Gcd(m, n) : RngIntElt, RngIntElt -> RngIntElt

GCD(m, n) : RngIntElt, RngIntElt -> RngIntElt

The positive integer that is the largest integer dividing both m and n. If m is zero and n is non-zero, this returns n, and vice versa. If m and n are both zero the result is zero.

GreatestCommonDivisor(s) : [RngIntElt] -> RngIntElt

Gcd(s) : [RngIntElt] -> RngIntElt

GCD(s) : [RngIntElt] -> RngIntElt

The positive integer that is the largest integer dividing each of the integers in the sequence s. If all entries of the sequence are zero, the result is zero. An error results if the sequence is empty.

Xgcd(m, n) : RngIntElt, RngIntElt -> RngIntElt, RngIntElt, RngIntElt

XGCD(m, n) : RngIntElt, RngIntElt -> RngIntElt, RngIntElt, RngIntElt

The extended gcd; returns integers g, x and y such that g is the greatest common divisor of the integers m and n, and g = x.m + y.n.

ExtendedGreatestCommonDivisor(s) : [RngIntElt] -> RngIntElt, [RngIntElt]

Xgcd(s) : [RngIntElt] -> RngIntElt, [RngIntElt]

XGCD(s) : [RngIntElt] -> RngIntElt, [RngIntElt]

Given a sequence of integers s = [s_1, ..., s_r], return an integer g and a sequence X=(x_1, ..., x_r) such that g is the greatest common divisor of the integers s_i and g is the sum over i of x_i.s_i.

Lcm(m, n) : RngIntElt, RngIntElt -> RngIntElt

LCM(m, n) : RngIntElt, RngIntElt -> RngIntElt

The smallest non-negative integer divisible by both m and n. If m or n equals zero, the result is zero; this ensures that lcm(m, n)gcd(m, n) = m.n.

LeastCommonMultiple(s) : [RngIntElt] -> RngIntElt

Lcm(s) : [RngIntElt] -> RngIntElt

LCM(s) : [RngIntElt] -> RngIntElt

Least common multiple of the sequence of integers s.