{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 } {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 "Maple Output" 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 45 "read \"/home/mat331/ Worksheets2/lsq_data.txt\";" }}{PARA 6 "" 1 "" {TEXT -1 82 "defined li ne_pts(), bad_line_pts(), quadratic_pts(), cubic_pts(), and circle_pts ()" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "points:=bad_line_pts( );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'pointsG7T7$$\"*snmm)!\")$\"+5 ;%F/$!+&>2*yGF/7$$\"*w;U)eF)$\"+[K3&z\"F)7$$!+qiE%z)F/$!+'H]lI\"F)7$$ \")%H4<'F)$\"+/X.7mF/7$$\"'!\\7%F)$\"+*=?9l&F/7$$\"*:\"**y9F)$\"+h+I7$ *F/7$$!*?UI$fF/$\"+)obg7%F/7$$!+$[(op%*F/$!+BWYG9F)7$$\"*Xs*47F)$\"+zK nG')F/7$$!+!)\\3)H#F/$\"*G%***o#FA7$$\"*@uJ&oF)$\"+ZxTF>F)7$$\"**eJ3IF )$\"+e\\DN7F)7$$!+'o7m]'F/$!+])GFm(F/7$$!+9MIh!)F/$!+^ybo6F)7$$!+c!H[2 \"F/$\"+M/(\\<$F/7$$\"*i_Yt%F)$\"+av3b:F)7$$\")z'\\*=F)$\"+:2\"pp*F/7$$\"*)H(Hk'F)$\"+L)oJ%>F)7$$\"*![L $e#F)$\"+v#*z46F)7$$!+Dkd\"*)*F/$!+SqEA:F)7$$!+G[T,()F/$!+z)yZA\"F)7$$ \"*bi,+'F)$\"+sC$G!=F)7$$\")#3e$pF)$\"+FML9vF/7$$!+yWg#\\\"F/$\"+d[z3G F/7$$!+5.L1))F/$!+kS#yK\"F)7$$!+e%G$eQF/$!+0o'y'=F/7$$\"*B/!ppF)$\"+aQ tH?F)7$$\"*K.7#pF)$\"+]0n;?F)7$$\"*ED\"enF)$\"+qms$*>F)7$$!+$G53X&F/$! *;Q)>cF/7$$!+C(y&*z)F/$!+)3mVj%F/7$$!+nNMGmF/$!+9dVgSF/7$$!+g=H3rF/$!+ $yC;p#F/7$$\"+m(e%RuF/$\"+BK9kRFhF/$\"+^L76&*F/7$$\"+/(Hc0 *F/$\"+89\"z;#F)7$\"\"*$\"+.bf\\A!\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "nops(points);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#] " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "plot(points,style=point );" }}{PARA 13 "" 1 "" {INLPLOT "6&-%'CURVESG6$7T7$$\"1+++?xmm')!#:$\" 1+++5;%F*$!1+++&>2*yGF*7$$\"1+++gn@%) eF*$\"1+++[K3&z\"F-7$$!1+++qiE%z)F*$!1+++'H]lI\"F-7$$\"1++++%H4<'FB$\" 1+++/X.7mF*7$$\"1+++++!\\7%!#=$\"1+++*=?9l&F*7$$\"1+++]6**y9F*$\"1+++h +I7$*F*7$$!1++++A/LfFB$\"1+++)obg7%F*7$$!1+++$[(op%*F*$!1+++BWYG9F-7$$ \"1+++]C(*47F*$\"1******yKnG')F*7$$!1+++!)\\3)H#F*$\"1+++!G%***o#!#<7$ $\"1+++5U<`oF*$\"1+++ZxTF>F-7$$\"1+++!