■サマーヴィルの等面四面体(その27)

α^2A=|D00,D01,D02,D03,D04,α|

    |D10,D11,D12,D13,D14,α|

    |D20,D21,D22,D23,D24,α|

    |D30,D31,D32,D33,D34,α|

    |D40,D41,D42,D43,D44,α|

    | α, α, α, α, α,0|

 まず,第1行を他の行から引いて

|D00,D01   ,D02   ,D03   ,D04   ,α|

|D10,D11−D01,D12−D02,D13−D03,D14−D04,0|

|D20,D21−D01,D22−D02,D23−D03,D24−D04,0|

|D30,D31−D01,D32−D02,D33−D03,D34−D04,0|

|D40,D41−D01,D42−D02,D43−D03,D44−D04,0|

| α, α−D01, α−D02, α−D03, α−D04,−α|

さらに第2列〜第n列を第1列に加えれば

|D00+D0x+ α,D01   ,D02   ,D03   ,D04   0,|

|D10+D1x−D0x,D11−D01,D12−D02,D13−D03,D14−D03,0|

|D20+D2x−D0x,D21−D01,D22−D02,D23−D03,D24−D03,0|

|D30+D3x−D0x,D31−D01,D32−D02,D33−D03,D34−D03,0|

|D40+D4x−D0x,D41−D01,D42−D02,D43−D03,D44−D03,0|

|   4α−D0x, α−D01, α−D02, α−D03, α−D03,−α|

α=D0x/4とおけば

−α^2|D11−D01,D12−D02,D13−D03,D14−D04|

   |D21−D01,D22−D02,D23−D03,D24−D04|

   |D31−D01,D32−D02,D33−D03,D34−D04|

   |D41−D01,D42−D02,D43−D03,D44−D04|

E44=−D04+(D14−D04)(D41−D01)/D01

−α^2|D11−D01,D12−D02,D13−D03,0|

   |D21−D01,D22−D02,D23−D03,D24−D04|

   |D31−D01,D32−D02,D33−D03,D34−D04|

   |    0,D42−D02,D43−D03,E44|

E33=−D03+(D13−D03)(D31−D01)/D01

−α^2|D11−D01,D12−D02,0     ,0|

   |D21−D01,D22−D02,D23−D03,D24−D04|

   |    0,D32−D02,E33   ,D34−D04|

   |    0,D42−D02,D43−D03,E44|

F44=E44+(D24−D04)(D42−D02)/D02

−α^2|D11−D01,D12−D02,0     ,0|

   |D21−D01,D22−D02,D23−D03,,0|

   |    0,D32−D02,E33   ,D34−D04|

   |    0,    0,D43−D03,F44|

E22=−D02+(D12−D02)(D21−D01)/D01

−α^2|D11−D01,0    ,0     ,0|

   |    0,E22   ,D23−D03,,0|

   |    0,D32−D02,E33   ,D34−D04|

   |    0,    0,D43−D03,F44|

F33=E33−(D23−D03)(D32−D02)/E22

α^2|D01,0  ,0    ,0|

  | 0,E22 ,0    ,0|

  | 0,0  ,F33   ,D34−D04|

  | 0,0  ,D43−D03,F44|

G44=F44−(D34−D04)(D43−D03)/F33

α^2|D01,0 ,0 ,0|

  | 0,E22,0 ,0|

  | 0,0 ,F33,0|

  | 0,0 ,0 ,G44|

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