{VERSION 3 0 "SUN SPARC SOLARIS" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 256 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 2 6 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 2 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple O utput" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 186 "restart;read \"lsq_ data.txt\";\npts:=line_pts():\nplot(pts,style=point);\nepsilon:= (m,b, pt) -> (m*pt[1] + b - pt[2]);\n\nE :=(m,b, pts) -> sum( ( epsilon(m, b, pts[i]))^2 , i=1..nops(pts));\n" }}{PARA 6 "" 1 "" {TEXT -1 82 "de fined line_pts(), bad_line_pts(), quadratic_pts(), cubic_pts(), and ci rcle_pts()" }}{PARA 13 "" 1 "" {INLPLOT "6&-%'CURVESG6$777$$\"1+++!>43 v%!#:$\"1+++$)fHm]F*7$$\"1******fC]A#)F*$\"1+++tQ<\"e\"!#97$$!1+++SACJ zF*$!1+++M1KjLF27$$!1+++)y$z**>F*$!1+++bmbt:F27$$\"1+++qL%e'oF*$\"1+++ ?u5l5F27$$!1+++h5yr*)F*$!1+++a2#[l$F27$$!1+++gWr9H!#;$!1+++bfa;5F27$$ \"1++++!)y4))!#<$!1,++YK;t)*F*7$$!1+++g>n/\"*FJ$!1+++,4a,8F27$$\"1+++! [\"['p#F*$!1+++3!=dn\"F*7$$\"1+++g\"=BC(F*$\"1+++r!*yn7F27$$!1+++gC0#[ &F*$!1+++o[%Rd#F27$$!1+++q3X*F*$\"1+++ :n)>x\"F27$$\"1+++5%[[/$F*$\"1+++S/\\;pFP7$$\"1,++!z%RH()F*$\"1+++#ppN i\"F27$$!1+++'3Ouw\"F*$!1+++$3u^Z\"F27$$\"1+++I$e6Q&F*$\"1+++$4asG'F*7 $$\"1+++!RDvt#F*$!1+++5Nc1CF*-%'COLOURG6&%$RGBG$\"#5!\"\"\"\"!Fer-%&ST YLEG6#%&POINTG-%+AXESLABELSG6$%!GF]s-%%VIEWG6$%(DEFAULTGFas" 2 426 426 426 5 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(epsilonGR6%%\"mG%\"bG%#ptG6\"6$%)operatorG%&arrowGF* ,(*&9$\"\"\"&9&6#F1F1F19%F1&F36#\"\"#!\"\"F*F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"EGR6%%\"mG%\"bG%$ptsG6\"6$%)operatorG%&arrowGF*-%$s umG6$*$)-%(epsilonG6%9$9%&9&6#%\"iG\"\"#\"\"\"/F;;\"\"\"-%%nopsG6#F9F* F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "m:='m':b:='b':\nso lve( \{ diff(E(m,b,pts), m) = 0,\n diff(E(m,b,pts), b) = 0\}, \+ \{m,b\});\nassign(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%\"mG$\"+f 77BI!\"*/%\"bG$!+qs@7'*F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(plots);m;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7U%(animateG%*an imate3dG%-animatecurveG%-changecoordsG%,complexplotG%.complexplot3dG%* conformalG%,contourplotG%.contourplot3dG%*coordplotG%,coordplot3dG%-cy linderplotG%,densityplotG%(displayG%*display3dG%*fieldplotG%,fieldplot 3dG%)gradplotG%+gradplot3dG%-implicitplotG%/implicitplot3dG%(inequalG% -listcontplotG%/listcontplot3dG%0listdensityplotG%)listplotG%+listplot 3dG%+loglogplotG%(logplotG%+matrixplotG%(odeplotG%'paretoG%*pointplotG %,pointplot3dG%*polarplotG%,polygonplotG%.polygonplot3dG%4polyhedra_su pportedG%.polyhedraplotG%'replotG%*rootlocusG%,semilogplotG%+setoption sG%-setoptions3dG%+spacecurveG%1sparsematrixplotG%+sphereplotG%)surfda taG%)textplotG%+textplot3dG%)tubeplotG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+f77BI!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "disp lay(\{plot(pts,style=point),plot(m*x+b,x=-8..8,color=blue)\});" }} {PARA 13 "" 1 "" {INLPLOT "6&-%'CURVESG6%777$$\"1+++!>43v%!#:$\"1+++$) fHm]F*7$$\"1******fC]A#)F*$\"1+++tQ<\"e\"!#97$$!1+++SACJzF*$!1+++M1KjL F27$$!1+++)y$z**>F*$!1+++bmbt:F27$$\"1+++qL%e'oF*$\"1+++?u5l5F27$$!1++ +h5yr*)F*$!1+++a2#[l$F27$$!1+++gWr9H!#;$!1+++bfa;5F27$$\"1++++!)y4))!# <$!1,++YK;t)*F*7$$!1+++g>n/\"*FJ$!1+++,4a,8F27$$\"1+++![\"['p#F*$!1+++ 3!=dn\"F*7$$\"1+++g\"=BC(F*$\"1+++r!*yn7F27$$!1+++gC0#[&F*$!1+++o[%Rd# F27$$!1+++q3X*F*$\"1+++:n)>x\"F27$$\"1 +++5%[[/$F*$\"1+++S/\\;pFP7$$\"1,++!z%RH()F*$\"1+++#ppNi\"F27$$!1+++'3 Ouw\"F*$!1+++$3u^Z\"F27$$\"1+++I$e6Q&F*$\"1+++$4asG'F*7$$\"1+++!RDvt#F *$!1+++5Nc1CF*-%'COLOURG6&%$RGBG$\"#5!\"\"\"\"!Fer-%&STYLEG6#%&POINTG- F$6$7S7$$!\")Fer$!1++?M(=(zLF27$$!1LLLLbC^wF*$!1z['*HgGuKF27$$!1mmmOhz ZtF*$!11bv(f\\D=$F27$$!1LLL`b`1qF*$!1L@K&Q#QzIF27$$!1LLLtG,jmF*$!1nkj8 8`vHF27$$!1nmm'*G7@jF*$!1mk'z#Q4^uDF27$$!1+++I]:)*\\F* $!1yqp*fCAZ#F27$$!1mmmEQ7]YF*$!1VytY0,nBF27$$!1LLL`xdVVF*$!1Y@i^zLuAF2 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QFl%*3tb)F*7$$\"1+++g,V>jF*$\"1q*=zVD \"F27$$\"1+++ION_wF*$\"1#)Q-nv<_8F27$$\"\")Fer$\"1++?!GvsX\"F2-F_r6&Fa rFerFer$\"*++++\"F_s-%+AXESLABELSG6$%!GFjbl-%%VIEWG6$;F^sF_bl%(DEFAULT G" 2 426 426 426 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(stats):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "fit[l eastsquare[[x,y]]]([[10,15,17,19],[3,4,5,6]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"yG,&#!#z\"$z\"\"\"\"%\"xG#\"#eF(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "xvalues:= [ seq( pts[i][1], i=1..nops( pts)) ];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(xvaluesG77$\"*>43v%!\") $\"*Y-DA)F($!+SACJz!\"*$!+)y$z**>F-$\"*PVe'oF($!+h5yr*)F-$!*Y9Z\"HF-$ \"()y4))F($!*'>n/\"*F-$\"*[\"['p#F($\"*;=BC(F($!+gC0#[&F-$!+q3X*F($\"*T[[/$F($\"*z%RH()F($!+'3Ouw\"F-$\" *Le6Q&F($\"*RDvt#F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "yval ues:= [ seq( pts[i][2], i=1..nops(pts)) ];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(yvaluesG77$\"+$)fHm]!\"*$\"+tQ<\"e\"!\")$!+M1KjLF+$! +bmbt:F+$\"+?u5l5F+$!+a2#[l$F+$!+bfa;5F+$!+YK;t)*F($!+,4a,8F+$!+3!=dn \"F($\"+r!*yn7F+$!+o[%Rd#F+$!+JHt+HF+$!+E'R@I&F($\"+j\"e%R=F+$\"+:n)>x \"F+$\"*W!\\;p!#5$\"+#ppNi\"F+$!+$3u^Z\"F+$\"+$4asG'F($!+5Nc1CF(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "fit[leastsquare[[x,y]]]([xva lues,yvalues]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"yG,&$!+ms@7'*! \"*\"\"\"%\"xG$\"+c77BIF(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "\nm:='m':b:='b':Q :=(m,b, pts) -> sum( ( epsilon(m, b, pts[i]))^4 \+ , i=1..nops(pts));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"QGR6%%\"mG% \"bG%$ptsG6\"6$%)operatorG%&arrowGF*-%$sumG6$*$)-%(epsilonG6%9$9%&9&6# %\"iG\"\"%\"\"\"/F;;\"\"\"-%%nopsG6#F9F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "simplify(diff(Q(m,b,pts), m)) = 0;" }}{PARA 12 " " 1 "" {XPPMATH 20 "6#/,6$!+KR->[!\"$\"\"\"*&%\"mGF()%\"bG\"\"#\"\"\"$ \"+5I7z%)!\"'F,$!+]>\"=?#!\"%F*$\"+i#)3%3%F'*$)F*F-F.$!+iMLN8F'*$)F,\" \"$F.$\"+(>YYT\"!\"(*$)F*F=F.$\"+TJ()Q " 0 "" {MPLTEXT 1 0 95 "solve( \{ simplify(diff(Q(m,b,pts), m)) = 0,\n \+ simplify(diff(Q(m,b,pts), b)) = 0\}, \{m,b\});" }}{PARA 7 "" 1 "" {TEXT -1 32 "Warning, computation interrupted" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "assign(\{m = 2.022255731, b = -14.55234924\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "plot( [pts,m*x+b],x=-10.. 10,color=[red,blue], style=[point,line]);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 257 44 "Consider n ow polinomials of higher degree..." