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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "with(combinat, choos
e);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#%'chooseG" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 12 "y := x^2-k;\n" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"yG,&*$%\"xG\"\"#\"\"\"%\"kG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 12 "A(0) := 1/y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%
\"AG6#\"\"!*$,&*$%\"xG\"\"#\"\"\"%\"kG!\"\"F/" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 20 "B(0) := diff(y,x)/y;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>-%\"BG6#\"\"!,$*&%\"xG\"\"\",&*$F*\"\"#F+%\"kG!\"\"F0F
." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "for i from 1 to 5 do w
 := i;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "A(w) := simplify(sum('(-1
)^(a-1)*y^(a-1)*diff(y,x$w)*y^(w-a+1)*A(w-a)/a!','a'=1..w)/y^(w+1));" 
}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "B(w) := simplify(sum('(-1)^(a)*y^
(a)*diff(y,x$(w+1))*y^(w-a+1)*A(w-a)/a!','a'=1..w)/y^(w+1));" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 104 "AL(L,w) := simplify(sum('(-1)^(a)*numbco
mb(a,a)*x^(l-a)*y^a*y^(w-a+1)*A(w-a)','a'=1..max(w,w))/y^(w+1));" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "BL(l,w) := simplify(sum('(-1)^(a)*
numbcomb(a,a)*x^(l-a)*y^a*y^(w-a+1)*B(w-a)','a'=1..max(w,w))/y^(w+1));
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "xprime := simplify(x -AL(l,w-1)
/AL(l,w));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "xxprime := simplify(x
 - BL(l,w-1)/BL(l,w));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG\"\"\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>-%\"AG6#\"\"\",$*&%\"xGF',&*$F*\"\"#F'%\"kG!\"\"!\"#F-
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6#\"\"\",$*$,&*$%\"xG\"\"#F
'%\"kG!\"\"F/!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%#ALG6$%\"lG\"
\"\",$*&)%\"xG,&F'F(!\"\"F(F(,&*$F,\"\"#F(%\"kGF.F.F." }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>-%#BLG6$%\"lG\"\"\",$*&)%\"xGF'F(,&*$F,\"\"#F(%\"
kG!\"\"F1!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'xprimeG,(%\"xG\"\"
\"*&-%#ALG6$%\"lG\"\"!F')F&,&F,!\"\"\"\"$F'F'F'*(F)F')F&,&F,F0F'F'F'%
\"kGF'F0" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(xxprimeG,(%\"xG\"\"\"*&
-%#BLG6$%\"lG\"\"!F')F&,&F,!\"\"\"\"#F'F'#F'F1*(F)F')F&,$F,F0F'%\"kGF'
#F0F1" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG\"\"#" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>-%\"AG6#\"\"#,$*&,(%\"xG!\"%*$F+F'\"\"\"%\"kG!\"\"F
.,&F-F.F/F0!\"$F0" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6#\"\"#\"
\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%#ALG6$%\"lG\"\"#,$*&,&)%\"xG
F'\"\"\"*&)F-,&F'F.!\"#F.F.%\"kGF.F.F.,&*$F-F(F.F3!\"\"F2F6" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>-%#BLG6$%\"lG\"\"#,$*&)%\"xG,&F'\"\"\"!\"\"
F.F.,&*$F,F(F.%\"kGF/F/\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'xpr
imeG,$*(%\"xG\"\"\"%\"kGF(,&*$F'\"\"#F(F)F(!\"\"F," }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%(xxprimeG,$%\"xG#\"\"$\"\"#" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"wG\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6
#\"\"$\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6#\"\"$\"\"!" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%#ALG6$%\"lG\"\"$,$*&,*)%\"xGF'\"\"%
)F-,&F'\"\"\"F1F1!\"#*&)F-,&F'F1!\"\"F1F1%\"kGF1F1*&)F-,&F'F1!\"$F1F1F
7\"\"#F1F1,&*$F-F<F1F7F6F;F6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%#BL
G6$%\"lG\"\"$,$*&)%\"xG,&F'\"\"\"!\"#F.F.,&*$F,\"\"#F.%\"kG!\"\"F4!\"%
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'xprimeG*(%\"xG\"\"\",**$F&\"\"$
!\"%*$F&\"\"%F**&F&\"\"#%\"kGF'!\"\"*$F0F/!\"#F',*F)F+F,F/F.F1F2F1F1" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(xxprimeG,$%\"xG\"\"#" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%\"wG\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>-%\"AG6#\"\"%\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6#\"\"%
\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%#ALG6$%\"lG\"\"%*&,*)%\"xG
,&F'\"\"\"!\"\"F.F()F,F'!\"#*&)F,,&F'F.F1F.F.%\"kGF.F.*&)F,,&F'F.!\"%F
.F.F5\"\"#F.F.,&*$F,F:F.F5F/!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-
%#BLG6$%\"lG\"\"%,$*&)%\"xG,&F'\"\"\"!\"$F.F.,&*$F,\"\"#F.%\"kG!\"\"F4
F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'xprimeG,$%\"xG\"\"#" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%(xxprimeG,$%\"xG\"\"#" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"wG\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6
#\"\"&\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6#\"\"&\"\"!" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%#ALG6$%\"lG\"\"&,$*&,*)%\"xG,&F'\"
\"\"!\"#F/\"\"%)F-,&F'F/!\"\"F/F0*&)F-,&F'F/!\"$F/F/%\"kGF/F/*&)F-,&F'
F/!\"&F/F/F9\"\"#F/F/,&*$F-F>F/F9F4F8F4" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>-%#BLG6$%\"lG\"\"&,$*&)%\"xG,&F'\"\"\"!\"%F.F.,&*$F,\"\"#F.%\"k
G!\"\"F4F/" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'xprimeG,$%\"xG\"\"#" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(xxprimeG,$%\"xG\"\"#" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 23 }{VIEWOPTS 1 
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