{VERSION 3 0 "IBM INTEL NT" "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 "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 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 "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 13 "with(linalg):" }} {PARA 7 "" 1 "" {TEXT -1 32 "Warning, new definition for norm" }} {PARA 7 "" 1 "" {TEXT -1 33 "Warning, new definition for trace" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "e:=[[1,1.2],[2,1.9],[3,3.1],[4,4.7] ,[5,5.2]];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"eG7'7$\"\"\"$\"#7!\" \"7$\"\"#$\"#>F*7$\"\"$$\"#JF*7$\"\"%$\"#ZF*7$\"\"&$\"#_F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "f:=[[1,4.9],[2,4.1],[3,3.3],[4,2.7] ,[5,0.8]];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG7'7$\"\"\"$\"#\\! \"\"7$\"\"#$\"#TF*7$\"\"$$\"#LF*7$\"\"%$\"#FF*7$\"\"&$\"\")F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "dbe:=5: dbf:=5:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "elso:=vector(dbe+dbf,0):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "for i from 1 to dbe do elso[ i]:=1: od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "masodik:=vect or(dbe+dbf,1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "for i fro m 1 to dbe do masodik[i]:=0: od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "harmadik:=vector(dbe+dbf,0):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "for i from 1 to dbe do harmadik[i]:=e[i][1]: od: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "for i from (dbe+1) to ( dbe+dbf) do harmadik[i]:=f[i-dbe][2]: od:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 28 "negyedik:=vector(dbe+dbf,0):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 48 "for i from 1 to dbe do negyedik[i]:=e[i][2]: o d:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "for i from (dbe+1) to (dbe+dbf) do negyedik[i]:=-f[i-dbe][1]: od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalm(elso);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# -%'vectorG6#7,\"\"\"F'F'F'F'\"\"!F(F(F(F(" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 15 "evalm(masodik);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# -%'vectorG6#7,\"\"!F'F'F'F'\"\"\"F(F(F(F(" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 16 "evalm(harmadik);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #-%'vectorG6#7,\"\"\"\"\"#\"\"$\"\"%\"\"&$\"#\\!\"\"$\"#TF.$\"#LF.$\"# FF.$\"\")F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "evalm(negyed ik);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7,$\"#7!\"\"$\"#>F )$\"#JF)$\"#ZF)$\"#_F)F)!\"#!\"$!\"%!\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "a:=augment(elso,masodik,harmadik,negyedik);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG-%'matrixG6#7,7&\"\"\"\"\"!F*$\"#7!\" \"7&F*F+\"\"#$\"#>F.7&F*F+\"\"$$\"#JF.7&F*F+\"\"%$\"#ZF.7&F*F+\"\"&$\" #_F.7&F+F*$\"#\\F.F.7&F+F*$\"#TF.!\"#7&F+F*$\"#LF.!\"$7&F+F*$\"#FF.!\" %7&F+F*$\"\")F.!\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "r:=e valf(QRdecomp(a,Q='q'));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG-%'m atrixG6#7,7&$\"+xz1OA!\"*\"\"!$\"+KR?3nF,$\"+)))Q,?(F,7&F-F*$\"+4[(f1( F,$!+KR?3nF,7&F-F-$\"+;)>)RWF,$\"+g5y%f%F,7&F-F-F-$\"+TDBV\"*!#57&F-F- F-F-F@F@F@F@F@" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "r1:=matri x(2,2,[r[1,1],r[1,2],0,r[2,2]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% #r1G-%'matrixG6#7$7$$\"+xz1OA!\"*\"\"!7$F-F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "r2:=matrix(2,2,[r[1,3],r[1,4],r[2,3],r[2,4]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#r2G-%'matrixG6#7$7$$\"+KR?3n!\"*$ \"+)))Q,?(F,7$$\"+4[(f1(F,$!+KR?3nF," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "B:=matrix(2,2,[r[3,3],r[3,4],0,r[4,4]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'matrixG6#7$7$$\"+;)>)RW!\"*$\"+g5y%f%F ,7$\"\"!$\"+TDBV\"*!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "e valf(Svd(B,V,'right')):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 " n:=vector(2,[V[1,2],V[2,2]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"n G-%'vectorG6#7$$!+w='>E(!#5$\"+^_([(oF+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "c:=evalf(evalm(-inverse(r1)&*(r2&*n)));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"cG-%'vectorG6#7$$!)p77N!\"*$\"+HDCdVF+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "p1:=plot(e,style=point,symbo l=circle):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "p2:=plot(f,st yle=point,symbol=circle):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "p3:=plot(-(n[1]*z+c[1])/n[2],z=e[1][1]..e[dbe][1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "p4:=plot((n[2]*z-c[2])/n[1],z=f[1][ 1]..f[dbf][1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "display( p1,p2,p3,p4);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6 (-%'CURVESG6&7'7$$\"\"\"\"\"!$\"1+++++++7!#:7$$\"\"#F*$\"1+++++++>F-7$ $\"\"$F*$\"1+++++++JF-7$$\"\"%F*$\"1+++++++ZF-7$$\"\"&F*$\"1+++++++_F- -%'COLOURG6&%$RGBG$\"#5!\"\"F*F*-%&STYLEG6#%&POINTG-%'SYMBOLG6#%'CIRCL EG-F$6&7'7$F($\"1+++++++\\F-7$F/$\"1+++++++TF-7$F4$\"1+++++++LF-7$F9$ \"1+++++++FF-7$F>$\"1+++++++!)!#;FBFIFM-F$6$7S7$F($\"1++:S4R26F-7$$\"1 nmm;')=(3\"F-$\"1Am)4n)[*>\"F-7$$\"1LL$e'40j6F-$\"1xO99Ciz7F-7$$\"1nmm 6hO[7F-$\"1_.D*=T(p8F-7$$\"1nmm\"yYUL\"F-$\"1om4ItXg9F-7$$\"1LL$eF>(>9 F-$\"1*ygHJU2b\"F-7$$\"1nm;>K'*)\\\"F-$\"1'4e$\\![Wj\"F-7$$\"1++]Kd,\" e\"F-$\"1M?(4\\?6s\"F-7$$\"1nm;fX(em\"F-$\"1y`2asv5=F-7$$\"1++]U7Y]F-7$$\"1LLLV!pu$=F-$\"1O_>&G8?*>F-7$$\"1nmmhb59>F-$\"1+3v 'ykH2#F-7$$\"1+++I,Q+?F-$\"1p8>/q4k@F-7$$\"1+++]*3q3#F-$\"1_DF>MgbAF-7 $$\"1+++q=\\q@F-$\"1j'Hf!oyVBF-7$$\"1nm;fBIYAF-$\"1SP8pd'QU#F-7$$\"1LL Lj$[kL#F-$\"1Mly,u3>DF-7$$\"1LLL`Q\"GT#F-$\"1pb)[h_(*f#F-7$$\"1++]s]k, DF-$\"1tb=Mae$p#F-7$$\"1LLL`dF!e#F-$\"1QaiyLkwFF-7$$\"1++]sgamEF-$\"1/ ?l26xnGF-7$$\"1++]q3XIF -7$$\"1LL$eDBJ\"HF-$\"1A#[OqJ#GJF-7$$\"1nmmTc-)*HF-$\"1$o'\\yW\"z@$F-7 $$\"1mm;f`@'3$F-$\"1U&zmnp5J$F-7$$\"1++]nZ)H;$F-$\"1JUa]:;#R$F-7$$\"1m mmJy*eC$F-$\"1vD!f*HuzMF-7$$\"1+++S^bJLF-$\"1R$3))>B-d$F-7$$\"1+++0TN: MF-$\"1\\4BD/ueOF-7$$\"1++]7RV'\\$F-$\"12eE$R&QWPF-7$$\"1+++:#fke$F-$ \"1.7?G&z%RQF-7$$\"1LLL`4NnOF-$\"1qJ#z$e#\\#RF-7$$\"1+++],s`PF-$\"1+5q 6!eh,%F-7$$\"1mm;zM)>$QF-$\"1%*3\"4#z#))4%F-7$$\"1+++qfa*\\jK1C)\\F-7$$\"1mmm1^rZZF-$\"1[\">#)Q>h1&F-7$$\"1++]sI@K[F-$\"1# =*Qs\\Pb^F-7$$\"1++]2%)38\\F-$\"1De>bR!3C&F-7$F>$\"1,+:k!4EL&F-FB-F$6$ 7S7$F($\"1++!eP$R`]F-7$Feo$\"1;,C,A&3(\\F-7$Fjo$\"1A3gmN.**[F-7$F_p$\" 1ACn+gE=[F-7$Fdp$\"10*))[0jpt%F-7$Fip$\"1,Y\"y_Ygl%F-7$F^q$\"1p-=\\l- \"e%F-7$Fcq$\"1o6j1xM.XF-7$Fhq$\"1dhaO@,BWF-7$F]r$\"1aKl.U$HM%F-7$Fbr$ \"1!yVo?k0E%F-7$Fgr$\"1s!>)oE,)=%F-7$F\\s$\"1&H)y?oL1TF-7$Fas$\"1]#yQg DV-%F-7$Ffs$\"1nk2+EHXRF-7$F[t$\"1st7hI_tQF-7$F`t$\"1s%=w8#=)y$F-7$Fet $\"1n!>7=()er$F-7$Fjt$\"1ZSJg4zJOF-7$F_u$\"1]oDb:NdNF-7$Fdu$\"1z!)*)H( zcZ$F-7$Fiu$\"1aAXQ)3zR$F-7$F^v$\"1+3$>2jnJ$F-7$Fcv$\"10tHFfCUKF-7$Fhv $\"17N*)>\"p=;$F-7$F]w$\"1f6\\1-QyIF-7$Fbw$\"1)oV>'Gq0IF-7$Fgw$\"1/:xQ $4s#HF-7$F\\x$\"1oyt[y6YGF-7$Fax$\"1z:=YcymFF-7$Ffx$\"1;D-hw-!p#F-7$F[ y$\"1)e\"Q05![g#F-7$F`y$\"1s&zY1@#GDF-7$Fey$\"18\">BjbkW#F-7$Fjy$\"1(y ny*ROsBF-7$F_z$\"1*GZ7Fi8H#F-7$Fdz$\"1p&4\"ff9:AF-7$Fiz$\"1ON>_zZN@F-7 $F^[l$\"1HsW8zed?F-7$Fc[l$\"1RHNhU/w>F-7$Fh[l$\"1'>$pK!3v*=F-7$F]\\l$ \"1l(\\cR$><=F-7$Fb\\l$\"1S5N/QaPa&*\\aU\"F-7$F[^l$\"1E!* pVb))[8F-7$F>$\"1+++Fmgm7F-FB-%+AXESLABELSG6$%!GF[hl-%%VIEWG6$;F(F>%(D EFAULTG" 1 2 0 1 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "display(p1,p2,p3,p4,scaling= constrained);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6 )-%'CURVESG6&7'7$$\"\"\"\"\"!$\"1+++++++7!#:7$$\"\"#F*$\"1+++++++>F-7$ $\"\"$F*$\"1+++++++JF-7$$\"\"%F*$\"1+++++++ZF-7$$\"\"&F*$\"1+++++++_F- -%'COLOURG6&%$RGBG$\"#5!\"\"F*F*-%&STYLEG6#%&POINTG-%'SYMBOLG6#%'CIRCL EG-F$6&7'7$F($\"1+++++++\\F-7$F/$\"1+++++++TF-7$F4$\"1+++++++LF-7$F9$ \"1+++++++FF-7$F>$\"1+++++++!)!#;FBFIFM-F$6$7S7$F($\"1++:S4R26F-7$$\"1 nmm;')=(3\"F-$\"1Am)4n)[*>\"F-7$$\"1LL$e'40j6F-$\"1xO99Ciz7F-7$$\"1nmm 6hO[7F-$\"1_.D*=T(p8F-7$$\"1nmm\"yYUL\"F-$\"1om4ItXg9F-7$$\"1LL$eF>(>9 F-$\"1*ygHJU2b\"F-7$$\"1nm;>K'*)\\\"F-$\"1'4e$\\![Wj\"F-7$$\"1++]Kd,\" e\"F-$\"1M?(4\\?6s\"F-7$$\"1nm;fX(em\"F-$\"1y`2asv5=F-7$$\"1++]U7Y]F-7$$\"1LLLV!pu$=F-$\"1O_>&G8?*>F-7$$\"1nmmhb59>F-$\"1+3v 'ykH2#F-7$$\"1+++I,Q+?F-$\"1p8>/q4k@F-7$$\"1+++]*3q3#F-$\"1_DF>MgbAF-7 $$\"1+++q=\\q@F-$\"1j'Hf!oyVBF-7$$\"1nm;fBIYAF-$\"1SP8pd'QU#F-7$$\"1LL Lj$[kL#F-$\"1Mly,u3>DF-7$$\"1LLL`Q\"GT#F-$\"1pb)[h_(*f#F-7$$\"1++]s]k, DF-$\"1tb=Mae$p#F-7$$\"1LLL`dF!e#F-$\"1QaiyLkwFF-7$$\"1++]sgamEF-$\"1/ ?l26xnGF-7$$\"1++]q3XIF -7$$\"1LL$eDBJ\"HF-$\"1A#[OqJ#GJF-7$$\"1nmmTc-)*HF-$\"1$o'\\yW\"z@$F-7 $$\"1mm;f`@'3$F-$\"1U&zmnp5J$F-7$$\"1++]nZ)H;$F-$\"1JUa]:;#R$F-7$$\"1m mmJy*eC$F-$\"1vD!f*HuzMF-7$$\"1+++S^bJLF-$\"1R$3))>B-d$F-7$$\"1+++0TN: MF-$\"1\\4BD/ueOF-7$$\"1++]7RV'\\$F-$\"12eE$R&QWPF-7$$\"1+++:#fke$F-$ \"1.7?G&z%RQF-7$$\"1LLL`4NnOF-$\"1qJ#z$e#\\#RF-7$$\"1+++],s`PF-$\"1+5q 6!eh,%F-7$$\"1mm;zM)>$QF-$\"1%*3\"4#z#))4%F-7$$\"1+++qfa*\\jK1C)\\F-7$$\"1mmm1^rZZF-$\"1[\">#)Q>h1&F-7$$\"1++]sI@K[F-$\"1# =*Qs\\Pb^F-7$$\"1++]2%)38\\F-$\"1De>bR!3C&F-7$F>$\"1,+:k!4EL&F-FB-F$6$ 7S7$F($\"1++!eP$R`]F-7$Feo$\"1;,C,A&3(\\F-7$Fjo$\"1A3gmN.**[F-7$F_p$\" 1ACn+gE=[F-7$Fdp$\"10*))[0jpt%F-7$Fip$\"1,Y\"y_Ygl%F-7$F^q$\"1p-=\\l- \"e%F-7$Fcq$\"1o6j1xM.XF-7$Fhq$\"1dhaO@,BWF-7$F]r$\"1aKl.U$HM%F-7$Fbr$ \"1!yVo?k0E%F-7$Fgr$\"1s!>)oE,)=%F-7$F\\s$\"1&H)y?oL1TF-7$Fas$\"1]#yQg DV-%F-7$Ffs$\"1nk2+EHXRF-7$F[t$\"1st7hI_tQF-7$F`t$\"1s%=w8#=)y$F-7$Fet $\"1n!>7=()er$F-7$Fjt$\"1ZSJg4zJOF-7$F_u$\"1]oDb:NdNF-7$Fdu$\"1z!)*)H( zcZ$F-7$Fiu$\"1aAXQ)3zR$F-7$F^v$\"1+3$>2jnJ$F-7$Fcv$\"10tHFfCUKF-7$Fhv $\"17N*)>\"p=;$F-7$F]w$\"1f6\\1-QyIF-7$Fbw$\"1)oV>'Gq0IF-7$Fgw$\"1/:xQ $4s#HF-7$F\\x$\"1oyt[y6YGF-7$Fax$\"1z:=YcymFF-7$Ffx$\"1;D-hw-!p#F-7$F[ y$\"1)e\"Q05![g#F-7$F`y$\"1s&zY1@#GDF-7$Fey$\"18\">BjbkW#F-7$Fjy$\"1(y ny*ROsBF-7$F_z$\"1*GZ7Fi8H#F-7$Fdz$\"1p&4\"ff9:AF-7$Fiz$\"1ON>_zZN@F-7 $F^[l$\"1HsW8zed?F-7$Fc[l$\"1RHNhU/w>F-7$Fh[l$\"1'>$pK!3v*=F-7$F]\\l$ \"1l(\\cR$><=F-7$Fb\\l$\"1S5N/QaPa&*\\aU\"F-7$F[^l$\"1E!* pVb))[8F-7$F>$\"1+++Fmgm7F-FB-%(SCALINGG6#%,CONSTRAINEDG-%+AXESLABELSG 6$%!GF_hl-%%VIEWG6$;F(F>%(DEFAULTG" 1 2 0 1 0 2 9 1 4 1 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}}{MARK "33 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }