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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 341 "`det wrt a column 1
`:=proc(M::matrix(square),j::posint)\n  local d,k;\n  d:=linalg[coldim
](M);\n  if j>d then ERROR(\"index of column\",j,\"larger than upper a
rray bound\",d) fi;\n  if d=1 then RETURN(M[1,1]) fi;\nadd((-1)^(j+k)*
M[k,j]*linalg[det](linalg[submatrix](M,[seq(i,i=1..k-1),seq(i,i=k+1..d
)],[seq(i,i=1..j-1),seq(i,i=j+1..d)])),k=1..d)\nend:" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 444 "`det wrt a column 2`:=proc(M::matrix(squ
are),j::posint)\n  local d,k;\n  d:=linalg[coldim](M);\n  if j>d then \+
ERROR(\"index of column\",j,\"larger than upper array bound\",d) fi;\n
  if d=1 then RETURN(M[1,1]) fi;\n    add((-1)^(j+k)*M[k,j]*\n        \+
`det wrt a column 2`(                linalg[submatrix](M,[seq(i,i=1..k
-1),seq(i,i=k+1..d)],\n                    [seq(i,i=1..j-1),seq(i,i=j+
1..d)]),\n                             1+(j-1 mod d)),k=1..d)\nend:" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "d:=4:" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 17 "A:=matrix(d,d,a):" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 22 "Delta:=linalg[det](A):" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 34 "Delta1:=`det wrt a column 1`(A,1);" }}{PARA 12 "" 
1 "" {XPPMATH 20 "6#>%'Delta1G,**&-%\"aG6$\"\"\"F*F*,.*(-F(6$\"\"#F/F*
-F(6$\"\"$F2F*-F(6$\"\"%F5F*F**(F-\"\"\"-F(6$F2F5F*-F(6$F5F2F*!\"\"*(-
F(6$F2F/F*-F(6$F/F2F*F3F7F<*(F>F7-F(6$F/F5F*F:F7F**(-F(6$F5F/F*F@F7F8F
7F**(FFF7FCF7F0F7F<F*F**&-F(6$F/F*F*,.*(-F(6$F*F/F*F0F7F3F7F**(FNF7F8F
7F:F7F<*(F>F7-F(6$F*F2F*F3F7F<*(F>F7-F(6$F*F5F*F:F7F**(FFF7FRF7F8F7F**
(FFF7FUF7F0F7F<F*F<*&-F(6$F2F*F*,.*(FNF7F@F7F3F7F**(FNF7FCF7F:F7F<*(F-
F7FRF7F3F7F<*(F-F7FUF7F:F7F**(FFF7FRF7FCF7F**(FFF7FUF7F@F7F<F*F**&-F(6
$F5F*F*,.*(FNF7F@F7F8F7F**(FNF7FCF7F0F7F<*(F-F7FRF7F8F7F<*(F-F7FUF7F0F
7F**(F>F7FRF7FCF7F**(F>F7FUF7F@F7F<F*F<" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 34 "Delta2:=`det wrt a column 2`(A,1);" }}{PARA 12 "" 1 "
" {XPPMATH 20 "6#>%'Delta2G,**&-%\"aG6$\"\"\"F*F*,(*&-F(6$\"\"#F/F*,&*
&-F(6$\"\"$F4F*-F(6$\"\"%F7F*F**&-F(6$F4F7F*-F(6$F7F4F*!\"\"F*F**&-F(6
$F4F/F*,&*&-F(6$F/F4F*F5\"\"\"F**&-F(6$F/F7F*F;FEF=F*F=*&-F(6$F7F/F*,&
*&FCFEF9FEF**&FGFEF2FEF=F*F*F*F**&-F(6$F/F*F*,(*&-F(6$F*F/F*F0FEF**&F?
FE,&*&-F(6$F*F4F*F5FEF**&-F(6$F*F7F*F;FEF=F*F=*&FJFE,&*&FYFEF9FEF**&Ff
nFEF2FEF=F*F*F*F=*&-F(6$F4F*F*,(*&FTFEFAFEF**&F-FEFWFEF=*&FJFE,&*&FYFE
FGFEF**&FfnFEFCFEF=F*F*F*F**&-F(6$F7F*F*,(*&FTFEFLFEF**&F-FEFinFEF=*&F
?FEFcoFEF*F*F=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "collect(D
elta1-Delta2,a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "collect(Delta1-Delta,a);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}}{MARK "8 1" 0 }{VIEWOPTS 1 1 0 1 1 1803 }