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File:NLC416-13jh009188-62137 高等方程式論.pdf

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高等方程式論   (Wikidata search (Cirrus search) Wikidata query (SPARQL)  Create new Wikidata item based on this file)
Author
余介石 陸子芬編著
image of artwork listed in title parameter on this page
Title
高等方程式論
Publisher
正中書局[發行者]
Description

目錄
第一章 整有理函數
1 引論
2 整有理函數
3 拉果蘭諸之推值式
4 對分部分數之應用
5 整函數之商
6 二整函數之最大公因式
7 二整函數之互質
8 未定係數法之一應用
9 與應用h.c.f法之比較
10 根之基本性質
11 根之函數
12 恆等式
13 普遍方程式之根
14 係數與根之獨立性
第二章 二，三，四次普遍方程式解法原理
1 二次方程式
2 三次方程式
3 根之公式中根式之討論
4 拉果蘭諸解三次方程式法
5 四次方程式
6 分解三次式之根
7 分解四次式所成兩個二次式之又一求法
8 拉果蘭諸解四次式法
9 分解三次方程式中之根式
10 拉果蘭諸解法舉例
第三章 置換；群
1 置換
2 n個文字之置換總數
3 置換之積
4 置換對函數之作用
5 乘積之結合性
6 乘冪
7 逆置換
8 周期
9 置換積等式中因式之消去
10 置換之簡單記法
11 三，四，五文字所成一切置換
12 群
13 群之級，次；對稱群
14 成績表
15 循數群
16 次群，最大公因群
17 以對換積表置換
18 置換之奇偶
19 交代群
20 次群之指數
21 群之級與其中置換之周期二者之關係
22 群之分解，附系
第四章 置換與有理函數
1 基本定理
2 求定一函數使屬於已知群
3 有理函數之配值
4 配群
5 分解方程式
6 拉果蘭諸定理
7 r(t)之又一求法
8 拉果蘭諸定理之逆
9 分解方程式之唯一性
第五章 自群之觀點以論普遍方程式之解法
1 卡蘭丹解法之線索
2 普遍三次方程式解法之線索
3 普遍四次方程式解法之線索
4 拉果蘭諸角四次方程式之線索
5 用24值函數解四次方程式法
6 用m值函數解n次普遍方程式之線索
7 分解方程式為二項式之必要條件
8 不變次群
9 置換之相配
10 相似置換
11 四次方程式解法之相關群
12 自群之觀點論三次四次方程式之解法
13 組合級數，單群與復群
14 對稱群與交代群之一充足條件
15 四文字以上對稱群之特性
16 四文字以上交代群之特注
17 四文字以外對稱群之組合級數
18 五次及高次方程式之不可解
第六章 體方程式之可約性
1 體
2 在一體內之代數解法
3 可約與不可約
4 有公根二式之整除法
5 高斯引題
6
7 分圓方程式之不可約
8 雙孫斯泰恩定理
9
10 有限根之方程式
11 三次方程式不可約款之討論
第七章 加拉理論之導引，m值函數
1 拉氏加氏理論區別之所在
2 體內之函數
3 相等之意義
4 不變之意義
5 體內不普遍方程式
6 m值函數之存在
7 加拉分解式
8 根之有理函數與m值函數
9 置換對關係式之影響
10 簡約之關係式
11 以m值函數表根
12 加拉分解式諸根之相互關係
第八章 方程式之群；置換群之可遷性
1 方程式之群
2 加拉群之基本特性
3 根之有理關係式在加拉群下之不變性
4 加拉群之充足條件
5 n次普遍方程式之群
6 —已知方程式之群之實際決定法
7 群之可遷性
8 可選群之級與次之關係
9 不可約方程式與可約群
10 有理函數之相關群
11 一已知群之函數
12 根之有理函數所定之分解式
13 加拉對拉氏定理之推廣
14 域之附加語群之化約
15 附加量與化約後之群之關係
16 拉加二氏理論之比較
第九章 用分解式之方程式解法
1 緒論
2 同型性
3 〓群之級
4 h為不變群之情形，商群
5 h為最大不變次群之情形
6 分解方程式之群
7 正單方程式在解法上之應用
8 質次數之循環方程式
9 方程式可用根式求解之充足條件
第十章 特種方程式根式解法之準則
1 亞培爾方程式
2 亞氏方程式之群
3 論分圓方程式
4 亞氏方程式之可解性
5 論質次數之二項方程式
6 佐爾登荷爾丹二氏定理
7 加拉之附加定理
8 方程式可用根式求解之必要條件
9 亞培爾定理
10 用一串亞氏方程式解法之例
參考書目
索引

Language Chinese
Publication date 民國三十三年[1944]
Source
institution QS:P195,Q732353
(民國時期文獻 民國圖書)
館藏信息
InfoField
MG/O151.1/4
主題
InfoField
代數方程
中圖分類
InfoField
O151.1
載體形態
InfoField
187頁

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