《Galois theory》 H.E. p. 54 (S42) * * * 10:44 第一段 Galois gives two examples of Galois groups of equations. ---- 伽罗瓦给出了方程的伽罗瓦群的两个例子。 . The first is what he calls an “algebraic” equation, by which he means an equation in which the coefficients ...
《Galois theory》 H.E. p. 57 (S43) * * * ??? 第三段 If the expression of a root involves taking a j th root and j is not prime, then j = j 1 j 2 where j 1 and j 2 are smaller ...
注:下文是群邮件的内容。 《Galois theory》 H.E. p. 58 (S43) * * * 11: 51 第五段 Thus, if the given equation f(x) = 0 is solvable by radicals, there is a sequence of fields K⊂K'⊂K''⊂ ... ⊂K^(μ),... - ...
《Galois theory》 H.E. p. 58 (S43) * * * 11: 13 第七段 The main step in Galois' analysis of solvable equations is to... ---- 伽罗瓦对于可解方程的分析的主要步骤是... . ... study the way the group of an equation can be reduced by the adjunction of a pth root ...
注:下文是群邮件的内容。 《Galois theory》 H.E. p. 57 (S43) * * * 15: 50 The essence of Galois' achievement was to determine the conditions imposed on the Galois group of an equation by the assumption that the equation is solvable by radicals . ---- 伽罗瓦的本 ...
取其形,而赋其实。 * * * 小学里学过矩形的面积公式。比如,长为 A 宽为 a 的矩形,其面积为 A x a。乘法符号 “x” 也经常用一个点 “·” 代替,即 A·a。更简单地,这个点也省略了 Aa。类似地,设有长为 B 宽为 b 的矩形,其面积为 Bb。类似地,可以有第三个矩形,其面积为 Cc。等等。所有这些矩形的面积加起来 ...