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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}
{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been r
edefined\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "Bestimmung der Ausg
leichsgerade:\nBeispielrechnung:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 50 "pkte:=[seq([rand(-5..5)(),rand(-5..5)()],j=1..4)];" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%pkteG7&7$!\"$\"\"$7$!\"&\"\"&7$F*!
\"%7$!\"\"F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "f:=sum((a*p
kte[j][1]+b-pkte[j][2])^2,j=1..nops(pkte));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"fG,**$),(%\"aG!\"$%\"bG\"\"\"\"\"$!\"\"\"\"#F,F,*$)
,(F)!\"&F+F,\"\"&F.F/F,F,*$),(F)F3F+F,\"\"%F,F/F,F,*$),(F)F.F+F,F-F,F/
F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "diff(f,a);\ndiff(f,
b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%\"aG\"$?\"*&\"#G\"\"\"%\"bGF
(!\"\"\"#AF(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%\"aG!#G*&\"\")\"\"
\"%\"bGF(F(\"\"#!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "kr
itpkt:=solve(\{diff(f,a),diff(f,b)\},\{a,b\});" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%(kritpktG<$/%\"bG#!#Z\"#A/%\"aG#!#:F*" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "ausglgerade:=subs(kritpkt,a*x+b);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,ausglgeradeG,&%\"xG#!#:\"#A#\"#ZF
)!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 111 "Das ganze als Prozedur
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igung a als Parameter))" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 256 
"ausgleichsgerade:=proc(pkte)\nlocal f,kritpkt;\nf:=sum((a*pkte[j][1]+
b-pkte[j][2])^2,j=1..nops(pkte));\nkritpkt:=solve(\{diff(f,a),diff(f,b
)\},\{b\});\nif nops([kritpkt])=0 then kritpkt:=solve(\{diff(f,a),diff
(f,b)\},\{a,b\});fi;\nreturn(subs(kritpkt,a*x+b));\nend proc:" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "Erzeuge zuf\344llige Punkte" }}}
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leichsgerade(pkte);\nplotgerade:=plot(L,x=-ra..ra,thickness=2,color=bl
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gerade,plotpkte);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG,&%\"xG#\"#
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}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG,&%\"xG#\"#j\"#A\"\"$!\"\"" }}
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{PARA 0 "" 0 "" {TEXT -1 78 "Wir zeichnen auch noch die Gerade mit der
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1 0 73 "pkte:=[[1,-2],[1,-3],[1,0],[1,4],[1,3],[1,2]];\nL:=ausgleichsg
erade(pkte);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%pkteG7(7$\"\"\"!\"#
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