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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 15 "p:=a*x^2+b*x+c;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"pG,(*&%\"aG\"\"\")%\"xG\"\"#F(F(*&%\"bGF(F*F(F(%\"c
GF(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "ddd:=diff(p,x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$dddG,&*&%\"aG\"\"\"%\"xGF(\"\"#%\"b
GF(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 122 "PrvniSoustavaRovnic
:=\nsubs(x=x[1],p)=y[1],\nsubs(x=x[2],p)=y[2],\nsubs(x=x[3],p)=y[3];\n
solve(\{PrvniSoustavaRovnic\},\{a,b,c\});" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%4PrvniSoustavaRovnicG6%/,(*&%\"aG\"\"\")&%\"xG6#F*\"
\"#F*F**&%\"bGF*F,F*F*%\"cGF*&%\"yGF./,(*&F)F*)&F-6#F/F/F*F**&F1F*F9F*
F*F2F*&F4F:/,(*&F)F*)&F-6#\"\"$F/F*F**&F1F*FAF*F*F2F*&F4FB" }}{PARA 
12 "" 1 "" {XPPMATH 20 "6#<%/%\"aG,$*&,.*&&%\"xG6#\"\"$\"\"\"&%\"yG6#F
.F.F.*&&F+F1F.&F0F,F.!\"\"*&F/F.&F+6#\"\"#F.F5*&F7F.F4F.F.*&F*F.&F0F8F
.F5*&F3F.F<F.F.F.,.*&F7F.)F*F9F.F5*&)F3F9F.F7F.F.*&F3F.F@F.F.*&F*F.)F7
F9F.F.*&F*F.FBF.F5*&F3F.FEF.F5F5F5/%\"bG*&,.*&FBF.F4F.F5*&FBF.F<F.F.*&
FEF.F4F.F.*&F/F.F@F.F.*&F/F.FEF.F5*&F<F.F@F.F5F.F>F5/%\"cG*&,.*(FBF.F7
F.F4F.F.*(FBF.F*F.F<F.F5*(FEF.F3F.F4F.F5*(F<F.F3F.F@F.F.*(F/F.F7F.F@F.
F5*(FEF.F*F.F/F.F.F.F>F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 
"SoustavaRovnic:=\nsubs(x=x[j],ddd)=der,\nsubs(x=x[j],p)=y[j],\nsubs(x
=x[j+1],p)=y[j+1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%/SoustavaRovni
cG6%/,&*&%\"aG\"\"\"&%\"xG6#%\"jGF*\"\"#%\"bGF*%$derG/,(*&F)F*)F+F/F*F
**&F0F*F+F*F*%\"cGF*&%\"yGF-/,(*&F)F*)&F,6#,&F.F*F*F*F/F*F**&F0F*F>F*F
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avaRovnic\},\{a,b,c\});" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<%/%\"bG,$*
&,**&&%\"xG6#%\"jG\"\"\"&%\"yGF,F.!\"#*(\"\"#F.F*F.&F06#,&F-F.F.F.F.F.
*&)F*F3F.%$derGF.F.*&F9F.)&F+F5F3F.!\"\"F.,(*$F8F.F.*$F;F.F.*(F3F.F<F.
