{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple P lot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q1:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 6 "f0:=1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f0 G\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "f1:=x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f1G%\"xG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "f2:=x^2-fsolve(int(cos(x)*(x^2-a),x=-Pi/2..Pi/2),a); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f2G,&*$)%\"xG\"\"#\"\"\"F*$\"+5 5,uY!#5!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "f3:=x^3-x*f solve(int(cos(x)*(x^2-a)*x^2,x=-Pi/2..Pi/2),a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f3G,&*$)%\"xG\"\"$\"\"\"F**&$\"+c7OD5!\"*F*F(F*!\"\" " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "f4:=x^4-a*x^2+b:\nfsolv e(\{int(cos(x)*f4,x=-Pi/2..Pi/2),int(cos(x)*f4*f2,x=-Pi/2..Pi/2)\},\{a ,b\}):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "assign(%): f4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"xG\"\"%\"\"\"F(*&$\"+WKo5;! \"*F()F&\"\"#F(!\"\"$\"+:9!et#!#5F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "x1:=-sqrt(3/2+sqrt(3/2.));x 2:=-sqrt(3/2-sqrt(3/2.));\nx3:=sqrt(3/2-sqrt(3/2.));x4:=sqrt(3/2+sqrt( 3/2.));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x1G$!+C,o];!\"*" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x2G$!+OiZY_!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x3G$\"+OiZY_!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %#x4G$\"+C,o];!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 133 "solv e(\{int(exp(-x^2),x=-infinity..infinity)=2*ci+2*co,\n int(exp(-x ^2)*x^2,x=-infinity..infinity)=2*ci*x3^2+2*co*x4^2\},\{ci,co\});" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%#coG$\"+LNGJ\")!#6/%#ciG$\"+,49\\! )!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "assign(%):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "int(1.*exp(-x^2)*x^6,x=-infi nity..infinity);2*ci*x3^6+2*co*x4^6;" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#$\"+r4NBL!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+p4NBL!\"*" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q3:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "x:=[-3,-1,0,3,8,11]: y:=[2.15,3.24,2.73,1.96,2.20,3.31]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "y1:=[seq((y[i]-y[i-1])/(x[i]-x[i-1] ),i=2..6)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y1G7'$\"++++]a!#5$!# ^!\"#$!+nmmmDF($\"+++++[!#6$\"+++++PF(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "y2:=[seq((y1[i]-y1[i-1])/(x[i+1]-x[i-1]),i=2..5)];" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y2G7&$!+nmm;N!#5$\"+KLLLj!#6$\"+ML L3QF+$\"++++DSF+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "y3:=[se q((y2[i]-y2[i-1])/(x[i+2]-x[i-1]),i=2..4)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y3G7%$\"+nmm;p!#6$!+`bb0G!#7$\"+kppp>!