*eJ3IF*$\"1+++e\\DN7F-7$$!1+++'o 7m]'F*$!1+++])GFm(F*7$$!1*****RT.81)F*$!1+++^ybo6F-7$$!1+++c!H[2\"F*$ \"1+++M/(\\<$F*7$$\"1+++?ElMZF*$\"1+++av3b:F-7$$\"1++++z'\\ *=F*$\"1+++:2\"pp*F*7$$\"1+++!)H(Hk'F*$\"1+++L)oJ%>F-7$$\"1++++[L$e#F* $\"1+++v#*z46F-7$$!1+++Dkd\"*)*F*$!1+++SqEA:F-7$$!1,++G[T,()F*$!1+++z) yZA\"F-7$$\"1+++]D;+gF*$\"1+++sC$G!=F-7$$\"1++++#3e$pFB$\"1+++FML9vF*7 $$!1+++yWg#\\\"F*$\"1+++d[z3GF*7$$!1+++5.L1))F*$!1+++kS#yK\"F-7$$!1+++ e%G$eQF*$!1+++0o'y'=F*7$$\"1+++IU+ppF*$\"1+++aQtH?F-7$$\"1+++?L?@pF*$ \"1+++]0n;?F-7$$\"1+++g_7enF*$\"1+++qms$*>F-7$$!1+++$G53X&F*$!1+++g\"Q )>cFB7$$!1+++C(y&*z)F*$!1+++)3mVj%F*7$$!1+++nNMGmF*$!1+++9dVgSF*7$$!1+ ++g=H3rF*$!1+++$yC;p#F*7$$\"1+++m(e%RuF*$\"1+++BK9kRFhF *$\"1+++^L76&*F*7$$\"1*****RqHc0*F*$\"1+++89\"z;#F-7$$\"\"*\"\"!$\"1++ +.bf\\A!#8-%'COLOURG6&%$RGBG$\"#5!\"\"F^[lF^[l-%&STYLEG6#%&POINTG-%+AX ESLABELSG6$%!GF`\\l-%%VIEWG6$%(DEFAULTGFd\\l" 2 435 435 435 5 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 -13636 8 0 0 0 0 0 0 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "epsilon2:=(m,b,i)->(points[i][2]-m*points[i][1]-b)^2;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%)epsilon2GR6%%\"mG%\"bG%\"iG6\"6$%)o peratorG%&arrowGF**$),(&&%'pointsG6#9&6#\"\"#\"\"\"*&9$F8&F26#F8F8!\" \"9%F=F7\"\"\"F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "E2: =(m,b)->sum(epsilon2(m,b,i),i=1..nops(points));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#E2GR6$%\"mG%\"bG6\"6$%)operatorG%&arrowGF)-%$sumG6$- %)epsilon2G6%9$9%%\"iG/F5;\"\"\"-%%nopsG6#%'pointsGF)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "solve( \{ diff(E2(m,b), m) = 0,\n \+ diff(E2(m,b), b) = 0\}, \{m,b\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%\"bG$\"+W0C>5!\")/%\"mG$\"+i$=!GI!\"*" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 21 "line2:=eval(m*x+b,%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&line2G,&%\"xG$\"+i$=!GI!\"*$\"+W0C>5!\")\"\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "plot([points,line2],x=-10..1 0,style=[point,line],color=[black,blue]);" }}{PARA 13 "" 1 "" {INLPLOT "6&-%'CURVESG6%7T7$$\"1+++?xmm')!#:$\"1+++5;%F*$!1+++&>2*yGF*7$$\"1+++gn@%)eF*$\"1+++[K3&z\"F-7$$ !1+++qiE%z)F*$!1+++'H]lI\"F-7$$\"1++++%H4<'FB$\"1+++/X.7mF*7$$\"1+++++ !\\7%!