■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|
===================================