bezout

Bezout equation for polynomials or integers

Calling Sequence

[thegcd,U]=bezout(p1,p2)

Arguments

:p1, p2 two real polynomials or two integer scalars (type equal to 8) :

Description

[thegcd,U]=bezout(p1,p2) computes GCD thegcd of p1 and p2 and in addition a (2x2) unimodular matrix U such that:

[p1,p2]*U = [thegcd,0]

The lcm of p1 and p2 is given by:

p1*U(1,2) (or -p2*U(2,2))

Examples

// polynomial case
x=`poly`_(0,'x');
p1=(x+1)*(x-3)^5;p2=(x-2)*(x-3)^3;
[thegcd,U]=bezout(p1,p2)
`det`_(U)
`clean`_([p1,p2]*U)
thelcm=p1*U(1,2)
`lcm`_([p1,p2])

// integer case
i1=`int32`_(2*3^5); i2=`int32`_(2^3*3^2);
[thegcd,U]=bezout(i1,i2)
V=`int32`_([2^2*3^5, 2^3*3^2,2^2*3^4*5]);
[thegcd,U]=`gcd`_(V)
V*U
`lcm`_(V)

See Also

• poly polynomial definition
• roots roots of polynomials
• simp rational simplification
• clean cleans matrices (round to zero small entries)
• lcm least common multiple