[代數] irreducible

看板Math作者 (Frank000)時間13年前 (2011/04/24 08:41), 編輯推噓2(2推 0噓 5→)
留言7則, 3人參與, 最新討論串3/6 (看更多)
證明t^8-t^4+1 irreducilbe over Q 如果沒辦法的話，有沒有別的方法證明exp(i*pi/12)的minimal polynomial是t^8-t^4+1? -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 108.65.2.220
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04/24 09:24, , 1F
cyclotomic polynomials are irr
04/24 09:24, 1F
推
04/24 12:13, , 2F
let x = t^4. then the polynomial becomes x^2 - x
04/24 12:13, 2F
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04/24 12:14, , 3F
+ 1, which is irreducible over Q. the rest of the
04/24 12:14, 3F
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04/24 12:15, , 4F
proof is left to you.
04/24 12:15, 4F
推
04/24 14:55, , 5F
好奇樓上的方法要怎麼做，t^4-1是reducible但x-1是
04/24 14:55, 5F
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04/24 14:56, , 6F
irreducible說。
04/24 14:56, 6F
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04/25 02:27, , 7F
我好像搞錯題型了。你說得對……
04/25 02:27, 7F
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文章代碼(AID): #1Dit7LiG (Math)
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文章代碼(AID): #1Dit7LiG (Math)