#8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "y4:=[seq((y3[i]-y3[i-1])/(x[i+3]-x[ i-1]),i=2..3)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y4G7$$!+$HHHa'!# 7$\"+uV5-D!#8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "y5:=[seq(( y4[i]-y4[i-1])/(x[i+4]-x[i-1]),i=2..2)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y5G7#$\"+kEC_[!#8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 174 "p:=y[1]+y1[1]*(X-x[1])+y2[1]*(X-x[1])*(X-x[2])+y3[1]*(X-x[1])*(X- x[2])*(X-x[3])\n+y4[1]*(X-x[1])*(X-x[2])*(X-x[3])*(X-x[4])+y5[1]*(X-x[ 1])*(X-x[2])*(X-x[3])*(X-x[4])*(X-x[5]);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"pG,.$\"++++&y$!\"*\"\"\"*&$\"++++]a!#5F)%\"XGF)F)*($\"+nmm;N F-F),&F.F)\"\"$F)F),&F.F)F)F)F)!\"\"**$\"+nmm;p!#6F)F2F)F4F)F.F)F)*,$ \"+$HHHa'!#7F)F2F)F4F)F.F),&F.F)F3F5F)F5*.$\"+kEC_[!#8F)F2F)F4F)F.F)F> F),&F.F)\"\")F5F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "with (plots): pointplot([seq([x[i],y[i]],i=1..6)]): plot(p,X=-3.2..11.2): \+ display(%,%%);" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name chang ecoords has been redefined\n" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-%'CURVESG6$7fp7$$!3;+++++++K!#<$\"3'Qld.t@Vo\"F*7$ $!3?+++X-`@JF*$\"3m9;@\"R1'y=F*7$$!3B+++!\\gI/$F*$\"3IGwB&=By0#F*7$$!3 E+++N2fkHF*$\"3Q[g:$o=EA#F*7$$!3G+++!)47')GF*$\"3+()\\7$pBOP#F*7$$!3:+ +vl[%y\"GF*$\"3%QL80$>F%\\#F*7$$!3-++]^(o&\\FF*$\"3#=BIkiT`g#F*7$$!3K+ +DPEH\"o#F*$\"3]%pl]y>sq#F*7$$!3?+++Bl,8EF*$\"3pDZqZZG+GF*7$$!3Y++]g# \\%fCF*$\"3/1N.'G.$zHF*7$$!3F+++)*>)eI#F*$\"3+FwuJRk>JF*7$$!37+++#z'H^ @F*$\"3J.f6brtDKF*7$$!3?+++'e6n*>F*$\"35-8fI=B+LF*7$$!3D++DTjy>>F*$\"3 ``*p\\@?mK$F*7$$!3H++]'4hG%=F*$\"3S(Q`MukkM$F*7$$!3M++v^e$fw\"F*$\"3w. vHT^;gLF*7$$!3Q+++21,*o\"F*$\"3Af+:B!4\"oLF*7$$!3O++]K3N`;F*$\"3#=q(*3 %Q%*pLF*7$$!3N+++e5p<;F*$\"3'41@G3f1P$F*7$$!3K++]$GJ?e\"F*$\"3#*>>Km2H qLF*7$$!3K+++4:PY:F*$\"3yeUvqV()oLF*7$$!3G+++g>0v9F*$\"3]1`t*eOIO$F*7$ $!3C+++6Ct.9F*$\"3#\\;D7%*=MN$F*7$$!3=+++()y.c7F*$\"3sSa)f)fhALF*7$$!3 O+++jLM36F*$\"3qg\\[:$o*yKF*7$$!3W,++qe^G!)!#=$\"3i`gdA1wcJF*7$$!3q,++ q_R$)\\Fbs$\"3WiilcUZ0IF*7$$!3-******RW6^=Fbs$\"3A./%3xkQ$GF*7$$\"3Go* ****>-!y!*!#>$\"3aRG()z5HzEF*7$$\"37)*****zYo8SFbs$\"3**=RT$>(o5DF*7$$ \"3R'******>AB8(Fbs$\"3GA&zS%Q%\\N#F*7$$\"3B+++K2x85F*$\"3iYCZf$pMA#F* 7$$\"3w*****H\\)o'G\"F*$\"3/k-`C6CB@F*7$$\"3`*****z597h\"F*$\"3KOFus:T I?F*7$$\"3q*****>()Hh)=F*$\"31#zsan$=v>F*7$$\"3k****\\mg-Y?F*$\"35?1*o bwH&>F*7$$\"3b*****4EAf?#F*$\"3bB**zPx#z$>F*7$$\"3I****\\'[duM#F*$\"3_ ?5nM+UI>F*7$$\"31*****>r#**)[#F*$\"3%\\$=VU\"y\"G>F*7$$\"3L****\\'GzUk #F*$\"3ou:U\"H0:$>F*7$$\"3g*****4'ec*z#F*$\"3`r\\:jWaS>F*7$$\"3)****** >SNu%HF*$\"3w`\")p`X4a>F*7$$\"3O+++V\\I&4$F*$\"3)=EU&Hn2s>F*7$$\"34+++ ]w(QS$F*$\"3hVkb.%>?-#F*7$$\"3u*****4sVso$F*$\"3!\\qG_K_)[F*$\"3WZd\"4::gO#F*7 $$\"3m*****R])f$>&F*$\"3*Rn=Ht9*GCF*7$$\"3u*****zxu_\\&F*$\"3a*o(f/D:y CF*7$$\"3e****\\J%=7k&F*$\"31RKx(zBm\\#F*7$$\"3S*****\\3iry&F*$\"3W(QD Tyv6^#F*7$$\"3;****\\Hw?