[代數] 請問幾題代數，關於Galois group of polynomial

看板Math作者 (non)時間14年前 (2011/05/27 17:16), 編輯推噓2(2推 0噓 3→)
留言5則, 1人參與, 最新討論串1/1
Find the Galois group of the polyomial over Q 1. x^4 - 5x^2 + 6 2. x^3 - 6x^2 + 2 謝謝各位幫忙 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 219.84.64.96
推
05/27 22:39, , 1F
1. (x^2-3)(x^2-2) Q(sqrt(2),sqrt(3)) 是splitting
05/27 22:39, 1F
→
05/27 22:40, , 2F
2. If f(x)=x^3+qx+r and let D^2=-4q^3-27r^2
05/27 22:40, 2F
→
05/27 22:40, , 3F
if D^2 is a square in Q, then Gal=A_3
05/27 22:40, 3F
→
05/27 22:40, , 4F
if not, then Gal=S_3
05/27 22:40, 4F
推
05/27 22:43, , 5F
To transfer to the form just Let X=x-1/3
05/27 22:43, 5F
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