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Scilabヘルプ >> Polynomials > bezout

# bezout

Bezout法により、2つの多項式または2つの整数の最大公約数を計算します

### Syntax

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

### Parameters

p1, p2

2つの実数多項式または2つの整数スカラー(8型)

thegcd

scalar with the type of `p1`: The Greatest Common Divisor of `p1` and `p2`.

U

`2x2` unimodular matrix of the type of `p1`, such that `[p1 p2]*U = [thegcd 0]`.

### 説明

`[thegcd,U]=bezout(p1,p2)` は GCD, `p1` および `p2``thegcd`および 以下のような(2x2) ユニモジュラ行列`U` を計算します:

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

`p1`および`p2`のlcmは 以下のように指定されます:

`p1*U(1,2)` (または `-p2*U(2,2)`)

### 例

```// 多項式の場合
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])

// 整数の場合
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)```

### 参照

• gcd — Greatest (positive) Common Divisor
• lcm — least common (positive) multiple of integers or of polynomials
• diophant — Solves the diophantine (Bezout) equation p1*x1 + p2*x2 = b
• sylm — シルベスタ行列
• poly — Polynomial definition from given roots or coefficients, or characteristic to a square matrix.
• roots — 多項式の根
• simp — 有理数の簡単化
• clean — 行列を消去 (小さなエントリをゼロに丸める)

### 履歴

 Version Description 6.0.1 The second output U is now optional.
 Report an issue << Polynomials Polynomials chepol >>

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