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Scilabヘルプ >> Polynomials > hrmt

hrmt

多項式の最大公約数

呼び出し手順

[pg, U] = hrmt(v)

Parameters

v

多項式の行,すなわち,1xk 多項式行列

pg

多項式

U

ユニモジュラ多項式行列.

説明

[pg,U]=hrmt(v) は,多項式vについて ユニモジュラ行列Uおよび v*U = [pg,0]となるような, pg = 多項式の行の最大公約数を返します.

x = poly(0,'x');
v = [x*(x+1), x^2*(x+1), (x-2)*(x+1), (3*x^2+2)*(x+1)]
[pg, U] = hrmt(v);
U = clean(U)
det(U)
--> v = [x*(x+1), x^2*(x+1), (x-2)*(x+1), (3*x^2+2)*(x+1)]
 v  =
  x +x²  x² +x³  -2 -x +x²  2 +2x +3x² +3x³

--> [pg, U] = hrmt(v);
--> U = clean(U)
 U  =
  x   -2 +x  1 +1.5x²   0.5
  -1  0      0          0
  0   -x     -1 -1.5x²  -0.5
  0   0      -1         0

--> det(U)
 ans  =
  1

参照

  • gcd — Greatest (positive) Common Divisor
  • htrianr — 多項式行列の三角化
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Last updated:
Mon Jan 03 14:37:49 CET 2022