純粋・応用数学・数学隣接分野（含むガロア理論）12

[過去ﾛｸﾞ] 純粋・応用数学・数学隣接分野（含むガロア理論）12 (1002ﾚｽ)
上下前次1-新
通常表示 512ﾊﾞｲﾄ分割ﾚｽ栞
抽出解除ﾚｽ栞

このｽﾚｯﾄﾞは過去ﾛｸﾞ倉庫に格納されています｡
次ｽﾚ検索歴削→次ｽﾚ栞削→次ｽﾚ過去ﾛｸﾞﾒﾆｭｰ

239: 現代数学の系譜 雑談 ◆yH25M02vWFhP  [] 2023/01/01(日) 09:36:57.23 ID:x1AjdVpC

>>238
つづき

２）
"P7 1.5. Minimal and characteristic polynomials and Resolvents"
https://hal.archives-ouvertes.fr/hal-00602882/document
Computing the Lagrange resolvent by effectiveness of
Galois Theorem
Ines Abdeljaoued, Faical Bouazizi, Annick Valibouze
HAL Id: hal-00602882
Preprint submitted on 9 Jul 2011

Abstract
In this article, we introduce a new method to calculate Lagrange resolvent. This technique is
based on Lagrange’s algorithm and it enables to calculate algebraically the resolvent. This algorithm is based on the fundamental theorem of symmetric functions:we generalize the effectivity
of this theorem to any surgroup of the Galois’s group of the polynomial.

P7
1.5. Minimal and characteristic polynomials and Resolvents
P13
Remark 20. Note that Algo2 is far more efficient than that proposed by Lagrange.
Indeed, the Lagrange’s method which is restricted to absolute resolvents (i.e. L = Sn)
enables to eliminate the variables xn, .. . ,x1 of the polynomial x - P with respect to
polynomials f(xn), .. . ,f(x1); he computes polynomial g of degree n
n where χP, b S is a factor. Next, with division of g by its”parasite’s factors”, which can be calculated by
eliminations too, he extracts the divisor χP, b S of g.
By using Algo2, elimination is achieved with the Cauchy moduli (here L = Sn) of
respective degrees n, n - 1, .. . , 1 en xn, .. . ,x1 and the result is the polynomial χP, b S
of degree n!.
Our function ABV does not include the optimizations propozed in the following section.
Nevertheless, this comparison demonstrates the efficiency of the function ABV.
(引用終り)
以上

http://rio2016.5ch.net/test/read.cgi/math/1671460269/239

上下前次1-新書関写板覧索設栞歴

ｽﾚ情報赤ﾚｽ抽出画像ﾚｽ抽出歴の未読ｽﾚ AAｻﾑﾈｲﾙ

ぬこの手ぬこTOP 0.030s