{VERSION 2 3 "IBM INTEL NT" "2.3" }
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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 660 "f:=y=x^3-c;\nA(0,0)
 := 1/y;\nB(0,0) := implicitdiff(f,y,x)/y;\nfor i from 1 to 7 do w := \+
i;\nA(0,w):= simplify(sum('(-1)^(a-1)*y^(a-1)*implicitdiff(f,y,x$a)*y^
(w-a+1)*A(0,w-a)/a!','a'=1..w)/y^(w+1));B(0,w):= simplify(sum('(-1)^(a
)*y^(a)*implicitdiff(f,y,x$(a+1))*y^(w-a+1)*A(0,w-a)/a!','a'=0..w)/y^(
w+1));A(l,0) := simplify(x^l*y*A(0,0)/y);\nB(l,0) := simplify(x^l*y*B(
0,0)/y);\nA(l,w) := simplify(sum('(-1)^(a)*l!/(a!*(l-a)!)*x^(l-a)*y^a*
y^(w-a+1)*A(0,w-a)','a'=0..w)/y^(w+1));\nB(l,w) := simplify(sum('(-1)^
(a)*l!/(a!*(l-a)!)*x^(l-a)*y^a*y^(w-a+1)*B(0,w-a)','a'=0..w)/y^(w+1));
\nxprimeA := x - simplify(A(l,w-1)/A(l,w));\nxprimeB := x - simplify(B
(l,w-1)/B(l,w));\nod;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG/%\"yG,
&*$%\"xG\"\"$\"\"\"%\"cG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"
AG6$\"\"!F'*$%\"yG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$\"
\"!F',$*&%\"xG\"\"#%\"yG!\"\"\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%\"wG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$\"\"!\"\"\",$
*&%\"xG\"\"#%\"yG!\"#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6
$\"\"!\"\"\",$*(%\"xGF(,&*$F+\"\"$F.%\"yG!\"#F(F/F0F." }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>-%\"AG6$%\"lG\"\"!*&)%\"xGF'\"\"\"%\"yG!\"\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$%\"lG\"\"!,$*&)%\"xG,&F'\"\"
\"\"\"#F.F.%\"yG!\"\"\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6
$%\"lG\"\"\",$*&,&)%\"xG,&F'F(\"\"#F(!\"$*(F'F()F-,&F'F(!\"\"F(F(%\"yG
F(F(F(F5!\"#F4" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$%\"lG\"\"\"
,$*(%\"xGF(,()F+,&F'F(\"\"$F(!\"$*&)F+F'F(%\"yGF(\"\"#*(F'F(F2F(F3F(F(
F(F3!\"#F0" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(xprimeAG,&%\"xG\"\"\"
*(F&F'%\"yGF',&*$F&\"\"$F,*&%\"lGF'F)F'!\"\"F/F/" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%(xprimeBG,&%\"xG\"\"\"*()F&,&%\"lGF'F'F'F'%\"yGF',()F
&,&F+F'\"\"$F'!\"$*&)F&F+F'F,F'\"\"#*(F+F'F3F'F,F'F'!\"\"F'" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"wG\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>-%\"AG6$\"\"!\"\"#,$*(%\"xG\"\"\",&*$F+\"\"$F/%\"yG!\"\"F,F0!\"$F/
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$\"\"!\"\"#,$*&,(*$%\"xG\"
\"'\"\"**&%\"yG\"\"\"F-\"\"$!\"**$F1F(F2F2F1!\"$F3" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>-%\"AG6$%\"lG\"\"!*&)%\"xGF'\"\"\"%\"yG!\"\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$%\"lG\"\"!,$*&)%\"xG,&F'\"\"
\"\"\"#F.F.%\"yG!\"\"\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6
$%\"lG\"\"#,$*&,,)%\"xG,&F'\"\"\"\"\"%F/\"#=*&)F-,&F'F/F/F/F/%\"yGF/!
