gcd

Arguments

p

a polynomial row vector p = [p1, ..., pn] (type equal to 2) or an integer row vector (type equal to 1 or 8).

pgcd

vector of the same type as p

U

matrix of the same type as p

Description

[pgcd, U] = gcd(p) computes the gcd of components of p (pgcd) and a unimodular matrix (with polynomial inverse) U, with minimal degree such that

p*U = [0 ... 0 pgcd].

In mathematics, a unimodular matrix U is a square integer matrix having determinant +1 or -1.

The greatest common divisor of an array p of real numbersof real numbers can be obtained by converting it to a polynomial before calling gcd, through p = inv_coeff(p, 0).

If p is given as an integer double (type 1), then it is treated as an int32.

Examples

// Polynomial case
s = %s;
p = [s  s*(s+1)^2 2*s^2+s^3];
[pgcd,u] = gcd(p);
p*u

// Integer case
V = int32([2^2*3^5 2^3*3^2 2^2*3^4*5]);
[thegcd,U] = gcd(V)
V*U

// Double case
V = [2^2*3^5 2^3*3^2 2^2*3^4*5];
[thegcd,U] = gcd(V)
V*U

gcd(uint8([15 20]))

gcd([iconvert(15, 4) iconvert(20, 4)])

gcd(iconvert([15 20], 4))

See also

• bezout — Bezout equation for polynomials or integers
• lcm — least common multiple
• hermit — Hermite form