{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 0 0 0 1 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 "moi" -1 256 "Times" 1 12 0 0 1 1 0 0 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 "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 1 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 3 0 3 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 1 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 3 0 3 0 2 2 0 1 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Monaco" 1 9 0 0 255 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 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 10 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 "Normal" -1 258 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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart:with(linalg) :" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has b een redefined\n" }}{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 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 62 "N:=vector([f,g,h]):N1:=vector([p,q,r]):N2:=vector([ pp,qq,rr]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#N2GK%'vectorG6#7%%#p pG%#qqG%#rrGQ)pprint276\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "M:=evalm(N+aa*N1+bb*N2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG K%'vectorG6#7%,(%\"fG\"\"\"*&%#aaGF+%\"pGF+F+*&%#bbGF+%#ppGF+F+,(%\"gG F+*&F-F+%\"qGF+F+*&F0F+%#qqGF+F+,(%\"hGF+*&F-F+%\"rGF+F+*&F0F+%#rrGF+F +Q)pprint286\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "sol:=solv e([dotprod(M,N1,orthogonal),dotprod(M,N2,orthogonal)],\{aa,bb\});" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%$solG<$/%#bbG,$*&,4*&)%\"qG\"\"#\"\" \")%#rrGF.F/F/*&)%\"rGF.F/)%#qqGF.F/F/*&F3F/)%#ppGF.F/F/*&)%\"pGF.F/F5 F/F/*&F;F/F0F/F/*&F,F/F8F/F/*,F.F/F9F/F " 0 "" {MPLTEXT 1 0 21 "assign(sol);eva lm(M);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'vectorG6#7%,(%\"fG\"\"\"* &%#aaGF)%\"pGF)F)*&%#bbGF)%#ppGF)F),(%\"gGF)*&F+F)%\"qGF)F)*&F.F)%#qqG F)F),(%\"hGF)*&F+F)%\"rGF)F)*&F.F)%#rrGF)F)Q)pprint296\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "f:=a*cos(u)*cos(v):g:=b*sin(u)*cos( v):h:=c*sin(v):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "p:=diff( f,u):q:=diff(g,u):r:=diff(h,u):pp:=diff(f,v):qq:=diff(g,v):rr:=diff(h, v):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "x:=simplify(M[1]);y: =simplify(M[2]);z:=simplify(M[3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%\"xG,$*.%\"cG\"\"#%\"bGF(%\"aG\"\"\"-%$cosG6#%\"uGF+-F-6#%\"vGF+,,** )F)F(F+)F,F(F+)F0F(F+)F'F(F+!\"\"*&F5F+)F*F(F+F9*(F5F+F;F+F7F+F+*(F;F+ F7F+F8F+F9**F;F+F7F+F8F+F6F+F+F9F9" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%\"yG,$*.%\"cG\"\"#%\"aGF(%\"bG\"\"\"-%$sinG6#%\"uGF+-%$cosG6#%\"vGF+ ,,**)F*F(F+)-F1F.F(F+)F0F(F+)F'F(F+!\"\"*&F6F+)F)F(F+F;*(F6F+F=F+F9F+F +*(F=F+F9F+F:F+F;**F=F+F9F+F:F+F7F+F+F;F;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG,$*,%\"aG\"\"#%\"bGF(%\"cG\"\"\"-%$sinG6#%\"vGF+, ,**)F)F(F+)-%$cosG6#%\"uGF(F+)-F5F.F(F+)F*F(F+!\"\"*&F2F+)F'F(F+F;*(F2 F+F=F+F8F+F+*(F=F+F8F+F:F+F;**F=F+F8F+F:F+F3F+F+F;F;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "simplify(a^2*x^2+b^2*y^2+c^2*z^2-(x^2+y^2 +z^2)^2);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }}{MARK "8 3 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }