Math - MrKaszeba19/PapajLang GitHub Wiki
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, allMathfunctions 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 |