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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 p2thegcd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))

// 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

VersionDescription
6.0.1 The second output U is now optional.
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Last updated:
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