{VERSION 6 0 "IBM INTEL NT" "6.0" } {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 "" {MPLTEXT 1 0 13 "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 27 "a:=matrix(2,2,[-3,4,6,-5]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aGK%'matrixG6#7$7$!\"$\"\"%7$\"\"'!\"&Q)pprint356\" " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "ft:=[sin(t),0];" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ftG7$-%$sinG6#%\"tG\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "aa:=[a1,a2]; bb:=[b1,b2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#aaG7$%#a1G%#a2G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#bbG7$%#b1G%#b2G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "guess:= evalm( aa*cos(t) + bb*sin(t));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%&guessGK%'vectorG6#7$,&*&-%$cosG6#%\"tG\"\"\"% #a1GF/F/*&-%$sinGF-F/%#b1GF/F/,&*&F+F/%#a2GF/F/*&F2F/%#b2GF/F/Q)pprint 366\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "gp:= map( x->diff( x,t), guess);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#gpGK%'vectorG6#7$, &*&-%$sinG6#%\"tG\"\"\"%#a1GF/!\"\"*&-%$cosGF-F/%#b1GF/F/,&*&F+F/%#a2G F/F1*&F3F/%#b2GF/F/Q)pprint376\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "right:= evalm(a&*guess+ ft);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&rightGK%'vectorG6#7$,,*(\"\"$\"\"\"-%$cosG6#%\"tGF,% #a1GF,!\"\"*(F+F,-%$sinGF/F,%#b1GF,F2*(\"\"%F,F-F,%#a2GF,F,*(F8F,F4F,% #b2GF,F,F4F,,**(\"\"'F,F-F,F1F,F,*(F>F,F4F,F6F,F,*(\"\"&F,F-F,F9F,F2*( FAF,F4F,F;F,F2Q)pprint386\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 181 "eq:=\{coeff(gp[1],cos(t))=coeff(right[1],cos(t)),\ncoeff(gp[1],si n(t))=coeff(right[1],sin(t)),\ncoeff(gp[2],cos(t))=coeff(right[2],cos( t)),\ncoeff(gp[2],sin(t))=coeff(right[2],sin(t))\};" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%#eqG<&/%#b1G,&*&\"\"$\"\"\"%#a1GF+!\"\"*&\"\"%F+%#a 2GF+F+/,$F,F-,(*&F*F+F'F+F-*&F/F+%#b2GF+F+F+F+/F6,&*&\"\"'F+F,F+F+*&\" \"&F+F0F+F-/,$F0F-,&*&F:F+F'F+F+*&F " 0 "" {MPLTEXT 1 0 30 "sol:=solve( eq,\{a1,a2,b1,b2\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$solG<&/%#a2G#!#7\"#T/%#a1G#!#D\"##)/%#b1G#!#@F/ /%#b2G#!#:F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "evalm(a&*ev alm(subs( sol,aa)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'vectorG6#7$ #!#@\"##)#!#:\"#TQ)pprint416\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "evalm(inverse(a&*a + diag(1,1))&*[-1,0]); evalm(a&*%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#K%'vectorG6#7$#!#D\"##)#!#7\"#TQ)pprin t446\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'vectorG6#7$#!#@\"##)#!