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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "with(CurveFitting);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7*%(BSplineG%-BSplineCurveG%,Inter
activeG%-LeastSquaresG%8PolynomialInterpolationG%6RationalInterpolatio
nG%'SplineG%4ThieleInterpolationG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 49 "PolynomialInterpolation([[0,1],[1,2],[-1,3]], z);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&#\"\"$\"\"#\"\"\"*$)%\"zGF'F(F(F(*
&#F(F'F(F+F(!\"\"F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "f:
=x^3-3*p*x+4*q;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,(*$)%\"xG\"
\"$\"\"\"F**(F)F*%\"pGF*F(F*!\"\"*&\"\"%F*%\"qGF*F*" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 13 "g:=diff(f,x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"gG,&*&\"\"$\"\"\")%\"xG\"\"#F(F(*&F'F(%\"pGF(!\"\"
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "res:=resultant(f,g,x);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$resG,&*&\"$3\"\"\"\")%\"pG\"\"$
F(!\"\"*&\"$K%F()%\"qG\"\"#F(F(" }}}{EXCHG }{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 31 "sols:=solve(subs(p=u^2,res),q);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%%solsG6$,$*&\"\"#!\"\"%\"uG\"\"$F),$*&F(F)F*F+\"\"\"
" }}}{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "sols:=solve(sub
s(p=u^2,q=sols[1],x^3-3*p*x+4*q),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%%solsG6%,$*&\"\"#\"\"\"%\"uGF)F),$F*!\"\"F+" }}}{EXCHG }{EXCHG }
{EXCHG }{EXCHG }{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "fact
or(x^4+x^3-4*x^2-x+1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(*$)%\"xG
\"\"#\"\"\"F)*&F(F)F'F)F)F)!\"\"F),(F%F)F'F+F)F+F)" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 24 "f:=x->x^4+x^3-4*x^2-x+1;" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrowGF(,,*$)9$\"\"%
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "lis:=[-1,0,1];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$lisG7%!\"\"\"\"!\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "val:=[seq(f(x),x=lis)];" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%$valG7%!\"#\"\"\"F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
16 "with(numtheory);" }}{PARA 7 "" 1 "" {TEXT -1 69 "Warning, the prot
ected name order has been redefined and unprotected\n" }}{PARA 12 "" 
1 "" {XPPMATH 20 "6#7Q%&GIgcdG%)bigomegaG%&cfracG%)cfracpolG%+cyclotom
icG%)divisorsG%)factorEQG%*factorsetG%'fermatG%)imagunitG%&indexG%/int
egral_basisG%)invcfracG%'invphiG%*issqrfreeG%'jacobiG%*kroneckerG%'lam
bdaG%)legendreG%)mcombineG%)mersenneG%(migcdexG%*minkowskiG%(mipolysG%
%mlogG%'mobiusG%&mrootG%&msqrtG%)nearestpG%*nthconverG%)nthdenomG%)nth
numerG%'nthpowG%&orderG%)pdexpandG%$phiG%#piG%*pprimrootG%)primrootG%(
quadresG%+rootsunityG%*safeprimeG%&sigmaG%*sq2factorG%(sum2sqrG%$tauG%
%thueG" }}}{EXCHG }{EXCHG }{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 12 "sig:=[-1,1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$sigG7$!\"\"
\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "divlis:=[seq(divi
sors(v) union map(x->-x,divisors(v)),v=val)];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%'divlisG7%<&!\"#!\"\"\"\"\"\"\"#<$F(F)F&" }}}{EXCHG }
{EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
136 "for d1 in divlis[1] do for d2 in divlis[2] do for d3 in divlis[3]
 do print(PolynomialInterpolation([[-1,d1],[0,d2],[1,d3]],x));od;od;od
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"xG\"\"#\"\"\"!\"\"F(F)" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&#\"\"\"\"\"#F&*$)%\"xGF'F&F&!\"\"
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#F&*$)%\"xGF'F&F&F&*&#\"\"$F'F&F*F&F&F&!\"\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,(*$)%\"xG\"\"#\"\"\"F(*&F'F(F&F(F(F(!\"\"" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#,&*&\"\"$\"\"\")%\"xG\"\"#F&!\"\"F&F&" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#,(*&#\"\"&\"\"#\"\"\"*$)%\"xGF'F(F(!\"\"*&#F
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20 "6#,(*$)%\"xG\"\"#\"\"\"!\"\"*&F'F(F&F(F(F(F(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,(*&#\"\"\"\"\"#F&*$)%\"xGF'F&F&!\"\"*&#F&F'F&F*F&F+F&F
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{XPPMATH 20 "6#,(*$)%\"xG\"\"#\"\"\"F(F&F(F(!\"\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,(*&#\"\"$\"\"#\"\"\"*$)%\"xGF'F(F(F(*&F%F(F+F(F(F(!\"
\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&#\"\"&\"\"#\"\"\"*$)%\"xGF'F
(F(!\"\"*&#F(F'F(F+F(F,F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\"
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\"xG\"\"#\"\"\"!\"\"F&F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&#
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1 "" {XPPMATH 20 "6#,(*&#\"\"\"\"\"#F&*$)%\"xGF'F&F&F&*&#\"\"$F'F&F*F&
!\"\"F&F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"xG\"\"#\"\"\"F(F&
!\"\"F(F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\"\"#\"\"\")%\"xGF%F&
F&F&!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&#\"\"&\"\"#\"\"\"*$)%
\"xGF'F(F(F(*&#F(F'F(F+F(F(F(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
,(*&#\"\"$\"\"#\"\"\"*$)%\"xGF'F(F(!\"\"*&#F&F'F(F+F(F,F(F(" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"xG\"\"#\"\"\"!\"\"F&F)F(F(" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(
*&#\"\"\"\"\"#F&*$)%\"xGF'F&F&F&*&F%F&F*F&F&F&F&" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,(*$)%\"xG\"\"#\"\"\"F(*&F'F(F&F(!\"\"F(F*" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#,(*&#\"\"$\"\"#\"\"\"*$)%\"xGF'F(F(F(*&#F&F'F(F
+F(!\"\"F(F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&#\"\"&\"\"#\"\"\"*
$)%\"xGF'F(F(F(*&#F(F'F(F+F(!\"\"F(F." }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#,&*&\"\"$\"\"\")%\"xG\"\"#F&F&F&!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,(*$)%\"xG\"\"#\"\"\"!\"\"*&F'F(F&F(F)F(F(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,(*&#\"\"\"\"\"#F&*$)%\"xGF'F&F&!\"\"*&#\"\"$F'F&F*F&F+
F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&#\"\"\"\"\"#F&*$)%\"xGF'F&
F&F&*&#F&F'F&F*F&!\"\"F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"
xG\"\"#\"\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG }}
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