■等面単体の体積(その232)

 n=5のとき,α^2Aの

 |0,5,8,9,8,5,α|

 |5,0,5,8,9,8,α|

 |8,5,0,5,8,9,α1

 |9,8,5,0,5,8,α1

 |8,9,8,5,0,5,α|

 |5,8,9,8,5,0,α|

 |α,α,α,α,α,α,0|

第1行を他の行から引いて

=|0, 5, 8, 9, 8, 5, α|

 |5,−5,−3,−1, 1, 3, 0|

 |8, 0,−8,−4, 0, 4, 01

 |9, 3,−3,−9,−3, 3, 01

 |8, 4, 0,−4,−8, 0, 0|

 |5, 3, 1,−1,−3,−5 ,0|

 |α,α−5,α−8,α−9,α−8,α−5,−α|

第2列〜第n列を第1列に加えれば

=|35+α,5,8, 9, 8, 5, α|

 | 0,−5,−3,−1, 1, 3, 0|

 | 0, 0,−8,−4, 0, 4, 01

 | 0, 3,−3,−9,−3, 3, 01

 | 0, 4, 0,−4,−8, 0, 0|

 | 0, 3, 1,−1,−3,−5, 0|

 |5α−35,α−5,α−8,α−9,α−8,α−5,−α|

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 α=7を代入すると

=|42, 5, 8, 9, 8, 5, 7|

 | 0,−5,−3,−1, 1, 3, 0|

 | 0, 0,−8,−4, 0, 4, 01

 | 0, 3,−3,−9,−3, 3, 01

 | 0, 4, 0,−4,−8, 0, 0|

 | 0, 3, 1,−1,−3,−5, 0|

 | 0, 2,−1,−2,−1, 2,−7|

=42|−5,−3,−1, 1, 3, 0|

   | 0,−8,−4, 0, 4, 01

   | 3,−3,−9,−3, 3, 01

   | 4, 0,−4,−8, 0, 0|

   | 3, 1,−1,−3,−5, 0|

   | 2,−1,−2,−1, 2,−7|

=−294|−5,−3,−1, 1, 3|

     | 0,−8,−4, 0, 41

     | 3,−3,−9,−3, 31

     | 4, 0,−4,−8, 0|

| 3, 1,−1,−3,−5|

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