#=$\"1+++*=?9l&F*7$$\"1+++]6**y9F*$\"1+++h+I7$*F*7$$!1++++A/LfFB $\"1+++)obg7%F*7$$!1+++$[(op%*F*$!1+++BWYG9F-7$$\"1+++]C(*47F*$\"1**** **yKnG')F*7$$!1+++!)\\3)H#F*$\"1+++!G%***o#!#<7$$\"1+++5U<`oF*$\"1+++Z xTF>F-7$$\"1+++!*eJ3IF*$\"1+++e\\DN7F-7$$!1+++'o7m]'F*$!1+++])GFm(F*7$ $!1*****RT.81)F*$!1+++^ybo6F-7$$!1+++c!H[2\"F*$\"1+++M/(\\<$F*7$$\"1++ +?ElMZF*$\"1+++av3b:F-7$$\"1++++z'\\*=F*$\"1+++:2\"pp*F*7$$ \"1+++!)H(Hk'F*$\"1+++L)oJ%>F-7$$\"1++++[L$e#F*$\"1+++v#*z46F-7$$!1+++ Dkd\"*)*F*$!1+++SqEA:F-7$$!1,++G[T,()F*$!1+++z)yZA\"F-7$$\"1+++]D;+gF* $\"1+++sC$G!=F-7$$\"1++++#3e$pFB$\"1+++FML9vF*7$$!1+++yWg#\\\"F*$\"1++ +d[z3GF*7$$!1+++5.L1))F*$!1+++kS#yK\"F-7$$!1+++e%G$eQF*$!1+++0o'y'=F*7 $$\"1+++IU+ppF*$\"1+++aQtH?F-7$$\"1+++?L?@pF*$\"1+++]0n;?F-7$$\"1+++g_ 7enF*$\"1+++qms$*>F-7$$!1+++$G53X&F*$!1+++g\"Q)>cFB7$$!1+++C(y&*z)F*$! 1+++)3mVj%F*7$$!1+++nNMGmF*$!1+++9dVgSF*7$$!1+++g=H3rF*$!1+++$yC;p#F*7 $$\"1+++m(e%RuF*$\"1+++BK9kRFhF*$\"1+++^L76&*F*7$$\"1** ***RqHc0*F*$\"1+++89\"z;#F-7$$\"\"*\"\"!$\"1+++.bf\\A!#8-%'COLOURG6&%$ RGBGF^[lF^[lF^[l-%&STYLEG6#%&POINTG-F$6%7S7$$!#5F^[l$!1+++=yx3?F-7$$!1 nmm;p0k&*F*$!1xz)=Xtn(=F-7$$!1LL$3w\"F-7$$!1mmmT%p\" e()F*$!1&R(oW#\\Fj\"F-7$$!1nmm\"4m(G$)F*$!1kp$=7DF]\"F-7$$!1LL$3i.9!zF *$!1ic%4)*=LP\"F-7$$!1nm;/R=0vF*$!1^.?BHM`7F-7$$!1,+]P8#\\4(F*$!1g&*ok Y6H6F-7$$!1mm;/siqmF*$!1Rt-Awj+5F-7$$!1****\\(y$pZiF*$!1ELqogsD()F*7$$ !1LLL$yaE\"eF*$!1j/!f(*>%3uF*7$$!1mmm\">s%HaF*$!1^]L_g8[iF*7$$!1****** \\$*4)*\\F*$!1j-!p;J>%\\F*7$$!1+++]_&\\c%F*$!1,$3(yGOIOF*7$$!1+++]1aZT F*$!1;9M0QUmBF*7$$!1mm;/#)[oPF*$!1qq>Rgk=7F*7$$!1LLL$=exJ$F*$\"1f!4>SF F-7$$\"1lmmmZvOLF*$\"1pdH9ghH?F-7$$\"1,++]2goPF*$\"1)p/5xz.;#F-7$$\" 1KL$eR<*fTF*$\"1b')*)p6()yAF-7$$\"1-++])Hxe%F*$\"1^&plc8%3CF-7$$\"1mm; H!o-*\\F*$\"1@=OmGIIDF-7$$\"1,+]7k.6aF*$\"1h+X0BrdEF-7$$\"1mmm;WTAeF*$ \"1>S[?$yAy#F-7$$\"1****\\i!*3`iF*$\"1Or/%R(o7HF-7$$\"1NLLL*zym'F*$\"1 nWPJoGQIF-7$$\"1OLL3N1#4(F*$\"1[.x'RIn;$F-7$$\"1pm;HYt7vF*$\"1$*\\f%Q5 TH$F-7$$\"1-+++xG**yF*$\"1w?Bk$f6T$F-7$$\"1qmmT6KU$)F*$\"1[n'Qq5`a$F-7 $$\"1OLLLbdQ()F*$\"1HdEhsHlOF-7$$\"1++]i`1h\"*F*$\"1>KJdzA$z$F-7$$\"1- +]P?Wl&*F*$\"1q'>q&Rn:RF-7$$\"#5F^[l$\"1+++1*es/%F--Fc[l6&Fe[lF^[lF^[l $\"*++++\"!