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "pts:=cubic_pts():\nplot(pts,style=point); " }}{PARA 13 "" 1 "" {INLPLOT "6&-%'CURVESG6$777$$\"1+++H^A!y\"!#:$\"1+++Hs>T&)F *7$$\"1+++8s4X:F*$\"1+++'p7lw&F*7$$\"1+++v\\tyDF*$\"1+++F!R^J'F*7$$\"1 +++\\]>yGF*$\"1+++\\sZ.mF*7$$!1+++q!Q\"=m!#;$\"1+++R/$)*>\"F?7$$!1++++ 9>Za!#<$!1+++sv%Gi%F?7$$\"1+++zy0-:F*$\"1+++I6W3tF*7$$!1+++jsx]HF*$\"1 +++([%*fO%!#97$$\"1+++>?:H@F*$\"1+++I\\y`zF*7$$!1+++IsId`F?$\"1+++?e9F KFE7$$\"1+++YsUy:F*$\"1+++xnK^kF*7$$\"1+++/lxJAF*$\"1+++,yrC!)F*7$$\"1 +++!*)*ex:F?$\"1+++#Qw#3$*F?7$$!1+++5Gu3!)F?$\"1+++&y%\\t6F*7$$!1+++I` muFF?$!1+++<$zI/&F?7$$!1+++)41Dp#F*$\"1+++q[7'H$FR7$$!1+++]$oBz&F?$\"1 +++]m/LZF?7$$\"1+++idc_7F*$\"1+++()p\\)Q&F*7$$!1+++qYe+MF?$\"1+++$ywla $F?7$$!1+++6mIb9F*$\"1+++o(H9K'F*7$$\"1+++xgqwCF*$\"1+++#z&H\"p'F*-%'C OLOURG6&%$RGBG$\"#5!\"\"\"\"!Fer-%&STYLEG6#%&POINTG-%+AXESLABELSG6$%!G F]s-%%VIEWG6$%(DEFAULTGFas" 2 426 426 426 5 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "n:=2;a:='a';" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aGF$ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "f:=(a,x)->sum(a[j]*x^j, j=0..n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6$%\"aG%\"xG6\"6$%) operatorG%&arrowGF)-%$sumG6$*&&9$6#%\"jG\"\"\")9%F4F5/F4;\"\"!%\"nGF)F )F)" }}}{PARA 11 "" 1 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "epsilon := (a,pt) -> (f(a,pt[1])- pt[2]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%(epsilonGR6$%\"aG%#ptG6\"6$%)operatorG%&arrowGF),&-%\"fG6$9$&9%6# \"\"\"F5&F36#\"\"#!\"\"F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "E :=(a, pts) -> sum( ( epsilon(a,pts[i]))^2 ,i=1..nops(pts));\n " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"EGR6$%\"aG%$ptsG6\"6$%)operato rG%&arrowGF)-%$sumG6$*$)-%(epsilonG6$9$&9%6#%\"iG\"\"#\"\"\"/F9;\"\"\" -%%nopsG6#F7F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "solv e( \{ diff(E(a,pts),a[0]) = 0,\n diff(E(a,pts), a[1]) = 0, d iff(E(a,pts),a[2])=0\}, \{a[0],a[1],a[2]\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%/&%\"aG6#\"\"#$\"+J[/zI!\"*/&F&6#\"\"\"$!+3'>Ao$F+/&F &6#\"\"!$!+8$oo1\"!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "as sign(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots);" } }{PARA 12 "" 1 "" {XPPMATH 20 "6#7U%(animateG%*animate3dG%-animatecurv eG%-changecoordsG%,complexplotG%.complexplot3dG%*conformalG%,contourpl otG%.contourplot3dG%*coordplotG%,coordplot3dG%-cylinderplotG%,densityp lotG%(displayG%*display3dG%*fieldplotG%,fieldplot3dG%)gradplotG%+gradp lot3dG%-implicitplotG%/implicitplot3dG%(inequalG%-listcontplotG%/listc ontplot3dG%0listdensityplotG%)listplotG%+listplot3dG%+loglogplotG%(log plotG%+matrixplotG%(odeplotG%'paretoG%*pointplotG%,pointplot3dG%*polar plotG%,polygonplotG%.polygonplot3dG%4polyhedra_supportedG%.polyhedrapl otG%'replotG%*rootlocusG%,semilogplotG%+setoptionsG%-setoptions3dG%+sp acecurveG%1sparsematrixplotG%+sphereplotG%)surfdataG%)textplotG%+textp lot3dG%)tubeplotG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "displa y(\{plot(pts,style=point),plot(f(a,x),x=-3..3,color=blue)\});" }} {PARA 13 "" 1 "" {INLPLOT 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