■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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