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Scilabヘルプ >> Polynomials > sylm

sylm

シルベスタ行列

呼び出し手順

[S]=sylm(a,b)

パラメータ

a,b

多項式

S

行列

説明

sylm(a,b) は,多項式aおよびb に関連するシルベスタ行列,すなわち, 以下のような行列Sを出力します:

coeff( a*x + b*y )' = S * [coeff(x)';coeff(y)'].

Sの次元はdegree(a)+degree(b)に等しくなります.

a およびbが規約分解多項式の場合,

rank(sylm(a,b))=degree(a)+degree(b)) となります. また,以下の命令は,

u = sylm(a,b) \ eye(na+nb,1)
x = poly(u(1:nb),'z','coeff')
y = poly(u(nb+1:na+nb),'z','coeff')

べズー分解,つまり, a*x+b*y = 1となるような最小次数の x および yを計算します.

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Last updated:
Wed Apr 01 10:25:01 CEST 2015