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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 26 "Vzd\341lenost bodu od p
\370\355mky:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "rho:=(x,y)-
>sqrt((x[1]-y[1])^2+(x[2]-y[2])^2);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "#rho:=sigma;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 12 "l:=x->p*x+q;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "Vzdalenost \+
bodu X od bodu na p\370\355mce, ktyer\375 m\341 prvn\355 sou\370adnici
 x je:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "R:=rho(X,[x,l(x)]
);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "Hled\341m x, pro kter\351 m
\341 R minimum:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "xx:=solv
e(diff(R,x)=0,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "xxx:=s
implify(rho(X,[xx,l(xx)]));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
46 "sigma:=(x,y)->(abs(x[1]-y[1])+abs(x[2]-y[2]));" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 21 "R:=sigma(X,[x,l(x)]);" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 28 "assume(-X[1]<x,-X[2]<p*x+q);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "diff(R,x);" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 73 "Body X, hodnoty Y, hled\341m p\370\355mku s nejmen\232
\355m sou\350tem \350tverc\371 vzd\341lenost\355:" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 34 "X:='X';\nRho:=unapply(xxx,X,p,rho);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "S:=simplify(sum(Rho(X[i],p,q
)^2,i=1..N));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "rce:(diff(
S,p)),simplify(diff(S,q));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
24 "res:=solve(\{rce\},\{p,q\});" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "params:=(allvalues(res));" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 15 "nops([params]);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 77 "pr[1]:=simplify(subs(params[1],l(x)));\npr[2]:=simpli
fy(subs(params[2],l(x)));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
57 "S:=simplify(subs(params[1],sum(Rho(X[i],p,q)^2,i=1..N)));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "X_:=[[1,2],[3,5],[4,3],[5,5]
];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "p1:=evalf(subs(X=X_,N
=4,pr[1]));\np2:=evalf(subs(X=X_,N=4,pr[2]));" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 71 "with(plots):\nA:=pointplot(X_):\nB:=plot(\{p1,p2
\},x=0..6):\ndisplay(\{A,B\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 85 "P:=subs(params[1],p);\nQ:=subs(params[1],q);\nS:=simplify(sum(
Rho(X[i],P,Q)^2,i=1..4));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 
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