\"'*(F'F/F3F/F5F/F6*(F'F()F-,&F'F/!\"#F/F/F5F(F/*(F'F/F9F/F5F(!\"\"F/F
5!\"$#F/F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$%\"lG\"\"#,$*&,
.)%\"xG,&F'\"\"\"\"\"'F/\"#=*&)F-,&F'F/\"\"$F/F/%\"yGF/!#=*&)F-F'F/F6F
(F(*(F'F/F3F/F6F/!\"'*(F'F/F9F/F6F(F5*(F'F(F9F/F6F(F/F/F6!\"$#F5F(" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(xprimeAG,&%\"xG\"\"\"**%\"yGF'F&F',
&*$F&\"\"$F,*&%\"lGF'F)F'!\"\"F',,*$F&\"\"'\"#=*&F)F'F&F,!\"'*(F.F'F&F
,F)F'F5*&F.\"\"#F)F8F'*&F.F'F)F8F/F/!\"#" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%(xprimeBG,&%\"xG\"\"\"**F&F',()F&,&%\"lGF'\"\"$F'!\"$*&)F&F,F'
%\"yGF'\"\"#*(F,F'F0F'F1F'F'F'F1F',.)F&,&F,F'\"\"'F'\"#=*&F*F'F1F'!#=*
&F0F'F1F2F2*(F,F'F*F'F1F'!\"'*(F,F'F0F'F1F2F-*(F,F2F0F'F1F2F'!\"\"F2" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG\"\"$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>-%\"AG6$\"\"!\"\"$*&,(*$%\"xG\"\"'\"#F*&%\"yG\"\"\"F,F
(!#=*$F0\"\"#F1F1F0!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$\"
\"!\"\"$,$*(%\"xG\"\"#,(*$F+\"\"'\"#F*&%\"yG\"\"\"F+F(!#O*$F2F,\"#5F3F
2!\"%F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$%\"lG\"\"!*&)%\"xG
F'\"\"\"%\"yG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$%\"lG\"
\"!,$*&)%\"xG,&F'\"\"\"\"\"#F.F.%\"yG!\"\"\"\"$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>-%\"AG6$%\"lG\"\"$,$*&,4)%\"xG,&F'\"\"\"\"\"'F/!$i\"*&
)F-,&F'F/F(F/F/%\"yGF/\"$3\"*&)F-F'F/F5\"\"#!\"'*(F'F/F3F/F5F/\"#a*(F'
F/F8F/F5F9!\"**(F'F9F8F/F5F9F>*(F'F()F-,&F'F/!\"$F/F/F5F(F/*(F'F9FAF/F
5F(FC*(F'F/FAF/F5F(F9F/F5!\"%#!\"\"F0" }}{PARA 12 "" 1 "" {XPPMATH 20 
"6#>-%\"BG6$%\"lG\"\"$,$*&,4)%\"xG,&F'\"\"\"\"\")F/!$i\"*&)F-,&F'F/\"
\"&F/F/%\"yGF/\"$;#*&)F-,&F'F/\"\"#F/F/F6F;!#g*(F'F/F3F/F6F/\"#a*(F'F/
F9F/F6F;!#X*(F'F/)F-,&F'F/!\"\"F/F/F6F(F;*(F'F;F9F/F6F;!\"**(F'F;FBF/F
6F(F(*(F'F(FBF/F6F(F/F/F6!\"%#FDF;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%(xprimeAG,&%\"xG\"\"\"**%\"yGF'F&F',,*$F&\"\"'\"#=*&F)F'F&\"\"$!\"'*
(%\"lGF'F&F/F)F'F0*&F2\"\"#F)F4F'*&F2F'F)F4!\"\"F',4*$F&\"\"*\"$i\"*&F
&F,F)F'!$3\"*&F)F4F&F/F,*(F2F'F&F,F)F'!#a*(F2F'F)F4F&F/F9*(F2F4F)F4F&F
/F9*&F2F/F)F/F6*&F2F4F)F/F/*&F2F'F)F/!\"#F6!\"$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%(xprimeBG,&%\"xG\"\"\"**%\"yGF'F&F',.*$F&\"\"'\"#=*&F
)F'F&\"\"$!#=*$F)\"\"#F2*(%\"lGF'F&F/F)F'!\"'*&F4F'F)F2F/*&F4F2F)F2F'F
',4*$F&\"\"*\"$i\"*&F&F,F)F'!$;#*&F)F2F&F/\"#g*(F4F'F&F,F)F'!#a*(F4F'F
)F2F&F/\"#X*&F4F'F)F/!\"#*(F4F2F)F2F&F/F:*&F4F2F)F/!\"$*&F4F/F)F/!\"\"
FJFH" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG\"\"%" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>-%\"AG6$\"\"!\"\"%,$*(%\"xG\"\"#,(*$F+\"\"'\"#F*&%\"
yG\"\"\"F+\"\"$!#F*$F2F,\"\"&F3F2!\"&F4" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>-%\"BG6$\"\"!\"\"%,$*(%\"xG\"\"\",**$F+\"\"*\"#\")*&F+\"\"'%\"y
GF,!$N\"*&F3\"\"#F+\"\"$\"#g*$F3F7!\"&F,F3F:F7" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>-%\"AG6$%\"lG\"\"!*&)%\"xGF'\"\"\"%\"yG!\"\"" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$%\"lG\"\"!,$*&)%\"xG,&F'\"\"\"\"\"#
F.F.%\"yG!\"\"\"\"$" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$%\"lG
\"\"%,$*&,:)%\"xG,&F'\"\"\"\"\")F/\"%W>*&)F-,&F'F/\"\"&F/F/%\"yGF/!%W>
*&)F-,&F'F/\"\"#F/F/F6F;\"$g$*(F'F/F3F/F6F/!$['*(F'F/F9F/F6F;\"$C$*(F'
F/)F-,&F'F/!\"\"F/F/F6\"\"$!#7*(F'F;F9F/F6F;\"$3\"*(F'FEFBF/F6FEFF*(F'
F()F-,&F'F/!\"%F/F/F6F(F/*(F'FEFKF/F6F(!\"'*(F'F;FKF/F6F(\"#6*(F'F/FKF
/F6F(FOF/F6!\"&#F/\"#C" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$%\"
lG\"\"%,$*&,>)%\"xG,&F'\"\"\"\"#5F/\"%W>*&)F-,&F'F/\"\"(F/F/%\"yGF/!%S
K*&)F-,&F'F/F(F/F/F6\"\"#\"%S9*&)F-,&F'F/F/F/F/F6\"\"$!$?\"*(F'F/F3F/F
6F/!$['*(F'F/F9F/F6F;\"$c(*(F'F/F>F/F6F@!$c\"*(F'F;F9F/F6F;\"$3\"*(F'F
;F>F/F6F@!#s*(F'F;)F-,&F'F/!\"#F/F/F6F(!\"\"*(F'F/FMF/F6F(FO*(F'F@F>F/
F6F@!#7*(F'F@FMF/F6F(F;*(F'F(FMF/F6F(F/F/F6!\"&#F/\"\")" }}{PARA 12 "
" 1 "" {XPPMATH 20 "6#>%(xprimeAG,&%\"xG\"\"\"**%\"yGF'F&F',4*$F&\"\"*
\"$i\"*&F&\"\"'F)F'!$3\"*&F)\"\"#F&\"\"$F/*(%\"lGF'F&F/F)F'!#a*(F5F'F)
F2F&F3F,*(F5F2F)F2F&F3F,*&F5F3F)F3!\"\"*&F5F2F)F3F3*&F5F'F)F3!\"#F',:*
$F&\"#7\"%W>*&F&F,F)F'!%W>*&F&F/F)F2\"$g$*(F5F'F&F,F)F'!$['*(F5F'F&F/F
)F2\"$C$*(F5F'F)F3F&F3!#7*(F5F2F&F/F)F2\"$3\"*(F5F3F)F3F&F3FK*&F5\"\"%
F)FPF'*&F5F3F)FP!\"'*&F5F2F)FP\"#6*&F5F'F)FPFRF:!\"%" }}{PARA 12 "" 1 
"" {XPPMATH 20 "6#>%(xprimeBG,&%\"xG\"\"\"**%\"yGF'F&F',4*$F&\"\"*\"$i
\"*&F&\"\"'F)F'!$;#*&F)\"\"#F&\"\"$\"#g*(%\"lGF'F&F/F)F'!#a*(F6F'F)F2F
&F3\"#X*&F6F'F)F3!\"#*(F6F2F)F2F&F3F,*&F6F2F)F3!\"$*&F6F3F)F3!\"\"F',>
*$F&\"#7\"%W>*&F&F,F)F'!%SK*&F&F/F)F2\"%S9*&F&F3F)F3!$?\"*(F6F'F&F,F)F
'!$['*(F6F'F&F/F)F2\"$c(*(F6F'F)F3F&F3!$c\"*(F6F2F&F/F)F2\"$3\"*(F6F2F
&F3F)F3!#s*&F6F2F)\"\"%F@*&F6F'F)FVF;*(F6F3F)F3F&F3!#7*&F6F3F)FVF2*&F6
FVF)FVF'F@!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG\"\"&" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$\"\"!\"\"&,$*(%\"xG\"\"\",**$
F+\"\"*\"#\")*&F+\"\"'%\"yGF,!$3\"*&F3\"\"#F+\"\"$\"#O*$F3F7!\"#F,F3!