\")-Fg[l6#%%LINEG-%+AXESLABELSG6$Q\"x6\"%!G-%%VIEWG6$;F^\\l F^[m%(DEFAULTG" 2 387 387 387 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "epsilon4:=(m,b,i)->(point s[i][2]-m*points[i][1]-b)^4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)eps ilon4GR6%%\"mG%\"bG%\"iG6\"6$%)operatorG%&arrowGF**$),(&&%'pointsG6#9& 6#\"\"#\"\"\"*&9$F8&F26#F8F8!\"\"9%F=\"\"%\"\"\"F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "E4:=(m,b)->sum(epsilon4(m,b,i),i=1. .nops(points));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#E4GR6$%\"mG%\"bG 6\"6$%)operatorG%&arrowGF)-%$sumG6$-%)epsilon4G6%9$9%%\"iG/F5;\"\"\"-% %nopsG6#%'pointsGF)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 " sols:=[solve( \{ diff(E4(m,b), m) = 0,\n diff(E4(m,b), b) = 0\}, \+ \{m,b\})];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%solsG7+<$/%\"mG,&$!+% =?%*3$!\"*\"\"\"%\"IG$!+TClWcF,/%\"bG,&$\"+A*Gf#H!\")F-F.$!+-6$fx'F6<$ /F(,&F*F-F.$\"+TClWcF,/F2,&F4F-F.$\"+-6$fx'F6<$/F(,&$\"+Acf%=#F,F-F.$! +PVy/5F6/F2,&$\"+z4> " 0 "" {MPLTEXT 1 0 8 "sols[9];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%\"bG$\"+yj " 0 "" {MPLTEXT 1 0 27 "line4:=eval(m*x+b,sols[9]); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&line4G,&%\"xG$\"+0\\7Uw!\"*$\"+ yj " 0 "" {MPLTEXT 1 0 27 "mylist:= [seq(2^i,i=1..14)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "myse t:=\{seq(2^i,i=1..14)\}:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 " mylist;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#70\"\"#\"\"%\"\")\"#;\"#K\" #k\"$G\"\"$c#\"$7&\"%C5\"%[?\"%'4%\"%#>)\"&%Q;" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 6 "myset;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<0\" \"#\"\"%\"\")\"#;\"#K\"#k\"$G\"\"&%Q;\"%[?\"%'4%\"%#>)\"$c#\"$7&\"%C5 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "plot([points,line2,line 4],x=-10..10,style=[point,line,line],color=[black,blue,green]);" }} {PARA 13 "" 1 "" {INLPLOT "6'-%'CURVESG6%7T7$$\"1+++?xmm')!#:$\"1+++5< A1C!#97$$!1+++s;!=,&F*$!1+++6+.?ZF*7$$\"1+++!=`AN&F*$\"1+++AfaT;%F*$!1+++&>2*yGF*7$$\"1+++gn@%)eF*$\" 1+++[K3&z\"F-7$$!1+++qiE%z)F*$!1+++'H]lI\"F-7$$\"1++++%H4<'FB$\"1+++/X .7mF*7$$\"1+++++!\\7%!#=$\"1+++*=?9l&F*7$$\"1+++]6**y9F*$\"1+++h+I7$*F *7$$!1++++A/LfFB$\"1+++)obg7%F*7$$!1+++$[(op%*F*$!1+++BWYG9F-7$$\"1+++ ]C(*47F*$\"1******yKnG')F*7$$!1+++!)