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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "Vydaleno\351st bodu od pri
mky:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 36 "primka:=y=p*x+q;\nprimka_:=yy=p*xx+q;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'primkaG/%\"yG,&*&%\"pG\"\"\"%\"xGF*
F*%\"qGF*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(primka_G/%#yyG,&*&%\"p
G\"\"\"%#xxGF*F*%\"qGF*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "
Primka:=rhs(primka)-lhs(primka)=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%'PrimkaG/,(*&%\"pG\"\"\"%\"xGF)F)%\"qGF)%\"yG!\"\"\"\"!" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 132 "mam bod [a,b] a na primce zvolim x[0]. V
zdalenost bodu [a,b] od vbodu na primce [x[0],?]. Hled\341m glob\341mn
\355 minimum v lok\341ln\355m minimu." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 57 "rho:=(((a-x[0])^2+(b-subs(x=x[0],rhs(primka)))^2))^(1
/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$rhoG*$-%%sqrtG6#,&*$),&%\"a
G\"\"\"&%\"xG6#\"\"!!\"\"\"\"#F.F.*$),(%\"bGF.*&%\"pGF.F/F.F3%\"qGF3F4
F.F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "xxx:=Diff(rho,x[0
])=diff(rho,x[0]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$xxxG/-%%DiffG
6$*$-%%sqrtG6#,&*$),&%\"aG\"\"\"&%\"xG6#\"\"!!\"\"\"\"#F2F2*$),(%\"bGF
2*&%\"pGF2F3F2F7%\"qGF7F8F2F2F2F3,$*&F-#F7F8,(F1!\"#*&F8F2F3F2F2*(F8F2
F;F2F>F2F7F2#F2F8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "z:=solve(rhs(xxx)=0,x[0]);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG*&,(%\"aG\"\"\"*&%\"pGF(%\"qGF
(!\"\"*&F*F(%\"bGF(F(F(,&F(F(*$)F*\"\"#F(F(F," }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 32 "rho:=simplify(subs(x[0]=z,rho));" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%$rhoG*$-%%sqrtG6#*&,(*&%\"aG\"\"\"%\"pGF-!\"\"%
\"qGF/%\"bGF-\"\"#,&F-F-*$)F.F2F-F-F/F-" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "rho:=unapply(rho,a,b);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%$rhoGf*6$%\"aG%\"bG6\"6$%)operatorG%&arrowGF)*$-%%sqrtG6#*&,(*
&9$\"\"\"%\"pGF5!\"\"%\"qGF79%F5\"\"#,&F5F5*$)F6F:F5F5F7F5F)F)F)" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "Soucet ctvercu vzdalenosti:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "Delta:=Sum(rho(x[i],y[i])^2
\n,i=1..N)=sum(rho(x[i],y[i])^2\n,i=1..N);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%&DeltaG/-%$SumG6$*&,(*&&%\"xG6#%\"iG\"\"\"%\"pGF0!\"
\"%\"qGF2&%\"yGF.F0\"\"#,&F0F0*$)F1F6F0F0F2/F/;F0%\"NG,&*(F<F0F7F2F3F6
F0-%$sumG6$,,*(F7F2F,F6F1F6F0*,F6F0F7F2F,F0F1F0F3F0F0*,F6F0F7F2F,F0F1F
0F4F0F2**F6F0F7F2F3F0F4F0F2*&F7F2F4F6F0F:F0" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 20 "#Delta:=rhs(Delta);\n" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 107 "Dp:=Diff(lhs(Delta),p)=simplify(diff(rhs(Delta),p)
);\nDq:=Diff(lhs(Delta),q)=simplify(diff(rhs(Delta),q));\n\n" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#DpG/-%%DiffG6$-%$SumG6$*&,(*&&%\"xG6#%\"i
G\"\"\"%\"pGF3!\"\"%\"qGF5&%\"yGF1F3\"\"#,&F3F3*$)F4F9F3F3F5/F2;F3%\"N
GF4,$*&,&*(F?F3)F6F9F3F4F3F3-%$sumG6$,0*&)F/F9F3F4F3F5*(F/F3F<F3F6F3F3
*&F/F3F6F3F5*(F/F3F<F3F7F3F5*&F/F3F7F3F3**F9F3F6F3F7F3F4F3F5*&)F7F9F3F
4F3F3F=F3F3F:!\"#FR" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#DqG/-%%DiffG
6$-%$SumG6$*&,(*&&%\"xG6#%\"iG\"\"\"%\"pGF3!\"\"%\"qGF5&%\"yGF1F3\"\"#
,&F3F3*$)F4F9F3F3F5/F2;F3%\"NGF6,$*&,&*&F?F3F6F3F3-%$sumG6$,&F.F3F7F5F
=F3F3F:F5F9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "solve(\{rhs(
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G,$*&,&*&-%'RootOfG6#,**&,&*&-%$sumG6$&%\"xG6#%\"iG/F7;\"\"\"%\"NGF:-F
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" 0 "" {MPLTEXT 1 0 18 "xxx:=allvalues(%);" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%$xxxG6$<$/%\"qG,$*&,&*(,&*&-%$sumG6$&%\"xG6#%\"iG/F5;
\"\"\"%\"NGF8-F06$&%\"yGF4F6F8F8*&-F06$*&F2F8F<F8F6F8F9F8!\"\"FB,,*$)F
:\"\"#F8F8*$)F/FFF8FB*&-F06$*$)F2FFF8F6F8F9F8F8*&-F06$*$)F<FFF8F6F8F9F
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BFCF8Ffo<$/Fho,$*&F-FB,,FDF8FGFBFIF8FNFBFSFBF8Ffo/F(,$*&,&*(F-FBF_pF8F
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xxx);" }}{PARA 8 "" 1 "" {TEXT -1 61 "Error, wrong number (or type) of
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1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 32 "N:=4; x:=[1,2,7,8];y:=[3,2,5,4];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"NG\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG7&
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{PARA 11 "" 1 "" {XPPMATH 20 "6$<$/%\"qG,&#\"$@#\"#A\"\"\"*&#\"\"*\"$w
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" 0 "" {MPLTEXT 1 0 53 "pr1:=subs(xxx[1],Y=p*X+q);\npr2:=subs(xxx[2],Y
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{MPLTEXT 1 0 2 "Y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"YG" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 12 "with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warnin
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0 "" {MPLTEXT 1 0 37 "pointplot([seq([x[i],y[i]],i=1..N)]);" }}{PARA 
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "seq([x[i],y[i]],i=1..N);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6&7$\"\"\"\"\"$7$\"\"#F'7$\"\"(\"\"&7$\"\")\"
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> " 0 "" {MPLTEXT 1 0 68 "Reseni:=fsolve(\{rhs(Dp)=0,rhs(Dq)=0\},\{p,q
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{XPPMATH 20 "6#>%&res_aG/%#yyG$\"+6666T!\"*" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 94 "A:=pointplot([seq([x[i],y[i]],i=1..N)]):\nB:=plot(
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" 0 "" {MPLTEXT 1 0 17 "display(\{A,B,C\});" }}{PARA 13 "" 1 "" 
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{PARA 12 "" 1 "" {XPPMATH 20 "6#7^r%.BlockDiagonalG%,GramSchmidtG%,Jor
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