bezout

Scilab Function
Last update : 25/04/2007

bezout - Bezout equation for polynomials or integers

### Calling Sequence

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

### Parameters

- `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` , `roots` , `simp` , `clean` , `lcm` ,

### Author

S. Steer INRIA