Bezout

Working with numbers? See Bezout (Arithmetic).

If $g$ is the greatest common divisor of two polynomials $a$ and $b$ , then there are two polynomials $u$ and $v$ such that

$a u + b v = g$

and $d e g (u) < d e g (b) - d e g (g)$ , $d e g (v) < d e g (a) - d e g (g)$ .

Syntax

bezout(Polynomial, Polynomial)

bezout(Polynomial, Polynomial, Polynomial)

Given two polynomials $a$ and $b$ , computes the greatest common divisor $g$ , and $u$ and $v$ , following the notation above.

Given three polynomials $a$ , $b$ and $r$ , computes $u$ and $v$ such that $u \cdot a + b \cdot v = r$ .