\"'F7" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$\"\"!\"\"&,$*&,,*$%
\"xG\"#7\"$V#*&F-\"\"*%\"yG\"\"\"!$'[*&F-\"\"'F2\"\"#\"$(H*&F-\"\"$F2F
:!#a*$F2\"\"%F3F3F2!\"'F:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$
%\"lG\"\"!*&)%\"xGF'\"\"\"%\"yG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>-%\"BG6$%\"lG\"\"!,$*&)%\"xG,&F'\"\"\"\"\"#F.F.%\"yG!\"\"\"\"$" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$%\"lG\"\"&,$*&,H*(F'\"\"%)%\"
xG,&F'\"\"\"!\"&F1F1%\"yGF(\"#5*(F'\"\"$F.F1F3F(!#N*(F'\"\"#F.F1F3F(\"
#]*(F'F(F.F1F3F(!\"\"*(F'F1F.F1F3F(!#C*&)F/,&F'F1F-F1F1F3F9\"&gH\"*(F'
F-)F/,&F'F1!\"#F1F1F3F-\"#:*&)F/,&F'F1\"\"(F1F1F3F1!&!))Q*&)F/,&F'F1F1
F1F1F3F6!$?(*(F'F1FDF1F3F-!#I*(F'F9FDF1F3F-\"#X)F/,&F'F1F4F1\"&g\"H*(F
'F1F@F1F3F9\"%+\")*(F'F1FIF1F3F1!%?(**(F'F1FNF1F3F6!%!3\"*(F'F9FNF1F3F
6!$S&*(F'F9F@F1F3F9\"%?;*(F'F6FNF1F3F6!$!=*(F'F6FDF1F3F-FRF1F3!\"'#F1
\"$?\"" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$%\"lG\"\"&,$*&,F*(F
'\"\"$)%\"xG,&F'\"\"\"F-F1F1%\"yGF-!$!=*(F'F1)F/,&F'F1\"\"'F1F1F2\"\"#
\"&!e9*(F'F8F.F1F2F-!%?;*(F'F-)F/F'F1F2\"\"%\"#!**(F'F1F.F1F2F-!%+a*(F
'F8F=F1F2F>\"$D#*(F'F>F=F1F2F>\"#:*(F'F1F=F1F2F>\"$q#*(F'F1)F/,&F'F1\"
\"*F1F1F2F1!%?(**(F'F()F/,&F'F1!\"$F1F1F2F(!\"\"*&FIF1F2F1!&?$e)F/,&F'
F1\"#7F1\"&g\"H*&F5F1F2F8\"&Sc$*&F=F1F2F>\"$?\"*(F'F8F5F1F2F8\"%?;*&F.
F1F2F-!%!['*(F'F-FNF1F2F(F(*(F'F1FNF1F2F(!\"%F1F2!\"'#F1\"#S" }}{PARA 
12 "" 1 "" {XPPMATH 20 "6#>%(xprimeAG,&%\"xG\"\"\"**%\"yGF'F&F',:*$F&
\"#7\"%W>*&F&\"\"*F)F'!%W>*&F&\"\"'F)\"\"#\"$g$*(%\"lGF'F&F/F)F'!$['*(
F6F'F&F2F)F3\"$C$*(F6F'F)\"\"$F&F;!#7*(F6F3F&F2F)F3\"$3\"*(F6F;F)F;F&F
;F<*&F6\"\"%F)FAF'*&F6F;F)FA!\"'*&F6F3F)FA\"#6*&F6F'F)FAFCF',H*&F6FAF)
\"\"&\"#5*&F6F;F)FI!#N*&F6F3F)FI\"#]*&F6FIF)FI!\"\"*&F6F'F)FI!#C*&F&F/
F)F3\"&gH\"*(F6FAF)FAF&F;\"#:*&F&F,F)F'!&!))Q*&F&F2F)F;!$?(*(F6F'F)FAF
&F;!#I*(F6F3F)FAF&F;\"#X*$F&FV\"&g\"H*(F6F'F&F/F)F3\"%+\")*(F6F'F&F,F)
F'!%?(**(F6F'F&F2F)F;!%!3\"*(F6F3F&F2F)F;!$S&*(F6F3F&F/F)F3\"%?;*(F6F;
F&F2F)F;!$!=*(F6F;F)FAF&F;FfnFP!\"&" }}{PARA 12 "" 1 "" {XPPMATH 20 "6
#>%(xprimeBG,&%\"xG\"\"\"**%\"yGF'F&F',>*$F&\"#7\"%W>*&F&\"\"*F)F'!%SK
*&F&\"\"'F)\"\"#\"%S9*&F&\"\"$F)F6!$?\"*(%\"lGF'F&F/F)F'!$['*(F9F'F&F2
F)F3\"$c(*(F9F'F)F6F&F6!$c\"*(F9F3F&F2F)F3\"$3\"*(F9F3F&F6F)F6!#s*&F9F
3F)\"\"%!\"\"*&F9F'F)FD!\"#*(F9F6F)F6F&F6!#7*&F9F6F)FDF3*&F9FDF)FDF'F'
,F*(F9F6F&F2F)F6!$!=*(F9F'F&F/F)F3\"&!e9*(F9F3F&F2F)F6!%?;*(F9F6F)FDF&
F6\"#!**(F9F'F&F2F)F6!%+a*(F9F3F)FDF&F6\"$D#*(F9FDF)FDF&F6\"#:*(F9F'F)
FDF&F6\"$q#*(F9F'F&F,F)F'!%?(**&F9\"\"&F)FjnFE*&F&F,F)F'!&?$e*$F&FZ\"&
g\"H*&F&F/F)F3\"&Sc$*&F)FDF&F6\"$?\"*(F9F3F&F/F)F3\"%?;*&F&F2F)F6!%!['
*&F9F6F)FjnFjn*&F9F'F)Fjn!\"%FE!\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%\"wG\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$\"\"!\"\"'*&,
,*$%\"xG\"#7\"$H(*&F,\"\"*%\"yG\"\"\"!%:7*&F,F(F1\"\"#\"$%f*&F,\"\"$F1
F8!#\")*$F1\"\"%F2F2F1!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6
$\"\"!\"\"',$*(%\"xG\"\"#,,*$F+\"#7\"$H(*&F+\"\"*%\"yG\"\"\"!%,<*&F+F(
F3F,\"%B8*&F+\"\"$F3F9!$y$*$F3\"\"%\"#GF4F3!\"(F9" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>-%\"AG6$%\"lG\"\"!*&)%\"xGF'\"\"\"%\"yG!\"\"" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$%\"lG\"\"!,$*&)%\"xG,&F'\"\"\"\"\"#
F.F.%\"yG!\"\"\"\"$" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$%\"lG
\"\"',$*&,V*(F'\"\"$)%\"xG,&F'\"\"\"F-F1F1%\"yGF-!%SK*(F'\"\"%)F/,&F'F
1!\"'F1F1F2F(\"#&)*(F'F1)F/,&F'F1F(F1F1F2\"\"#\"'?T?*(F'F=F.F1F2F-!&S%
>*(F'F-)F/F'F1F2F5\"$S&*(F'F1F.F1F2F-!&!3b*(F'F=FBF1F2F5\"%!*=*(F'F5FB
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