F*F.F=F=F=/%\"aG*&,*F/F=*&F<F.F9F.F=F4F.*&F*F.F9F.F.F.F>F=/%\"cG*&,,*(
F8F.F<F.F9F.F.*&F8F.F4F.F.*(F*F.F9F.F;F.F=*&F/F.F;F.F.**F3F.F/F.F<F.F*
F.F=F.F>F=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1372 "Spl1:=proc(
x,y)\nlocal N,K,j,a,b,c,Q,z;\nN:=nops(x); # pocet bodu\nK:=N-2; # poce
t polynomu\na := -(x[3]*y[1]-x[1]*y[3]-y[1]*x[2]+x[2]*y[3]-x[3]*y[2]+x
[1]*y[2])/(-x[2]*x[3]^2+x[1]^2*x[2]+x[1]*x[3]^2+x[3]*x[2]^2-x[3]*x[1]^
2-x[1]*x[2]^2); \nb := (-x[1]^2*y[3]+x[1]^2*y[2]+x[2]^2*y[3]+y[1]*x[3]
^2-y[1]*x[2]^2-y[2]*x[3]^2)/(-x[2]*x[3]^2+x[1]^2*x[2]+x[1]*x[3]^2+x[3]
*x[2]^2-x[3]*x[1]^2-x[1]*x[2]^2); \nc := (x[1]^2*x[2]*y[3]-x[1]^2*x[3]
*y[2]-x[2]^2*x[1]*y[3]+y[2]*x[1]*x[3]^2-y[1]*x[2]*x[3]^2+x[2]^2*x[3]*y
[1])/(-x[2]*x[3]^2+x[1]^2*x[2]+x[1]*x[3]^2+x[3]*x[2]^2-x[3]*x[1]^2-x[1
]*x[2]^2);\np[1]:=a*z^2+b*z+c;\n# Pvni (kubicky) polynom vztvorim tak,
 ze bude prochazet prvnimi trema body\n\nQ:=z<x[3],p[1];\n\nfor i from
 2 to K do\n  j:=i+1; # cislo prvniho z obou bodu, kterym prochazi dal
si parabola\n\n#print(i,j,`|`,`|`,p[i-1]);\n#print(x[i],y[j]);\n#print
(x[i+1],y[j+1]);\n\n  der:=2*a*x[j]+b; # derivace posledniho polynomu \+
v poslednim bode\n  b := -(-2*x[j]*y[j]+2*x[j]*y[j+1]+x[j]^2*der-der*x
[j+1]^2)/(x[j]^2+x[j+1]^2-2*x[j+1]*x[j]); \n  a := (-y[j]-x[j+1]*der+y
[j+1]+x[j]*der)/(x[j]^2+x[j+1]^2-2*x[j+1]*x[j]);   c := (x[j]^2*x[j+1]
*der+x[j]^2*y[j+1]-x[j]*der*x[j+1]^2+y[j]*x[j+1]^2-2*y[j]*x[j+1]*x[j])
/(x[j]^2+x[j+1]^2-2*x[j+1]*x[j]);\np[i]:=a*z^2+b*z+c;\n\nif i<K then\n
   Q:=Q,z<x[j+1],p[i];\n  else\n   Q:=Q,p[i]\nfi\n\n\nod; #vytvori se \+
postupne vsechny oplynomy\n\nQ:=piecewise(Q);\nunapply(Q,z)\nend;\n" }
}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "Spl1([1,2,3,4,5,6,7],[1,2,1,3,4,3,
2]);" }}{PARA 7 "" 1 "" {TEXT -1 62 "Warning, `p` is implicitly declar
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, `i` is implicitly declared local to procedure `Spl1`\n" }}{PARA 7 "
" 1 "" {TEXT -1 64 "Warning, `der` is implicitly declared local to pro
cedure `Spl1`\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%Spl1Gf*6$%\"xG%
\"yG6-%\"NG%\"KG%\"jG%\"aG%\"bG%\"cG%\"QG%\"zG%\"pG%\"iG%$derG6\"F5C,>
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*(FjnF@FIF@FLF@F@F@FYFB>&8,FN,(*&FDF@)8+FAF@F@*&F^oF@FgpF@F@FhoF@>8*6$
2FgpFIFbp?(8-FAF@F>%%trueGC)>8&,&F^qF@F@F@>8.,&*&FDF@&F<6#FbqF@FAF^oF@
>F^o,$*&,**&FhqF@&FMFiqF@!\"#*(FAF@FhqF@&FM6#,&FbqF@F@F@F@F@*&)FhqFAF@
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{XPPMATH 20 "6#f*6#%\"zG6\"6$%)operatorG%&arrowGF&-%*piecewiseG6+29$\"
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