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Scilab help >> Polynomials > bezout

# 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)```

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

### Authors

S. Steer INRIA

 << Polynomials Polynomials clean >>

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