#: \"#TQ)pprint456\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "xpt:= \+ evalm(subs(sol, evalm(guess)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ xptGK%'vectorG6#7$,&*&#\"#D\"##)\"\"\"-%$cosG6#%\"tGF.!\"\"*&#\"#@F-F. -%$sinGF1F.F3,&*&#\"#7\"#TF.F/F.F3*&#\"#:F=F.F7F.F3Q)pprint476\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "eigenvectors(a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$7%\"\"\"F$<#K%'vectorG6#7$F$F$Q)pprint486\"7 %!\"*F$<#KF'6#7$F$#!\"$\"\"#Q)pprint49F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "Phi:=matrix(2,2, [exp(t),2*exp(-9*t), exp(t),-3*exp(- 9*t)]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$PhiGK%'matrixG6#7$7$-%$e xpG6#%\"tG,$*&\"\"#\"\"\"-F+6#,$*&\"\"*F1F-F1!\"\"F1F17$F*,$*&\"\"$F1F 2F1F7Q)pprint506\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "xct:= evalm( Phi&*[c1,c2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$xctGK%'vec torG6#7$,&*&-%$expG6#%\"tG\"\"\"%#c1GF/F/*(\"\"#F/-F,6#,$*&\"\"*F/F.F/ !\"\"F/%#c2GF/F/,&F*F/*(\"\"$F/F3F/F9F/F8Q)pprint516\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "ext:=evalm(xct+xpt);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%$extGK%'vectorG6#7$,**&-%$expG6#%\"tG\"\"\"%#c 1GF/F/*(\"\"#F/-F,6#,$*&\"\"*F/F.F/!\"\"F/%#c2GF/F/*&#\"#D\"##)F/-%$co sGF-F/F8*&#\"#@F=F/-%$sinGF-F/F8,*F*F/*(\"\"$F/F3F/F9F/F8*&#\"#7\"#TF/ F>F/F8*&#\"#:FKF/FCF/F8Q)pprint526\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "ex0:= map(x->eval(x),subs( t=0, evalm(ext)));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ex0GK%'vectorG6#7$,(%#c1G\"\"\"*&\" \"#F+%#c2GF+F+#\"#D\"##)!\"\",(F*F+*&\"\"$F+F.F+F2#\"#7\"#TF2Q)pprint5 46\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "x0:=[1,0];" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x0G7$\"\"\"\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "eqs:=\{ex0[1]=x0[1], ex0[2]=x0[2]\};" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eqsG<$/,(%#c1G\"\"\"*&\"\"#F)%#c2GF )F)#\"#D\"##)!\"\"F)/,(F(F)*&\"\"$F)F,F)F0#\"#7\"#TF0\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "solc:=solve( eqs,\{c1,c2\});" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%solcG<$/%#c2G#\"#$)\"$5%/%#c1G#\"\" *\"#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "tada:=subs( solc, \+ evalm(ext));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%tadaGK%'vectorG6#7$ ,**&#\"\"*\"#5\"\"\"-%$expG6#%\"tGF.F.*&#\"#$)\"$0#F.-F06#,$*&F,F.F2F. !\"\"F.F.*&#\"#D\"##)F.-%$cosGF1F.F;*&#\"#@F?F.-%$sinGF1F.F;,**&F+F.F/ F.F.*&#\"$\\#\"$5%F.F7F.F;*&#\"#7\"#TF.F@F.F;*&#\"#:FPF.FEF.F;Q)pprint 566\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "plot( [tada[1],tad a[2]],t=0..3, color=[red,blue]);" }}{PARA 13 "" 1 "" {GLPLOT2D 558 220 220 {PLOTDATA 2 "6&-%'CURVESG6$7S7$$\"\"!F)$\"\"\"F)7$$\"3s****** \\i9Rl!#>$\"3aTNvVrCY')!#=7$$\"3/++vVA)GA\"F2$\"3Y&RN'\\)H#z\")F27$$\" 3+++]Peui=F2$\"3D(>Ztk,(H\")F27$$\"3A++]i3&o]#F2$\"3_HKctX[*R)F27$$\"3 %)***\\(oX*y9$F2$\"3]e\\?A*Qg())F27$$\"3z***\\P9CAu$F2$\"3S\"=?&)=;.X* F27$$\"3!)***\\P*zhdVF2$\"3@@,ab)e],\"!#<7$$\"31++v$>fS*\\F2$\"3co7'G; ,s4\"FQ7$$\"3$)***\\(=$f%GcF2$\"3/'QA4]]\")=\"FQ7$$\"3Q+++Dy,\"G'F2$\" 3!e%R8j!*)3H\"FQ7$$\"33++]7FQ7$$\"3,++]siL -5FQ$\"3)\\iM])pFs?FQ7$$\"3-+++!R5'f5FQ$\"3HZ$>?\">CCAFQ7$$\"3)***\\P/ QBE6FQ$\"3/)p\"f5BJ8CFQ7$$\"3!******\\\"o?&=\"FQ$\"3YJTuagF#f#FQ7$$\"3 1+]Pa&4*\\7FQ$\"3a6)=;XV=!GFQ7$$\"33+]7j=_68FQ$\"3X6+LVs$\\,$FQ7$$\"33 ++vVy!eP\"FQ$\"3;Jg&)\\\"FQ$\"3KkJ)y)p5]PFQ7$$\"3)***\\P>:mk:FQ$\"35U9OUz)\\/%FQ 7$$\"3'***\\iv&QAi\"FQ$\"3b,n(>M\"*yJ%FQ7$$\"31++vtLU%o\"FQ$\"3vr40t+` IYFQ7$$\"3!******\\Nm'[FQ$\" 3duW=*pCI8'FQ7$$\"3z*****\\@80+#FQ$\"3e_>y&\\mxa'FQ7$$\"31++]7,Hl?FQ$ \"3>*p,@x)4=qFQ7$$\"3()**\\P4w)R7#FQ$\"3q9-8!)fEquFQ7$$\"3;++]x%f\")=# FQ$\"3#Rd-;`qX*zFQ7$$\"3!)**\\P/-a[AFQ$\"3PiNh%yy\"=&)FQ7$$\"3/+](=Yb; J#FQ$\"3+K\\(3.-))4*FQ7$$\"3')****\\i@OtBFQ$\"3ijx:eZP,(*FQ7$$\"3')** \\PfL'zV#FQ$\"3RTTm60:P5!#;7$$\"3>+++!*>=+DFQ$\"35Sl'=XHd5\"F\\x7$$\"3 -++DE&4Qc#FQ$\"3EvXF3)=-=\"F\\x7$$\"3=+]P%>5pi#FQ$\"3euM&\\l=(e7F\\x7$ $\"39+++bJ*[o#FQ$\"3^[9!Gxm^L\"F\\x7$$\"33++Dr\"[8v#FQ$\"3$fQvPW*=G9F \\x7$$\"3++++Ijy5GFQ$\"3$3;xT;&e;:F\\x7$$\"31+]P/)fT(GFQ$\"3)z`ud([e;; F\\x7$$\"31+]i0j\"[$HFQ$\"3(RD2ml/#=$\"3;l=Q(Rm]=(F 27$FC$\"3cnl5k:qc!)F27$FH$\"3TgEBZ(GQ\"))F27$FM$\"3S8,I#R.uf*F27$FS$\" 3B]oXh%RS/\"FQ7$FX$\"3_*)e/x?^L6FQ7$Fgn$\"3_qtVjGrK7FQ7$F\\o$\"3l@WW)[ xpK\"FQ7$Fao$\"3RI_y?FQ7$Fjp$\"36kH_S%4W8#FQ7$F_q$ \"3n)e!H\">H%>BFQ7$Fdq$\"3%zsiclT^\\#FQ7$Fiq$\"3(*3'*\\)*H_,FFQ7$F^r$ \"3R+f'eho>\"HFQ7$Fcr$\"3%eAqop8o9$FQ7$Fhr$\"3EBjH#)o$pP$FQ7$F]s$\"3I! =k?Rjh*FQ7$Fhw$\"3dUl(G`>\"H5F\\x7$F^x$\"3uvD G=`=)4\"F\\x7$Fcx$\"3Mwv4BF?t6F\\x7$Fhx$\"3w2u![HaAD\"F\\x7$F]y$\"39k^ tH@BH8F\\x7$Fby$\"3XL3)yL')GU\"F\\x7$Fgy$\"3@7U(>$o'=^\"F\\x7$F\\z$\"3 f6\"[*Q$3Dh\"F\\x7$Faz$\"33%RFUwdZr\"F\\x7$Ffz$\"31Qq5'y5:$=F\\x-F[[l6 &F][lF(F(F^[l-%+AXESLABELSG6$Q\"t6\"Q!F^el-%%VIEWG6$;F(Ffz%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Cur ve 2" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "plot( [tada[1],tad a[2],t=0..3]);" }}{PARA 13 "" 1 "" {GLPLOT2D 556 177 177 {PLOTDATA 2 " 6%-%'CURVESG6$7S7$$\"\"\"\"\"!$\"3s#yDJ7:6b&!#M7$$\"3aTNvVrCY')!#=$\"3 +rCiO:0xIF17$$\"3Y&RN'\\)H#z\")F1$\"3[HfO6=3*z%F17$$\"3D(>Ztk,(H\")F1$ \"3gHwdw)QJ:'F17$$\"3_HKctX[*R)F1$\"3;l=Q(Rm]=(F17$$\"3]e\\?A*Qg())F1$ \"3cnl5k:qc!)F17$$\"3S\"=?&)=;.X*F1$\"3TgEBZ(GQ\"))F17$$\"3@@,ab)e],\" !#<$\"3S8,I#R.uf*F17$$\"3co7'G;,s4\"FP$\"3B]oXh%RS/\"FP7$$\"3/'QA4]]\" )=\"FP$\"3_*)e/x?^L6FP7$$\"3!e%R8j!*)3H\"FP$\"3_qtVjGrK7FP7$$\"3Mu$=+0 V\"*Q\"FP$\"3l@WW)[xpK\"FP7$$\"3k#[p-3!o3:FP$\"3RI_y?FP$\"3:FP7$$\"3HZ$>? \">CCAFP$\"36kH_S%4W8#FP7$$\"3/)p\"f5BJ8CFP$\"3n)e!H\">H%>BFP7$$\"3YJT uagF#f#FP$\"3%zsiclT^\\#FP7$$\"3a6)=;XV=!GFP$\"3(*3'*\\)*H_,FFP7$$\"3X 6+LVs$\\,$FP$\"3R+f'eho>\"HFP7$$\"3;JgM\"*yJ%FP$\"3CPAv1Hl2UFP7$$\"3v r40t+`IYFP$\"3O8'p+x)4?XFP7$$\"37]s._g7u\\FP$\"3SQjkCP%R'[FP7$$\"3cYCZ vOrJ`FP$\"3%)p\")\\'y9AA&FP7$$\"3AH'y=Vh!*p&FP$\"3u31?#QN1f&FP7$$\"3du W=*pCI8'FP$\"3\"z)\\u2#fi-'FP7$$\"3e_>y&\\mxa'FP$\"3CobhX$3HW'FP7$$\"3 >*p,@x)4=qFP$\"3:L-r:Gq:pFP7$$\"3q9-8!)fEquFP$\"3i:B(QQs/P(FP7$$\"3#Rd -;`qX*zFP$\"3I!*=Fg\\,)*yFP7$$\"3PiNh%yy\"=&)FP$\"3m+p;bJ.D%)FP7$$\"3+ K\\(3.-))4*FP$\"3t`vXdMe4!*FP7$$\"3ijx:eZP,(*FP$\"3q#**p>?Rjh*FP7$$\"3 RTTm60:P5!#;$\"3dUl(G`>\"H5F[x7$$\"35Sl'=XHd5\"F[x$\"3uvDG=`=)4\"F[x7$ $\"3EvXF3)=-=\"F[x$\"3Mwv4BF?t6F[x7$$\"3euM&\\l=(e7F[x$\"3w2u![HaAD\"F [x7$$\"3^[9!Gxm^L\"F[x$\"39k^tH@BH8F[x7$$\"3$fQvPW*=G9F[x$\"3XL3)yL')G U\"F[x7$$\"3$3;xT;&e;:F[x$\"3@7U(>$o'=^\"F[x7$$\"3)z`ud([e;;F[x$\"3f6 \"[*Q$3Dh\"F[x7$$\"3(RD2ml/#= " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "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 92 "A:= matrix( 3,3,[1,-1,1,33,14,-19,3 2,11,-16]);\nA2:= evalm(A-2*diag(1,1,1)):\nft:=[6*t,5,4*t];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AGK%'matrixG6#7%7%\"\"\"!\"\"F*7%\"#L\"# 9!#>7%\"#K\"#6!#;Q)pprint586\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f tG7%,$*&\"\"'\"\"\"%\"tGF)F)\"\"&,$*&\"\"%F)F*F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "Phi:= transpose( matrix( 3,3,[ 0,exp(-5*t) ,exp(-5*t),\nexp(2*t),2*exp(2*t),3*exp(2*t),\nt*exp(2*t),(2*t-3)*exp(2 *t),(3*t-2)*exp(2*t)]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$PhiGK%' matrixG6#7%7%\"\"!-%$expG6#,$*&\"\"#\"\"\"%\"tGF1F1*&F2F1F+F17%-F,6#,$ *&\"\"&F1F2F1!\"\",$*&F0F1F+F1F1*&,&*&F0F1F2F1F1\"\"$F:F1F+F17%F5,$*&F @F1F+F1F1*&,&*&F@F1F2F1F1F0F:F1F+F1Q)pprint596\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "cee:=[c1,c2,c3]:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 16 "evalm(Phi&*cee);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6 #K%'vectorG6#7%,&*&-%$expG6#,$*&\"\"#\"\"\"%\"tGF/F/F/%#c2GF/F/*(F0F/F )F/%#c3GF/F/,(*&-F*6#,$*&\"\"&F/F0F/!\"\"F/%#c1GF/F/*(F.F/F)F/F1F/F/*( ,&*&F.F/F0F/F/\"\"$F;F/F)F/F3F/F/,(F5F/*(FAF/F)F/F1F/F/*(,&*&FAF/F0F/F /F.F;F/F)F/F3F/F/Q)pprint606\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "map(x->simplify(x),map( x->diff(x,t), Phi)); \nmap(x->simplify (x),evalm(A&*Phi));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'matrixG6#7%7 %\"\"!,$*&\"\"#\"\"\"-%$expG6#,$*&F+F,%\"tGF,F,F,F,*&F-F,,&*&F+F,F2F,F ,F,F,F,7%,$*&\"\"&F,-F.6#,$*&F9F,F2F,!\"\"F,F>,$*&\"\"%F,F-F,F,,$*(FAF ,F-F,,&F2F,F,F>F,F,7%F7,$*&\"\"'F,F-F,F,*&F-F,,&*&FHF,F2F,F,F,F>F,Q)pp rint656\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'matrixG6#7%7%\"\"!,$*& \"\"#\"\"\"-%$expG6#,$*&F+F,%\"tGF,F,F,F,*&F-F,,&*&F+F,F2F,F,F,F,F,7%, $*&\"\"&F,-F.6#,$*&F9F,F2F,!\"\"F,F>,$*&\"\"%F,F-F,F,,$*(FAF,F-F,,&F2F ,F,F>F,F,7%F7,$*&\"\"'F,F-F,F,*&F-F,,&*&FHF,F2F,F,F,F>F,Q)pprint666\" " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "Phi1:=inverse(Phi);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Phi1GK%'matrixG6#7%7%,$*&\"\"&\"\" \"-%$expG6#,$*&F,F-%\"tGF-!\"\"F4F4,$*&\"\"#F-F.F4F4,$*&\"\"$F-F.F4F-7 %*&-F/6#,$*&F7F-F3F-F-F4,&F3F-F-F-F-*&F=F4F3F-,$FBF47%,$*&F-F-F=F4F4FE FFQ)pprint676\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "exoft:=m ap(x->simplify(x),evalm(Phi&*(map(x->int(x,t),evalm(Phi1&*ft))+[c1,c2, c3])));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&exoftGK%'vectorG6#7%,*# \"#8\"\"%!\"\"*(\"\"(\"\"\"\"\"#F-%\"tGF0F-*&-%$expG6#,$*&F1F0F2F0F0F0 %#c2GF0F0*(F2F0F4F0%#c3GF0F0,.#\"$R)\"#]F-*(\"#oF0\"\"&F-F2F0F-*&-F56# ,$*&FBF0F2F0F-F0%#c1GF0F0*(F1F0F4F0F9F0F0**F1F0F2F0F4F0F;F0F0*(\"\"$F0 F4F0F;F0F-,.#\"%.<\"$+\"F-*(\"$h\"F0\"#5F-F2F0F-FCF0*(FLF0F4F0F9F0F0** FLF0F2F0F4F0F;F0F0*(F1F0F4F0F;F0F-Q)pprint756\"" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 74 "exoft:=map(x->simplify(x),evalm(Phi&*(map(x->i nt(x,t),evalm(Phi1&*ft)))));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&exo ftGK%'vectorG6#7%,&#\"#8\"\"%!\"\"*(\"\"(\"\"\"\"\"#F-%\"tGF0F-,&#\"$R )\"#]F-*(\"#oF0\"\"&F-F2F0F-,&#\"%.<\"$+\"F-*(\"$h\"F0\"#5F-F2F0F-Q)pp rint746\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "cee:=map(x->si mplify(x),evalm((subs( t=0,evalm(Phi1))&*[5,-2,4])));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ceeGK%'vectorG6#7%!\"*\"\"&\"\"\"Q)pprint786\" " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "xt:=evalm(subs( \{c1=ce e[1],c2=cee[2],c3=cee[3]\},evalm(exoft)));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#xtGK%'vectorG6#7%,*#\"#8\"\"%!\"\"*(\"\"(\"\"\"\"\"# F-%\"tGF0F-*&\"\"&F0-%$expG6#,$*&F1F0F2F0F0F0F0*&F2F0F5F0F0,,#\"$R)\"# ]F-*(\"#oF0F4F-F2F0F-*&\"\"*F0-F66#,$*&F4F0F2F0F-F0F-*&F/F0F5F0F0*(F1F 0F2F0F5F0F0,,#\"%.<\"$+\"F-*(\"$h\"F0\"#5F-F2F0F-*&FBF0FCF0F-*&F+F0F5F 0F0*(\"\"$F0F2F0F5F0F0Q)pprint806\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "35 0 0" 0 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }