBeta	NUM1 NUM2 NUM3 function	Number	Returns a PDF (i.e. f(NUM1)) of the beta distribution (α = NUM2, β = NUM3)	0.5.2
Math.randomBeta	NUM1 NUM2 function	Number	Generate a random number using the beta distribution (α = NUM1, β = NUM2)	0.5.2
Math.genBeta	NUM1 NUM2 NUM3 function	set of Number	Generate N1 random numbers using the beta distribution (α = NUM2, β = NUM3)	0.5.2
Math.distF	NUM1 NUM2 NUM3 function	Number	Returns a CDF (i.e. P(X ≤ NUM1)) of Fisher-Snedecor (F) distribution (d1 = NUM2, d2 = NUM3)	0.5.2
Math.funcF	NUM1 NUM2 NUM3 function	Number	Returns a PDF (i.e. f(NUM1)) of Fisher-Snedecor (F) distribution (d1 = NUM2, d2 = NUM3)	0.5.2
Math.randomF	NUM1 NUM2 function	Number	Generate a random number using Fisher-Snedecor (F) distribution (d1 = NUM1, d2 = NUM2)	0.5.2
Math.genF	NUM1 NUM2 NUM3 function	set of Number	Generate N1 random numbers using Fisher-Snedecor (F) distribution (d1 = NUM2, d2 = NUM3)	0.5.2
Math.distArcsine	NUM1 function	Number	Returns a CDF (i.e. P(X ≤ NUM1)) of the arcsine distribution	0.5.3
Math.funcArcsine	NUM1 function	Number	Returns a PDF (i.e. f(NUM1)) of the arcsine distribution	0.5.3
Math.randomArcsine	(no args) function	Number	Generate a random number using the arcsine distribution	0.5.3
Math.genArcsine	NUM1 function	set of Number	Generate N1 random numbers using the arcsine distribution	0.5.3

Number theory

Package Function	Syntax	Output type	Purpose	Since
Math.genDivisors	NUM1 function	set of Number	Generate all divisors of NUM1 (including negative ones)	0.5.1.1
Math.genNaturalDivisors	NUM1 function	set of Number	Generate all positive divisors of NUM1	0.5.1.1
Math.countNaturalDivisors	NUM1 function	Number	Return the count of N1's natural divisors	0.5.1.2
Math.sumNaturalDivisors	NUM1 function	Number	Return the sum of N1's natural divisors	0.5.1.2
Math.factorize	NUM1 function	set(2) of Number	Divides N1 to 2 factors, one of which is prime	0.5.2
Math.primeDistribution	NUM1 function	set of Number	Divides N1 to all prime factors	0.5.2
Math.leastPrimeDivisor	NUM1 function	Number	Get the least prime divisor of N1	0.5.2
Math.euclidean	NUM1 NUM2 function	Number	Get the Bezout coefficients of N1 and N2 using extended Euclidean algorithm	0.5.2
Math.bezoutCoefs	NUM1 NUM2 function	Number	Same as Math.euclidean	0.5.2
Math.coprimes	NUM1 NUM2 function	Boolean	Checks if N1 and N2 are coprimes	0.5.2.2
Math.countDistinctFactors	NUM1 function	Number	Count all distinct prime factors of N1	0.5.2
Math.countAllFactors	NUM1 function	Number	Count all prime factors of N1	0.5.2
Math.fEuler	NUM1 function	Number	Return the value of Euler's totient function for NUM1 number	0.5.1.2
Math.fLiouville	NUM1 function	Number	Liouville function	0.5.2
Math.fLambda	NUM1 function	Number	Same as Math.fLiouville	0.5.2
Math.fMobius	NUM1 function	Number	Return the value of Möbius function for NUM1 number	0.5.1.2
Math.fMu	NUM1 function	Number	Alias for Math.fMobius	0.5.1.2
Math.fomega	NUM1 function	Number	Same as Math.countDistinctFactors	0.5.2
Math.fOmega	NUM1 function	Number	Same as Math.countAllFactors	0.5.2
Math.fPhi	NUM1 function	Number	Alias for Math.fEuler	0.5.1.2
Math.fPi	NUM1 function	Number	Return the value of pi function for NUM1 number	0.5.1.2
Math.fSigma	NUM1 function	Number	Alias for Math.sumNaturalDivisors	0.5.1.2
Math.fTau	NUM1 function	Number	Alias for Math.countNaturalDivisors	0.5.1.2
Math.isSquareFree	NUM1 function	Boolean	Determine if a number is square-free	0.5.2
Math.isCarmichael	NUM1 function	Boolean	Checks if N1 is a Carmichael number	0.5.2.2
Math.modularPower	NUM1 NUM2 NUM3 function	Boolean	Raise N1 to the power of N2 modulo N3 (all numbers are integers)	0.5.2.2
Math.modPower	NUM1 NUM2 NUM3 function	Boolean	Alias for Math.modularPower	0.5.2.2
Math.modPow	NUM1 NUM2 NUM3 function	Boolean	Alias for Math.modularPower	0.5.2.2
Math.modularInverse	NUM1 NUM2 function	Boolean	Find the smallest multiplicative inverse of N1 modulo N2	0.5.2.2
Math.modularMulInverse	NUM1 NUM2 function	Boolean	Alias for Math.modularInverse	0.5.2.2
Math.modMulInv	NUM1 NUM2 function	Boolean	Alias for Math.modularInverse	0.5.2.2

List of obsolete Math functions

Package Function	Syntax	Output type	Purpose	Since	Latest version
Math.Gamma	NUM1 function	Number	Returns a Gamma function value	0.4.3	0.5.0
Math.arcsinh	NUM1 function	Number	hyperbolic area sine	0.5.0	0.5.1.2
Math.arccosh	NUM1 function	Number	hyperbolic area cosine	0.5.0	0.5.1.2
Math.arctanh	NUM1 function	Number	hyperbolic area tangent	0.5.0	0.5.1.2
Math.arccoth	NUM1 function	Number	hyperbolic area cotangent	0.5.0	0.5.1.2
Math.sqr	NUM1 function	Number	Raise a number to the power of 2	0.5.1	0.5.2.2
Math.cub	NUM1 function	Number	Raise a number to the power of 3	0.5.1.2	0.5.2.2
Math.inv	NUM1 function	Number	Return 1/x	0.5.1.2	0.5.2.2
Math.cbrt	NUM1 function	Number	cubic root	0.5.1	0.5.2.2
Math.log	NUM1 NUM2 function	Number	Logarithm of N1 to base N2	0.4.3	0.5.2.2
Math.lbin	NUM1 function	Number	Binary logarithm of N1	0.4.3	0.5.2.2
Math.log2	NUM1 function	Number	Binary logarithm of N1	0.5.1	0.5.2.2
Math.ldec	NUM1 function	Number	Decimal logarithm of N1 (to base 10)	0.5.1	0.5.2.2
Math.log10	NUM1 function	Number	Decimal logarithm of N1 (to base 10)	0.5.1	0.5.2.2
Math.lhex	NUM1 function	Number	Hexadecimal logarithm of N1 (to base 16)	0.5.1	0.5.2.2
Math.log16	NUM1 function	Number	Hexadecimal logarithm of N1 (to base 16)	0.5.1	0.5.2.2
Math.abs	NUM1 function	Number	Absolute value	0.4.3	0.5.2.2
Math.factorial	NUM1 function	Number	Factorial	0.4.3	0.5.2.2
Math.sign	NUM1 function	Number	Sign function (-1 if N1 is negative, 1 if N is positive, 0 if N1 = 0)	0.5.2	0.5.2.2
Math.sgn	NUM1 function	Number	Alias for Math.sign	0.5.2	0.5.2.2
Math.round	NUM1 function	Number	round	0.4.3	0.5.2.2
Math.floor	NUM1 function	Number	floor	0.4.3	0.5.2.2
Math.ceiling	NUM1 function	Number	ceiling	0.4.3	0.5.2.2
Math.isPrime	NUM1 function	Boolean	returns TRUE if a number is a prime, otherwise it returns FALSE	0.4.3	0.5.2.2
Math.isEven	NUM1 function	Boolean	checks if a number is even	0.4.3	0.5.2.2
Math.isOdd	NUM1 function	Boolean	checks if a number is odd	0.4.3	0.5.2.2
Math.isInteger	NUM1 function	Boolean	checks if a number is integer	0.4.3	0.5.2.2
Math.isNatural	NUM1 function	Boolean	checks if a number is natural (non-negative integer)	0.5.1	0.5.2.2
Math.!	NUM1 function	Number	Factorial	0.4.3	0.5.2.2
Math.ln	NUM1 function	Number	natural logarithm	0.4.3	0.5.2.2
Math.exp	NUM1 function	Number	Euler's number raised to the power of N1	0.4.3	0.5.2.2