\\3)H#F*$\"1+++!G%***o#!#<7$$\"1++ +5U<`oF*$\"1+++ZxTF>F-7$$\"1+++!*eJ3IF*$\"1+++e\\DN7F-7$$!1+++'o7m]'F* $!1+++])GFm(F*7$$!1*****RT.81)F*$!1+++^ybo6F-7$$!1+++c!H[2\"F*$\"1+++M /(\\<$F*7$$\"1+++?ElMZF*$\"1+++av3b:F-7$$\"1++++z'\\*=F*$\" 1+++:2\"pp*F*7$$\"1+++!)H(Hk'F*$\"1+++L)oJ%>F-7$$\"1++++[L$e#F*$\"1+++ v#*z46F-7$$!1+++Dkd\"*)*F*$!1+++SqEA:F-7$$!1,++G[T,()F*$!1+++z)yZA\"F- 7$$\"1+++]D;+gF*$\"1+++sC$G!=F-7$$\"1++++#3e$pFB$\"1+++FML9vF*7$$!1+++ yWg#\\\"F*$\"1+++d[z3GF*7$$!1+++5.L1))F*$!1+++kS#yK\"F-7$$!1+++e%G$eQF *$!1+++0o'y'=F*7$$\"1+++IU+ppF*$\"1+++aQtH?F-7$$\"1+++?L?@pF*$\"1+++]0 n;?F-7$$\"1+++g_7enF*$\"1+++qms$*>F-7$$!1+++$G53X&F*$!1+++g\"Q)>cFB7$$ !1+++C(y&*z)F*$!1+++)3mVj%F*7$$!1+++nNMGmF*$!1+++9dVgSF*7$$!1+++g=H3rF *$!1+++$yC;p#F*7$$\"1+++m(e%RuF*$\"1+++BK9kRFhF*$\"1+++ ^L76&*F*7$$\"1*****RqHc0*F*$\"1+++89\"z;#F-7$$\"\"*\"\"!$\"1+++.bf\\A! #8-%'COLOURG6&%$RGBGF^[lF^[lF^[l-%&STYLEG6#%&POINTG-F$6%7S7$$!#5F^[l$! 1+++=yx3?F-7$$!1nmm;p0k&*F*$!1xz)=Xtn(=F-7$$!1LL$3w \"F-7$$!1mmmT%p\"e()F*$!1&R(oW#\\Fj\"F-7$$!1nmm\"4m(G$)F*$!1kp$=7DF]\" F-7$$!1LL$3i.9!zF*$!1ic%4)*=LP\"F-7$$!1nm;/R=0vF*$!1^.?BHM`7F-7$$!1,+] P8#\\4(F*$!1g&*okY6H6F-7$$!1mm;/siqmF*$!1Rt-Awj+5F-7$$!1****\\(y$pZiF* $!1ELqogsD()F*7$$!1LLL$yaE\"eF*$!1j/!f(*>%3uF*7$$!1mmm\">s%HaF*$!1^]L_ g8[iF*7$$!1******\\$*4)*\\F*$!1j-!p;J>%\\F*7$$!1+++]_&\\c%F*$!1,$3(yGO IOF*7$$!1+++]1aZTF*$!1;9M0QUmBF*7$$!1mm;/#)[oPF*$!1qq>Rgk=7F*7$$!1LLL$ =exJ$F*$\"1f!4>SFF-7$$\"1lmmmZvOLF*$\"1pdH9ghH?F-7$$\"1,++]2goPF*$\" 1)p/5xz.;#F-7$$\"1KL$eR<*fTF*$\"1b')*)p6()yAF-7$$\"1-++])Hxe%F*$\"1^&p lc8%3CF-7$$\"1mm;H!o-*\\F*$\"1@=OmGIIDF-7$$\"1,+]7k.6aF*$\"1h+X0BrdEF- 7$$\"1mmm;WTAeF*$\"1>S[?$yAy#F-7$$\"1****\\i!*3`iF*$\"1Or/%R(o7HF-7$$ \"1NLLL*zym'F*$\"1nWPJoGQIF-7$$\"1OLL3N1#4(F*$\"1[.x'RIn;$F-7$$\"1pm;H Yt7vF*$\"1$*\\f%Q5TH$F-7$$\"1-+++xG**yF*$\"1w?Bk$f6T$F-7$$\"1qmmT6KU$) F*$\"1[n'Qq5`a$F-7$$\"1OLLLbdQ()F*$\"1HdEhsHlOF-7$$\"1++]i`1h\"*F*$\"1 >KJdzA$z$F-7$$\"1-+]P?Wl&*F*$\"1q'>q&Rn:RF-7$$\"#5F^[l$\"1+++1*es/%F-- Fc[l6&Fe[lF^[lF^[l$\"*++++\"!\")-Fg[l6#%%LINEG-F$6%7S7$F^\\l$!1+++F&[H J&F-7$Fc\\l$!1&epvP&zz\\F-7$Fh\\l$!1*Q5Og?**o%F-7$F]]l$!1yqB.h#RO%F-7$ Fb]l$!1OXq*pqd.