{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 } {CSTYLE "" -1 256 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{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 "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Ti mes" 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 Plot " -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 {PARA 0 "" 0 "" {TEXT 256 22 "1.4 Asymptotick\351 sm\354ry" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "with(LinearA lgebra):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "X:=Vector[row]( [x,y,z,1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"XG-%'RTABLEG6%\"*[J Zs\"-%'VECTORG6#7&%\"xG%\"yG%\"zG\"\"\"&%'VectorG6#%$rowG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "K:=Matrix(a,1..4,1..4,shape=symmetr ic);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"KG-%'RTABLEG6%\"*oMZs\"-%' MATRIXG6#7&7&-%\"aG6$\"\"\"F1-F/6$F1\"\"#-F/6$F1\"\"$-F/6$F1\"\"%7&F2- F/6$F4F4-F/6$F4F7-F/6$F4F:7&F5F>-F/6$F7F7-F/6$F7F:7&F8F@FE-F/6$F:F:%'M atrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "Kv:=expand(X.K.Tr anspose(X))=0;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#KvG/,6*&)%\"xG\" \"#\"\"\"-%\"aG6$F+F+F+F+**F*F+F)F+%\"yGF+-F-6$F+F*F+F+**F*F+F)F+%\"zG F+-F-6$F+\"\"$F+F+*(F*F+F)F+-F-6$F+\"\"%F+F+*&)F0F*F+-F-6$F*F*F+F+**F* F+F0F+F4F+-F-6$F*F7F+F+*(F*F+F0F+-F-6$F*F;F+F+*&)F4F*F+-F-6$F7F7F+F+*( F*F+F4F+-F-6$F7F;F+F+-F-6$F;F;F+\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "M:=[m,n,p]; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"M G7%%\"mG%\"nG%\"pG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Primk a:=[x=m+t*u,y=n+t*v,z=p+t*w];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'Pr imkaG7%/%\"xG,&%\"mG\"\"\"*&%\"tGF*%\"uGF*F*/%\"yG,&%\"nGF**&F,F*%\"vG F*F*/%\"zG,&%\"pGF**&F,F*%\"wGF*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "Kv1:=simplify(eval(Kv,Primka));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$Kv1G/,Z**\"\"#\"\"\"-%\"aG6$\"\"$\"\"%F)%\"tGF)%\"wG F)F)*,F(F)-F+6$F)F)F)%\"mGF)F/F)%\"uGF)F)*,F(F)-F+6$F)F(F)F4F)F/F)%\"v GF)F)*,F(F)F7F)F/F)F5F)%\"nGF)F)*,F(F)F7F))F/F(F)F5F)F9F)F)*,F(F)-F+6$ F)F-F)F4F)F/F)F0F)F)*,F(F)F?F)F/F)F5F)%\"pGF)F)*,F(F)F?F)F=F)F5F)F0F)F )*,F(F)-F+6$F(F(F)F;F)F/F)F9F)F)*,F(F)-F+6$F(F-F)F;F)F/F)F0F)F)*,F(F)F HF)F/F)F9F)FBF)F)*,F(F)FHF)F=F)F9F)F0F)F)*,F(F)-F+6$F-F-F)FBF)F/F)F0F) F)*(F2F)F=F))F5F(F)F)**F(F)F7F)F4F)F;F)F)**F(F)F?F)F4F)FBF)F)**F(F)-F+ 6$F)F.F)F/F)F5F)F)*(FEF)F=F))F9F(F)F)**F(F)FHF)F;F)FBF)F)**F(F)-F+6$F( F.F)F/F)F9F)F)*(FMF)F=F))F0F(F)F)-F+6$F.F.F)*&FMF))FBF(F)F)*(F(F)F*F)F BF)F)*&F2F))F4F(F)F)*(F(F)FTF)F4F)F)*&FEF))F;F(F)F)*(F(F)FZF)F;F)F)\" \"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "A:=coeff(lhs(Kv1),t^ 2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG,.**\"\"#\"\"\"-%\"aG6$F( F'F(%\"uGF(%\"vGF(F(**F'F(-F*6$F(\"\"$F(F,F(%\"wGF(F(**F'F(-F*6$F'F1F( F-F(F2F(F(*&-F*6$F(F(F()F,F'F(F(*&-F*6$F'F'F()F-F'F(F(*&-F*6$F1F1F()F2 F'F(F(" }}}{PARA 11 "" 1 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 8 "P\370\355klad:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "a(1,1) :=1: a(2,2):=1: a(3,3):=0: a(4,4):=-1: a(1,2):=0: a(1,3):=0: a(1,4):=0 : a(2,3):=0: a(2,4):=0: a(3,4):=0: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "Kv;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,(*$)%\"xG\"\" #\"\"\"F)F)!\"\"*$)%\"yGF(F)F)\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "RovAsSm:=A=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(R ovAsSmG/,&*$)%\"uG\"\"#\"\"\"F+*$)%\"vGF*F+F+\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 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