\\fF*$\"34%>qI!zTADF*7$$\"3!*)****R<`76'F*$\"3 nAYkzx>GDF*7$$\"3o)****HIeoD'F*$\"3QZr^#HV&GDF*7$$\"3Y)****>VjCS'F*$\" 33N`N**[=CDF*7$$\"3E*****f)z#zb'F*$\"3H@P*eX!G9DF*7$$\"32+++SDR8nF*$\" 3%)=3FPf'*)\\#F*7$$\"3;*****\\_S^*pF*$\"3w)F*$\"3%)*oNr!>tS@F*7$$\"3\"z* ***\\7CA])F*$\"3oI=%yR7([?F*7$$\"3x)****>bt3!))F*$\"3G=!R-.@L(>F*7$$\" 35******Q'zN&*)F*$\"3)y6Np1lN%>F*7$$\"3T*****fs&G1\"*F*$\"37[d%eIu?#>F *7$$\"3e***\\x_1?=*F*$\"3#ok\"Qos2:>F*7$$\"3y****\\Htsd#*F*$\"3`\"=\\m yR3\">F*7$$\"3%****\\78[ML*F*$\"3!)4]9/Ji4>F*7$$\"37+++L*o\"4%*F*$\"3u r,AV$)p6>F*7$$\"3u***\\d[[(y%*F*$\"3<'*e(*H&[n\">F*7$$\"3M****\\Q!G$[& *F*$\"3w@Db+8/D>F*7$$\"3&*)**\\7f2zh*F*$\"3cf3O.(4o$>F*7$$\"3a)****R9( [(o*F*$\"3')eMkEUH_>F*7$$\"3U)****H=zp%)*F*$\"3-^9EIC;.?F*7$$\"3$)**** >Ark+5!#;$\"3mlx&=K8!y?F*7$$\"3#*****H!G7\\,\"Fhcl$\"3_&eGNS'3$F*7$$\"3w**\\ -qQ`'4\"Fhcl$\"3.y#=F#)4&QKF*7$$\"3()***\\L\"fN/6Fhcl$\"3y$GL$G)HMS$F* 7$$\"3****\\ncz<76Fhcl$\"3;98`7>a\"e$F*7$$\"3$*************>6Fhcl$\"3e \\0\\R$[Mx$F*-%'COLOURG6&%$RGBG$\"#5!\"\"$\"\"!F_hlF^hl-%'POINTSG6(7$$ !\"$F_hl$\"$:#!\"#7$$F]hlF_hl$\"$C$Fhhl7$F^hl$\"$t#Fhhl7$$\"\"$F_hl$\" $'>Fhhl7$$\"\")F_hl$\"$?#Fhhl7$$\"#6F_hl$\"$J$Fhhl-%+AXESLABELSG6$Q\"X 6\"Q!Fcjl-%%VIEWG6$;$!#KF]hl$\"$7\"F]hl%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q4:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "n:=8: A: =1.: B:=5: h:=(B-A)/n:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "p:=z->-exp(-z)/(1+z^2): q:=z->1/(1+z^2):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 17 "r:=z->-z/(1+z^2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "x:=[seq(A+h*i,i=1..n-1)]: MC:=matrix(n-1,n-1,0):" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "for i to n-1 do MC[i,i]:=- 2+h^2*q(x[i]) end do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "fo r i to n-2 do MC[i,i+1]:=1+h/2*p(x[i]):\nMC[i+1,i]:=1-h/2*p(x[i+1]) e nd do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "R:=[seq(h^2*r(x[i ]),i=1..n-1)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "R[1]:=R[1 ]-3*(1-h/2*p(x[1])):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "R[n -1]:=R[n-1]+(1+h/2*p(x[n-1])):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "with(linalg): y1:=evalm(inverse(MC)&*R);" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and trace have been red efined and unprotected\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y1G-%'v ectorG6#7)$\"+\"))HZD$!\"*$\"+H5AYJF+$\"+)eprx#F+$\"+,^`BAF+$\"+'epx` \"F+$\"+Ct:hv!#5$!*+.@f*F6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "y2:=evalm(inverse(MC)&*R);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y 2G-%'vectorG6#7)$\"+\"))HZD$!\"*$\"+H5AYJF+$\"+)eprx#F+$\"+,^`BAF+$\"+ 'epx`\"F+$\"+Ct:hv!#5$!*+.@f*F6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "(4*y2[2]-y1[1])/3; (4*y2[4]-y1[2])/3; (4*y2[6]-y1[3])/3; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+7905J!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+DJ(f\">!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"* S6JC)!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q5:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "y:=exp(2*X+1)/(3+2*X):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 144 "a:=evalf(int(y,X=-1..1)/2):\nb:=evalf(int(y*X,X=-1.. 1)/2*3):\nc:=evalf(int(y*(X^2-1/3),X=-1..1)/8*45):\nd:=evalf(int(y*(X^ 3-3/5*X),X=-1..1)/8*175):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "p:=a+b*X+c*(X^2-1/3)+d*(X^3-3/5*X):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "plot(\{y,p\},X=-1..1);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-%'CURVESG6$7S7$$!\"\"\"\"!$\"3MBWr6WzyO!#= 7$$!3ommm;p0k&*F-$\"3mc?E_z.#p$F-7$$!3wKL$3-A1y@Ks$F-7$$! 3mmmmT%p\"e()F-$\"3sdy$H)4qxPF-7$$!3:mmm\"4m(G$)F-$\"3CFY5M(3:&QF-7$$! 3\"QLL3i.9!zF-$\"3\"30Lp%*=E%RF-7$$!3\"ommT!R=0vF-$\"3/^U/=:9USF-7$$!3 u****\\P8#\\4(F-$\"35EGn()e2gTF-7$$!3+nm;/siqmF-$\"3SR)yrREyH%F-7$$!3[ ++](y$pZiF-$\"3Q>a@V,<^WF-7$$!33LLL$yaE\"eF-$\"3Qs$Hujsei%F-7$$!3hmmm \">s%HaF-$\"3cLY(=#*fVz%F-7$$!3Q+++]$*4)*\\F-$\"3zm\\j00&4+&F-7$$!39++ +]_&\\c%F-$\"3]qpZD(GrA&F-7$$!31+++]1aZTF-$\"3KOPokKojaF-7$$!3umm;/#)[ oPF-$\"3OYJ\\Qi2&p&F-7$$!3hLLL$=exJ$F-$\"3+s#3^bd=*fF-7$$!3*RLLLtIf$HF -$\"3=fe'>#=miiF-7$$!3]++]PYx\"\\#F-$\"3qwYWj\"*R,mF-7$$!3EMLLL7i)4#F- $\"3mn6Za()zBpF-7$$!3c****\\P'psm\"F-$\"3mm%)fp@X.tF-7$$!3')****\\74_c 7F-$\"3QK$3!4kz\"p(F-7$$!3)3LLL3x%z#)!#>$\"3Y^huTSvE\")F-7$$!3KMLL3s$Q M%Fdr$\"3cWx<8Zra&)F-7$$!3]^omm;zr)*!#@$\"3q-3StG-\\!*F-7$$\"3%pJL$ezw 5VFdr$\"3&)G$QrZ\")3g*F-7$$\"3s*)***\\PQ#\\\")Fdr$\"3>8;+cY`65!#<7$$\" 3GKLLe\"*[H7F-$\"3y#4@r(o!42\"F\\t7$$\"3I*******pvxl\"F-$\"393)fxx%oO6 F\\t7$$\"3#z****\\_qn2#F-$\"3+vO<5_r07F\\t7$$\"3U)***\\i&p@[#F-$\"3ae, M`dAx7F\\t7$$\"3B)****\\2'HKHF-$\"3Y%R\"***eiCO\"F\\t7$$\"3ElmmmZvOLF- $\"3qhcQP1nW9F\\t7$$\"3i******\\2goPF-$\"3o.;XOOvQ:F\\t7$$\"3UKL$eR<*f TF-$\"3(R$=n#4M+j\"F\\t7$$\"3m******\\)Hxe%F-$\"3kL'QX(G'ot\"F\\t7$$\" 3ckm;H!o-*\\F-$\"3#4IWDepX%=F\\t7$$\"3y)***\\7k.6aF-$\"3Y$eDHp^^'>F\\t 7$$\"3#emmmT9C#eF-$\"37P&f)p$>:4#F\\t7$$\"33****\\i!*3`iF-$\"3?6Yt%RjM B#F\\t7$$\"3%QLLL$*zym'F-$\"3U&4$*H?'>!Q#F\\t7$$\"3wKLL3N1#4(F-$\"3?2& p$o#*=TDF\\t7$$\"3Nmm;HYt7vF-$\"3!*[r6y%*e7FF\\t7$$\"3Y*******p(G**yF- $\"3?!=kjO]6)GF\\t7$$\"3]mmmT6KU$)F-$\"3u]q:]5M)3$F\\t7$$\"3fKLLLbdQ() F-$\"3_%o]'Q4D(G$F\\t7$$\"3[++]i`1h\"*F-$\"3pC'*4N&RX^$F\\t7$$\"3W++]P ?Wl&*F-$\"3QxE.MC'yu$F\\t7$$\"\"\"F*$\"3eLvj%Q2r,%F\\t-%'COLOURG6&%$RG BG$\"#5F)$F*F*Fa[l-F$6$7S7$F($\"3'ommm'Gd#3$F-7$F/$\"3*y5fw>NaK$F-7$F4 $\"3$f!>jKe^>NF-7$F9$\"39*\\YG%HH@PF-7$F>$\"3u#on9*)>'4RF-7$FC$\"35F_% H.g_3%F-7$FH$\"3264cB%\\,C%F-7$FM$\"35)fxCf>]R%F-7$FR$\"3g;;^0q,_XF-7$ FW$\"3:XCC%*>73ZF-7$Ffn$\"3a-R]bnq]g>]F-7$F`o$\"3Y'3 %3l4\\%>&F-7$Feo$\"3QH#o&y#[9Q&F-7$Fjo$\"3s`w!o^F_d&F-7$F_p$\"3YRS'o'Q 4ldF-7$Fdp$\"3uZ-o*='*4,'F-7$Fip$\"3)z[E>7H)QiF-7$F^q$\"3ZSxV_9JHlF-7$ Fcq$\"3l@mk3>z6oF-7$Fhq$\"3M7rloB$>:(F-7$F]r$\"3(RlFr_%)y](F-7$Fbr$\"3 eB46r5[:zF-7$Fhr$\"3dCX'zXP[K)F-7$F]s$\"3-p/7\"*pr1))F-7$Fcs$\"3A*)p*f V\"ea$*F-7$Fhs$\"33sl4?cBt)*F-7$F^t$\"3yqK$Hqfz/\"F\\t7$Fct$\"3iqpF(R= f6\"F\\t7$Fht$\"3cLaxc0\"z=\"F\\t7$F]u$\"3eczs,P,j7F\\t7$Fbu$\"3_oa#*H j)HN\"F\\t7$Fgu$\"3h_`d9@,S9F\\t7$F\\v$\"3&f)Rd\"3!oR:F\\t7$Fav$\"3>Y2 rS7EO;F\\t7$Ffv$\"35-r2jA%*['=F\\t7$F`w$\"3')\\j (G:(p()>F\\t7$Few$\"3B0)zBUC$=@F\\t7$Fjw$\"3gS!)[\"3YNE#F\\t7$F_x$\"3q 6yI*Gv=T#F\\t7$Fdx$\"3[#=MgkMCd#F\\t7$Fix$\"3C9)Q&RS!3u#F\\t7$F^y$\"3[ '4Z$*f#y.HF\\t7$Fcy$\"3OUA4%Q'f+JF\\t7$Fhy$\"3u!*)e+d_fG$F\\t7$F]z$\"3 %[-^n\\^N\\$F\\t7$Fbz$\"3Gz=c]P9-PF\\t7$Fgz$\"3%pmmYXzt$RF\\t-F\\[l6&F ^[lFa[lF_[lFa[l-%+AXESLABELSG6$Q\"X6\"Q!F^el-%%VIEWG6$;F(Fgz%(DEFAULTG " 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "C urve 2" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "expand(subs(X=(x -1)/2.,p));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,*^$$\"+#)yp$>&!#5$\"\" !F)\"\"\"*&$\"+v+1'3#F'F*%\"xGF*F**&$\"*&35ovF'F*)F.\"\"#F*F**&$\"+]-v =y!#6F*)F.\"\"$F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "sqrt ((evalf(int(y^2,X=-1..1))-2*a^2-2/3*b^2-8/45*c^2-8/175*d^2)/2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#^$$\"+fa$*[A!#6$\"\"!F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q6:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "solve(\{ cm2+c0+c1+c3=0,-2*cm2+c1+3*c3=0,4*cm2+c1+9*c3=2,-8*cm2+c1+27*c3=0\},\{ cm2,c0,c1,c3\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<&/%$cm2G#\"\"%\"# :/%#c1G#\"\"\"\"\"$/%#c0G#!\"#F-/%#c3G#F,F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "assign(%):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "y:=[0.84147098,0.93203909,0.96355819,0.99749499]:\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "(cm2*y[1]+c0*y[2]+c1*y[3]+c3 *y[4])/.1^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!*q-9G*!\"*" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q7:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name change coords has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 148 "implicitplot(x[1]^2*ln(x[2])-x[1]/(1+x[2])=3,x[1]=0..3,x[2]=0..3) :\nimplicitplot(x[2]/(1+x[1]^2)+x[2]*ln(x[1])=2,x[1]=0..3,x[2]=0..3): \ndisplay(%,%%);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6$-%'CURVESG6@7$7$$\"3R++++++S9!#<$\"3_1LjeQd)*GF*7$$\"3#fg'3cr\"zP \"F*$\"3y,++++++IF*7$7$$\"3s++++++g:F*$\"3POaM(*pmv BQqZGF*7$7$$\"3/(o)\\**Q^]9F*$\"3m,+++++!)GF*FA7$7$$\"3E(o)\\**Q^]9F*F JF'7$7$$\"3g++++++!o\"F*$\"3%o'>+6qviDF*7$$\"36#*\\W`d>:;F*$\"3Y,+++++ SEF*7$FV7$$\"3]++++++g:F*F67$7$$\"3q+++++++=F*$\"38]_WjzDGCF*7$$\"3`V \"3.[pTr\"F*$\"3N,+++++?DF*7$F_oFQ7$7$$\"3#3++++++#>F*$\"3m3L99iC5BF*7 $$\"3(H*p#yb'eD=F*$\"3C,++++++CF*7$7$$\"3?$*p#yb'eD=F*F^pFjn7$7$$\"3#4 ++++++/#F*$\"3\"p.9\\+Ie?#F*7$$\"3)zPCz9U8&>F*$\"39,+++++!G#F*7$Fjp7$$ \"3f++++++?>F*Fio7$7$$\"3/,+++++g@F*$\"3^C@)p)zz7@F*7$$\"3!p_W1sQ]4#F* Feq7$FiqFep7$7$F]q$\"3KWmA[9TH?F*7$$\"3C0Gnf_%HE#F*Ffp7$FarFdq7$F^r7$$ \"3/2gA-$=dI#F*$\"3-&*Rx(p\"G9?F*7$7$F^p$\"3?,^&>TuU&>F*Ffr7$7$Fbo$\"3 +\"f#ov![i)=F*7$$\"3yQP83)))oX#F*Fgo7$Fcs7$F^p$\"3)45b>TuU&>F*7$F`s7$$ \"3M/FKbPH'e#F*$\"3Q(HxYC1P&=F*7$7$FY$\"3*H9zW$=RC=F*F[t7$7$F;$\"3=\\$ R!**4#zw\"F*7$$\"3;j)o#F*F[o7$FhtFat7$Fet7$$\"3)[k>7$7$F[o$\"3!yA $\\AkU4HF*7$$\"3O&>i2)QNpF *FY7$7$$\"3alpd]Gl/>F*FY7$$\"3#z!)3Hj/^*=F*$\"3!R>\"4n`*[m#F*7$7$$\"31 $HH!3D%R&=F*F;Fhw7$7$$\"3G$HH!3D%R&=F*F;7$$\"3WLyIdj$o\"=F*$\"3%*o@pUO ;jGF*7$7$$\"3\"3zYu-u*4=F*FJFex7$7$F\\y$\"37-+++++!)GF*Fgv7$7$Ffp$\"3q [l=$=ZsP#F*7$$\"3F!R(40lLE?F*F^p7$Ffy7$$\"3!*eq$[P1@,#F*$\"3FVH;DO*yU# F*7$7$$\"39'36u.c4'>F*FboFjy7$F`zF^w7$7$Feq$\"3iz#3PD.#)>#F*7$$\"3Jo*R hmV35#F*F]q7$FhzFcy7$7$F]q$\"3ENoT7#4c0#F*7$$\"3o.8s'zv\"*=#F*Feq7$F`[ lFez7$7$F^p$\"3#ReA^j='R>F*7$$\"3mPx8*RjXH#F*Ffp7$Fh[lF][l7$7$Fbo$\"3: FC$QrhP%=F*7$$\"33%[P\\@1DU#F*Fgo7$F`\\lFe[l7$7$FY$\"3O6+(=l>Ow\"F*7$$ \"3;Ld')>)HDe#F*F[o7$Fh\\lF]\\l7$Fe\\l7$$\"3d;>O7.#3s#F*$\"3/'3Qwoz\"> ]HF*$\"3%G^dje 1)4;F*7$7$F0$\"3[D)z)RoK(e\"F*Fb^lF^v" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "F:=[x[1]^2*ln(x[2])-x[1]/(1+x[2])-3,x[2]/ (1+x[1]^2)+x[2]*ln(x[1])-2]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "J:=matrix(2,2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "fo r i to 2 do for j to 2 do\nJ[i,j]:=diff(F[i],x[j]) end do end do: " }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "x:=[2.,2.5]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with (linalg):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and trace have been red efined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "for i to 5 do x:=evalm(x-inverse(J)&*F) end do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG-%'vectorG6#7$$\"+V(>^@#!\"*$\"+)4XX.#F+" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG-%'vectorG6#7$$\"+WIkcB!\"*$\"+$ HOl(>F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG-%'vectorG6#7$$\"+^O# >N#!\"*$\"+`FX$)>F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG-%'vector G6#7$$\"+>E*>N#!\"*$\"+@F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"xG-%'vectorG6#7$$\"+@E*>N#!\"*$\"+?F+" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 3 "Q8:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "x:=[-3,-1,0,3,8,11]: \+ y:=[2.15,3.24,2.73,1.96,2.20,3.31]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 141 "s1:=sum(x[i],i=1..6): s2:=sum(1/(1+x[i]^2),i=1..6): \ns3:=sum(x[i]^2,i=1..6): s4:=sum(1/(1+x[i]^2)^2,i=1..6):\ns5:=sum(x[ i]/(1+x[i]^2),i=1..6):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "X :=matrix(3,3,[6,s1,s2,s1,s3,s5,s2,s5,s4]):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 72 "Y:=[sum(y[i],i=1..6),sum(x[i]*y[i],i=1..6),sum(y[i] /(1+x[i]^2),i=1..6)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "wi th(linalg): linsolve(X,Y);" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, th e protected names norm and trace have been redefined and unprotected\n " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7%$\"+DTw2A!