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# bezout

Bezout equation for polynomials or integers

### Syntax

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

### Arguments

- p1, p2
two real polynomials or two integer scalars (type equal to 1, 2 or 8)

- thegcd
scalar of the same type as

`p1`

and`p2`

- U
`2x2`

matrix of the same type as`p1`

and`p2`

### Description

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

computes the 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)`

)

If `p1`

or `p2`

are given as doubles (type 1), then they are treated as
null degree polynomials.

### 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]) // Double case i1 = 2*3^5; i2 = 2^3*3^2; [thegcd,U] = bezout(i1, i2) V = [2^2*3^5 2^3*3^2 2^2*3^4*5]; [thegcd,U] = gcd(V) V*U lcm(V) // 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)

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