%F-7$Fg]l$!1gF_h\\<4PF-7$F\\^l$!1@P10*yjS$F-7$Fa^l$!1nC BF6&G4$F-7$Ff^l$!1gK*3D+'oFF-7$F[_l$!1`nA^#*QXCF-7$F`_l$!1/zQ5q#H6#F-7 $Fe_l$!1xSp(3%4?=F-7$Fj_l$!1J*HSdL/\\\"F-7$F_`l$!1]NiU%>%f6F-7$Fd`l$!1 ))['e\"*fUS)F*7$Fi`l$!103EzP\\2bF*7$F^al$!1?#>;meH1#F*7$Fcal$\"1YUQMS9 ]&)FB7$Fhal$\"1/R6l2J\\UF*7$F]bl$\"1::e'=QQD(F*7$Fbbl$\"1%4\"*f4G]0\"F -7$Fgbl$\"1VI4-u#*o8F-7$F\\cl$\"1<3\"yR[kp\"F-7$Facl$\"1-$pG\"\\@(*>F- 7$Ffcl$\"1>Z]JAj@BF-7$F[dl$\"1_0u\\1heEF-7$F`dl$\"1#pBMN^>&HF-7$Fedl$ \"1nEt\\twoKF-7$Fjdl$\"1\"Q(Qu#pgf$F-7$F_el$\"1Vs5`.F;RF-7$Fdel$\"1A9? h83EUF-7$Fiel$\"1D\"fVmt+d%F-7$F^fl$\"1y?U[g;z[F-7$Fcfl$\"1ow&G9)=4_F- 7$Fhfl$\"1mSM6sB3bF-7$F]gl$\"1%p4C$o$o`,G9'F-7$Fggl$ \"17G)4*zNkkF-7$F\\hl$\"1PR3+#Q(ynF-7$Fahl$\"1M9xV^'y5(F-7$Ffhl$\"1Uw? 3N&[U(F-7$F[il$\"1'e([%*)>!\\xF-7$F`il$\"1b5U>?]q!)F-7$Feil$\"1>IR/2\" fO)F-7$Fjil$\"1*)QA%R#[/()F-7$F_jl$\"1M5v\\\\I2!*F-7$Fdjl$\"16%4V&p " 0 "" {MPLTEXT 1 0 12 "?leastsquare" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "xpoints:=[seq(points[i][1],i =1..nops(points))]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "ypoi nts:=[seq(points[i][2],i=1..nops(points))]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(stats):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "fit[leastsquare[[x,y]]]([xpoints,ypoints]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"yG,&%\"xG$\"+i$=!GI!\"*$\"+W0C>5!\")\"\" \"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "read \"/home/mat331/Worksheets2/lsq _data.txt\";" }}{PARA 6 "" 1 "" {TEXT -1 82 "defined line_pts(), bad_l ine_pts(), quadratic_pts(), cubic_pts(), and circle_pts()" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "smith:=circle_pts():" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "nops(smith);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#@" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "epsi lon:=(a,b,r,i)->(r^2 - (smith[i][1]-a)^2 -\n (smith[i][ 2]-b)^2)^2; \n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(epsilonGR6&% \"aG%\"bG%\"rG%\"iG6\"6$%)operatorG%&arrowGF+*$),(*$)9&\"\"#\"\"\"\"\" \"*$),&&&%&smithG6#9'6#F7F79$!\"\"F5F6FB*$),&&F<6#F5F79%FBF5F6FBF5F6F+ F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "Ecircle:=(a,b,r)->s um(epsilon(a,b,r,i),i=1..nops(smith));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(EcircleGR6%%\"aG%\"bG%\"rG6\"6$%)operatorG%&arrowGF*-%$sumG6$ -%(epsilonG6&9$9%9&%\"iG/F7;\"\"\"-%%nopsG6#%&smithGF*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "Ecircle(a,b,r);" }}{PARA 12 "" 1 " " {XPPMATH 20 "6#,L*$),(*$)%\"rG\"\"#\"\"\"\"\"\"*$),&$!+d:PsY!\"*F,% \"aG!\"\"F*F+F4*$),&$!+h]ZdAF2F,%\"bGF4F*F+F4F*F+F,*$),(F'F,*$),&$\"+@ g=j7F2F,F3F4F*F+F4*$),&$\"+$*f%[=$F2F,F:F4F*F+F4F*F+F,*$),(F'F,*$),&$ \"+F&yIS#F2F,F3F4F*F+F4*$),&$!+I'\\/b&F2F,F:F4F*F+F4F*F+F,*$),(F'F,*$) ,&$\"+$3Gh5%F2F,F3F4F*F+F4*$),&$\"*Q&)=1*F2F,F:F4F*F+F4F*F+F,*$),(F'F, *$),&$!+UA-H[F2F,F3F4F*F+F4*$),&$!+C(3[%HF2F,F:F4F*F+F4F*F+F,*$),(F'F, *$),&$\"+>8&zy%F2F,F3F4F*F+F4*$),&$!+CwU*4\"F2F,F:F4F*F+F4F*F+F,*$),(F 'F,*$),&$\"+Q>>$Q\"F2F,F3F4F*F+F4*$),&$\"+$*p7YJF2F,F:F4F*F+F4F*F+F,*$ ),(F'F,*$),&$!+YlwCKF2F,F3F4F*F+F4*$),&$!+*Q@CC&F2F,F:F4F*F+F4F*F+F,*$ ),(F'F,*$),&$\"+_\"=z([F2F,F3F4F*F+F4*$),&$!+C8r+?F2F,F:F4F*F+F4F*F+F, *$),(F'F,*$),&$\"+B1*zY%!#6F,F3F4F*F+F4*$),&$!+#\\j#\\iF2F,F:F4F*F+F4F *F+F,*$),(F'F,*$),&$!+rx#3%\\F2F,F3F4F*F+F4*$),&$!+4+]C=F2F,F:F4F*F+F4 F*F+F,*$),(F'F,*$),&$\"+%>F%e*)!#5F,F3F4F*F+F4*$),&$!+-qBZiF2F,F:F4F*F +F4F*F+F,*$),(F'F,*$),&$\"+yr))[BF2F,F3F4F*F+F4*$),&$!+RLf$e&F2F,F:F4F *F+F4F*F+F,*$),(F'F,*$),&$\"+X,l(y%F2F,F3F4F*F+F4*$),&$!+!oA6J\"F2F,F: F4F*F+F4F*F+F,*$),(F'F,*$),&$\"+5!\\Ng%F2F,F3F4F*F+F4*$),&$!+NxMw#)F`u F,F:F4F*F+F4F*F+F,*$),(F'F,*$),&$!+8dIxK[S &F2F,F:F4F*F+F4F*F+F,*$),(F'F,*$),&$!+tPc/DF2F,F3F4F*F+F4*$),&$!+ " 0 "" {MPLTEXT 1 0 131 "sols:=solve( \{ diff(Ecircle(a,b,r), a) = 0,\n diff(Ecirc le(a,b,r), b) = 0,\n diff(Ecircle(a,b,r), r) = 0\}, \n\{a,b,r \});" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%solsG6)<%/%\"aG,&$\"+*ot=U) !#5\"\"\"%\"IG$!+76'\\<'!\"*/%\"bG,&$!+kr#z/%F1F-F.$!+!Q%R$p$F1/%\"rG \"\"!<%/F(,&F*F-F.$\"+76'\\<'F1/F3,&F5F-F.$\"+!Q%R$p$F1F9<%/F3,&$!+Ixk xBF1F-F.$!+os]:cF1/F(,&$\"+17e%3\"F1F-F.$\"+H=2IGF1F9<%/F3,&FHF-F.$\"+ os]:cF1/F(,&FNF-F.$!+H=2IGF1F9<%/F3$!+h:)>6#F1/F($\"+\"4W\"e%)!#6F9<%/ F($!+dhFMaF\\o/F3$!+(p/'*[\"F1/F:$!+w,(p\"[F1<%/F:$\"+w,(p\"[F1F^oFao " }}}}{MARK "32" 0 }{VIEWOPTS 1 1 0 2 1 1805 }