\"*$\"+\"o T " 0 "" {MPLTEXT 1 0 23 "restart: with(linalg):" }} {PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and tra ce have been redefined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "A:=matrix(4,4,[0,3,-3,2,3,1,4,-2,-3,4,-3,2,2,-2,2,3]* 1.):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "u:=submatrix(A,1..4 ,[1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "h:=norm(u,2): u[ 2,1]:=u[2,1]-h: H:=h*(h-A[2,1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "P:=evalm(Matrix(4,4,shape=identity)-u&*transpose(u)/H ):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "A:=evalm(P&*A&*P);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7&7&$\"\"!F+$\"+fdT !p%!\"*$!\"\"F.$\"\"%!#57&F,$!+DFFFdF.$\"*?coX)F3$\"+K>ww " 0 "" {MPLTEXT 1 0 49 "u:=submatrix(A,1..4,[2]): u[1,1]:= 0: u[2,1]:=0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "h:=norm(u ,2): u[3,1]:=u[3,1]-h: H:=h*(h-A[3,2]):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 55 "P:=evalm(Matrix(4,4,shape=identity)-u&*transpose(u) /H):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "A:=evalm(P&*A&*P); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7&7&$\"\"!F+$\"+ fdT!p%!\"*$\"+Z![gh$!#>$!+Jc^95!#=7&F,$!+DFFFdF.$\"+YPP>AF.$\"\"&!#67& F/$\"+[PP>AF.$\"+B@oQCF.$\"+N-'eH'F<7&F2$!\"$F<$\"*CgeH'!#5$\"++1f)G%F ." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Q10:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the prote cted names norm and trace have been redefined and unprotected\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "A:=matrix(5,5,[3,-1,0,0,0,2, -1,2,0,0,0,3,1,-4,0,0,0,1,0,-2,0,0,0,4,-1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "LUdecomp(transpose(A),L=`U`,U=`L`):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "U:=transpose(U); L:=transpose(L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"UG-%'matrixG6#7'7'\"\"\"#!\"\"\" \"$\"\"!F.F.7'F.F*!\"'F.F.7'F.F.F*#!\"%\"#>F.7'F.F.F.F*#!#>\"\"#7'F.F. F.F.F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG-%'matrixG6#7'7'\"\"$ \"\"!F+F+F+7'\"\"##!\"\"F*F+F+F+7'F+F*\"#>F+F+7'F+F+\"\"\"#\"\"%F1F+7' F+F+F+F5\"#P" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "y:=linsolve (L,[7,-4,0,3,-2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG-%'vectorG 6#7'#\"\"(\"\"$\"#E#!#y\"#>#\"$N\"\"\"%#!$P\"\"#P" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 17 "x:=linsolve(U,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG-%'vectorG6#7'#\"#\")\"#P#!#;F+#!$j\"F+#!$6#\"$[ \"#!$P\"F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Q11:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "restart: with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and trace have \+ been redefined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 425 "step:=proc(A) local n,a,i,j,p; n:= rowdim(A):\nf or i to n-1 do a:= submatrix(A,i..i+1,1..n):\np[i]:= matrix(2,2,[a[1 ,i],a[2,i],-a[2,i],a[1,i]])/ sqrt(a[1,i]^2+a[2,i]^2):\na:= evalm(p[i] \+ &* a):\nfor j to n do A[i,j]:=a[1,j]: A[i+1,j]:=a[2,j]end do: end do:\nfor i to n-1 do a:= submatrix(A,1..n,i..i+1):\na:= evalm(a &* \+ transpose(p[i])):\nfor j to n do A[j,i]:=a[j,1]: A[j,i+1]:=a[j,2]end \+ do: end do:\nevalm(A) end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "A:=matrix(3,3,[2,-3,0,-3,0,4,0,4,-1]*1.):" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 207 "shift:=proc(A)local s,a,n: n:=rowdim(A):\n a:=submatrix(A,n-1..n,n-1..n): s:=(a[1,1]+a[2,2])/2:\nif (s>=0) then \ns:=s-sqrt((a[1,1]-a[2,2])^2/4+a[1,2]^2) else\ns:=s+sqrt((a[1,1]-a[2, 2])^2/4+a[1,2]^2) end if end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "s1:=shift(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#s1G$\"+u)G6` $!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "A:=evalm(A-s1*Matr ix(3,3,shape=identity)): A:=step(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7%7%$!+&=^sa&!\"*$!+,\"\\to$F,$F,!#57%$!++\"\\to$ F,$!+j.U#H$F,$\"+-k(e#GF,7%$\"\"!F:$\"+,k(e#GF,$!+a2:PvF0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "s2:=shift(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#s2G$\"+Nz![2\"!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "A:=evalm(A-s2*Matrix(3,3,shape=identity)): A:=step(A );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7%7%$!+hk%HA*! \"*$!+%[q.p\"F,$\"\"#!#57%$!+&[q.p\"F,$!+)4]T9%F,$\"*H;xn(F,7%$!\"!\" \"!$\"+'G;xn(F1$\"+?8'G\\&F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "s3:=shift(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#s3G$\"*`\"*o r'!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "A:=evalm(A-s3*Mat rix(3,3,shape=identity)): A:=step(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7%7%$!+Z!z6.\"!\")$!+sj*\\i(!#5$!\"'F/7%$!+)Q' *\\i(F/$!+>4nGX!\"*$\")dw/8F/7%$!\"!\"\"!$\"+gjw/8!#7$\"+,.^$e(F@" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "s4:=shift(A);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%#s4G$\"(%)Qe(!\"*" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 55 "A:=evalm(A-s4*Matrix(3,3,shape=identity)): A:=step (A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7%7%$!+#>/+/ \"!\")$!+a\"QAH$!#5$\"&cY'!#97%$!+o\"QAH$F/$!+DwebW!\"*$\"$9'!#77%$!\" !\"\"!$\"+e)QK%=!#@$\"+u>b6j!#=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "A[3,3]+s1+s2+s3+s4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+_)4 _G&!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "(A[1,1]+A[2,2])/ 2-sqrt((A[1,1]-A[2,2])^2/4+A[1,2]^2)+s1+s2+s3+s4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+/+,L^!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "(A[1,1]+A[2,2])/2+sqrt((A[1,1]-A[2,2])^2/4+A[1,2]^2)+s1+s2+s3+s4; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*`,!y%)!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "103 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }