{VERSION 6 0 "IBM INTEL LINUX" "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 "" 0 1 0 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 "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "W := [rho,rho*u,E]; \nF := [rho*u,rho*u^2+p,u*(E+p)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %\"WG7%%$rhoG*&F&\"\"\"%\"uGF(%\"EG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%\"FG7%*&%$rhoG\"\"\"%\"uGF(,&*&F'F()F)\"\"#F(F(%\"pGF(*&F)F(,&%\"EG F(F.F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "with(LinearAlge bra):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "W := subs(u=m/rho, W); F := subs(u=m/rho,subs(p=(gamma-1)*(E - 1/2*rho*u^2),F));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"WG7%%$rhoG%\"mG%\"EG" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"FG7%%\"mG,&*&%$rhoG!\"\"F&\"\"#\"\"\"*&,&%&g ammaGF,F,F*F,,&%\"EGF,*(F+F*F)F*F&F+F*F,F,*(F&F,F)F*,&F1F,F-F,F," }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 170 "J := Matrix(3):L := Matrix( 3):A:=Matrix(3):\nfor i from 1 to 3 do\n for j from 1 to 3 do\n J [i,j] := simplify(diff(F[i],W[j]));\n end do;\n L[i,i] := 1:\nend do :\nJ := J;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"JG-%'RTABLEG6% \"*K*R4:-%'MATRIXG6#7%7%\"\"!\"\"\"F.7%,$**\"\"#!\"\"%\"mGF3,&\"\"$F4% &gammaGF/F/%$rhoG!\"#F/,$*(F5F/F6F/F9F4F4,&F8F/F/F47%,$*(F5F/,(*(F8F/% \"EGF/F9F/F/*&F8F/)F5F3F/F4*$FEF/F/F/F9!\"$F4,$*(F3F4,(**F3F/F8F/FCF/F 9F/F/*(F7F/F8F/FEF/F4*&F7F/FEF/F/F/F9F:F/*(F5F/F9F4F8F/%'MatrixG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "A := Matrix(evalm(J - lambda *L));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'RTABLEG6%\"*!=]6:-%' MATRIXG6#7%7%,$%'lambdaG!\"\"\"\"\"\"\"!7%,$**\"\"#F0%\"mGF6,&\"\"$F0% &gammaGF1F1%$rhoG!\"#F1,&*(F7F1F8F1F;F0F0F/F0,&F:F1F1F07%,$*(F7F1,(*(F :F1%\"EGF1F;F1F1*&F:F1)F7F6F1F0*$FGF1F1F1F;!\"$F0,$*(F6F0,(**F6F1F:F1F EF1F;F1F1*(F9F1F:F1FGF1F0*&F9F1FGF1F1F1F;F " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "pol := collect(Determinant(A),lambda);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$polG,**$)%'lambdaG\"\"$\"\"\"!\"\" **F)F*%\"mGF*%$rhoGF+F(\"\"#F***F/F+,,**F/F*)F.F/F*%&gammaGF*%\"EGF*F* *()F-F/F*F4F*F.F*F+*(F.F*F7F*)F4F/F*F**(\"\"'F*F.F*F7F*F***F/F*F3F*F9F *F5F*F+F*F.!\"$F(F*F+*(F/F+,,*,F/F*F-F*F9F*F5F*F.F*F**&)F-F)F*F4F*F**& FBF*F9F*F+*,F/F*F-F*F4F*F5F*F.F*F+*&F/F*FBF*F+F*F.F=F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "sol := solve(pol=0,lambda);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$solG6%*&%\"mG\"\"\"%$rhoG!\"\"*&,&F 'F(*&\"\"#F*,**(F.F(%&gammaGF()F'F.F(F(*(F.F(F2F()F1F.F(F***\"\"%F(F1F (%\"EGF(F)F(F***F6F(F4F(F7F(F)F(F(#F(F.F(F(F)F**&,&F'F(*&F.F*F/F9F*F(F )F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "simplify(subs(m=u*rh o,E=p/(gamma-1)+1/2*rho*u^2,[sol]));" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#7%%\"uG*&,&*&F$\"\"\"%$rhoGF(F(*&%&gammaG#F(\"\"#*&%\"pGF(F)F(F,F(F( F)!\"\"*&,&F'F(F*F0F(F)F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "9 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 150939932 151150180 } {RTABLE M7R0 I6RTABLE_SAVE/150939932X,%)anythingG6"6"[gl!"%!!!#*"$"$""!,$*(%"mG""#,&!"$"""%& gammaGF.F.%$rhoG!"##F.F+,$*(F*F.,(*(F/F.%"EGF.F0F.F.*&F/F.F*F+!""*$F*F+F.F.F0F- F9F.,$*(F*F.F,F.F0F9F9,$*&,(F6F+F8F-F:""$F.F0F1F2F',&F/F.F9F.*(F*F.F0F9F/F.F& } {RTABLE M7R0 I6RTABLE_SAVE/151150180X,%)anythingG6"6"[gl!"%!!!#*"$"$,$%'lambdaG!"",$*(%"mG"" #,&!"$"""%&gammaGF0F0%$rhoG!"##F0F-,$*(F,F0,(*(F1F0%"EGF0F2F0F0*&F1F0F,F-F)*$F, F-F0F0F2F/F)F0,&*(F,F0F.F0F2F)F)F(F),$*&,(F8F-F:F/F;""$F0F2F3F4""!,&F1F0F)F0,&* (F,F0F2F)F1F0F0F(F)F& }