Arithmetic

Given a number, returns the absolute value. 

absolute(Real)

Given a number, returns the decimals. 

decimal(Real) 
decimal(Complex)

Given a fraction, returns the denominator.

denominator(Fraction) 

Given a number, returns the divisors.

divisors(Integer) 
divisors(Integer, Boolean) 

Given an integer, returns a list with the positive divisors in ascending order. Given an integer and a boolean b, if b=false it is the same as divisors(Integer); if b=true it returns the negative divisors too. 

Given an integer, returns the prime factorization.

factor(Integer) 

Given an integer n, returns the number decomposed in prime factors. 

Given a number, returns the greatest integer that is less than or equal to it. 

floor(Real) 
floor(Complex) 

Given a real number x, returns the greates integer that is lower than or equal to x. 

Given a complex number z, returns a complex number with the floor function applied to its real and imaginary parts. 

Given a set of integers, returns the greatest common divisor.  

gcd(Integer, ..., Integer) 
gcd(List)
gcd(Vector) 
gcd(Fraction, Fraction) 

Given a set of integers a1,…,an, returns the largest number that divides a1,…,an simultaneously.

Given a list of integers {a1,…,an}, returns the largest number that divides a1,…,an simultaneously. 

Given a vector of integers [a1,…,an], returns the largest number that divides a1,…,an simultaneously. 

Given two fractions a/b and c/d, returns its greatest common divisor defined as: 

Given a number, returns the hexadecimal representation.

hexadecimal(Real) 

Given an integer n in decimal base, returns a string with its representation in the hexadecimal system. 

Given a set of integers, returns the least common multiple.

lcm(Integer, ..., Integer) 
lcm(List) 
lcm(Vector) 
lcm(Fraction, Fraction)

Given a set of integers a1,…,an, returns the least number that is a multiple of a1,…,an simultaneously.

Given a list of integers {a1,…,an}, returns the least number that is a multiple of a1,…,an simultaneously. 

Given a vector of integers [a1,…,an], returns the least number that is a multiple of a1,…,an simultaneously. 

Given two fractions a/b and c/d, returns its least common multiple defined as: 

Given a division of one number by another, returns the remainder. 

Integer mod Integer
Fraction mod Integer

Given two integers a and m, returns the remainder of the division a/m. 

Given a fraction a/b and an integer m, returns a·b-1 mod m, as long as b is invertible modulo m. 

Given a number, checks if it is negative. 

negative?(Real)

Given a real number x, returns true if it is negative, and false otherwise. 

Given a fraction, returns the numerator

numerator(Fraction)

Given a fraction, returns an expression with the numerator. 

Given a number, checks if it is postivie. 

positive?(Real)

Given a real number x, returns true if it is positive, and false otherwise. 

Returns a prime number

prime(Integer)

Given an integer n, returns the n-th prime. 

Given a number, checks if it is a prime. 

prime?(Integer)

Given an integer n, returns true if it is prime, and false otherwise. 

Given a number, checks if it is a prime power.

prime_power?(Integer)

Given an integer n, returns false if the input is not a prime power. If indeed it is a prime power returns a list with two elements: the first one is the prime and the second one is the power. 

Given two integers, computes the quotient of the division. 

quotient(Integer, Integer)

Given two integers a and b, the operation a divided by b, with a≥b. Then the equality a=q·b+r; has quotient q and remainder r. This function returns q. 

Given two integers, computes the quotient and remainder of the division. 

quotient_and_remainder(Integer, Integer)

Given two integers a and b, the operation a divided by b, with a≥b. Then the equality a=q·b+r; has quotient q and remainder r. This function returns a list: the first element is the quotient, and the second is the remainder. 

Given a decimal number, converts it into a rational number (in its fraction expression), if possible. 

rational(Rational)

Given a rational number a, returns its fraction form. 

Given a fraction, rationalizes it. 

rationalize(Fraction)

Given a fraction, rationalize stands for simplifying the fraction and taking off the denominator those radicals. 

Given two integers, computes the remainder of the division.  

remainder(Integer, Integer)

Given two integers a and b, the operation a divided by b, with a≥b. Then the equality a=q·b+r; has quotient q and remainder r. This function returns r. 

Given a number, rounds it to its closest integer

round(Real)
round(Complex)

Given a real number x, returns its closest integer. 

Given a complex number z, returns a complex number with the round function applied to its real and imaginary parts. 

Given a number, returns the sign. 

sign(Real)
sign(Complex)

Given a real number x, returns 0 if x=0, 1 if x>0 and -1 if x<0. 

Given a complex number z, returns 0 if z=0 and z/|z| if z≠0.