{VERSION 3 0 "IBM INTEL LINUX" "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 "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 "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart:with(Indiff) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7,%$HNIG%)IKolRittG%(IdSpolyG%&Id iffG%+IdiffparseG%-InvariantizeG%/IorthreduceallG%(IreduceG%+Ireduceal lG%%KmatG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "vars:=[x];ukns :=[u];GroupP:=[a,b,theta];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%varsG 7#%\"xG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%uknsG7#%\"uG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'GroupPG7%%\"aG%\"bG%&thetaG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "XiPhis:=matrix([[1,0],[0,1],[-u(x), x]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'XiPhisG-%'matrixG6#7%7$\" \"\"\"\"!7$F+F*7$,$-%\"uG6#%\"xG!\"\"F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "Neqs:=[In[x],In[u,[]],In[u,[1]]];" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%%NeqsG7%&%#InG6#%\"xG&F'6$%\"uG7\"&F'6$F,7#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "HNI([[1],[u]],tdeg);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<$&%#InG6$%\"uG7\"&F%6$F'7#\"\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "Kmat();" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7#7%\"\"\"\"\"!&%#InG6$%\"uG7$F(F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "for j to 5 do Idiff(In[u,[1$ j]],1) od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#&%#InG6$%\"uG7%\"\"\"F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&&%#InG6$%\"uG7&\"\"\"F)F)F)F)*$)&F%6$F'7$F)F)\"\"$\" \"\"!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&&%#InG6$%\"uG7'\"\"\"F)F )F)F)F)*&)&F%6$F'7$F)F)\"\"#\"\"\"&F%6$F'7%F)F)F)F)!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(&%#InG6$%\"uG7(\"\"\"F)F)F)F)F)F)*&&F%6$F'7&F)F) F)F)F))&F%6$F'7$F)F)\"\"#\"\"\"!#:*&F/F))&F%6$F'7%F)F)F)F2F3!#5" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "with(PDEtools,dchange);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7#%(dchangeG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "tr:=\{y=cos(theta)*(x-a)+sin(theta)*(u(x)-b),v(y )=-sin(theta)*(x-a)+cos(theta)*(u(x)-b)\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#trG<$/%\"yG,&*&-%$cosG6#%&thetaG\"\"\",&%\"xGF.%\"aG !\"\"F.F.*&-%$sinGF,F.,&-%\"uG6#F0F.%\"bGF2F.F./-%\"vG6#F',&*&F4\"\"\" F/FAF2*&F*FAF6FAF." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "dchan ge(tr,diff(v(y),y),[x,u(x)]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&- %$sinG6#%&thetaG!\"\"*&-%$cosGF'\"\"\"-%%diffG6$-%\"uG6#%\"xGF4\"\"\"F -F5,&F+F-*&F%F-F.F-F-!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "frame:=sin(theta)=diff(u(x),x)/sqrt(1+diff(u(x),x)^2),cos(theta)=1 /sqrt(1+diff(u(x),x)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&frameG6 $/-%$sinG6#%&thetaG*&-%%diffG6$-%\"uG6#%\"xGF2\"\"\"*$-%%sqrtG6#,&\"\" \"F9*$)F,\"\"#F3F9F3!\"\"/-%$cosGF)*&F3F3*$-F66#F8F3F=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "dchange(tr,diff(v(y),y,y),[x,u(x)]) :II[11]:=factor(subs(frame,%));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> &%#IIG6#\"#6*&-%%diffG6$-%\"uG6#%\"xG-%\"$G6$F/\"\"#\"\"\"*$),&\"\"\"F 8*$)-F*6$F,F/F3F4F8#\"\"$F3F4!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "dchange(tr,diff(v(y),y,y,y),[x,u(x)]):II[111]:=factor (subs(frame,%));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#IIG6#\"$6\"*&, (*&)-%%diffG6$-%\"uG6#%\"xG-%\"$G6$F2\"\"#F6\"\"\"-F-6$F/F2\"\"\"!\"$- F-6$F/-F46$F2\"\"$F:*&F " 0 "" {MPLTEXT 1 0 68 "dchange(tr,diff(v(y),y$4),[ x,u(x)]):II[1111]:=factor(subs(frame,%));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>&%#IIG6#\"%66*&,.*&)-%%diffG6$-%\"uG6#%\"xG-%\"$G6$F2 \"\"#\"\"$\"\"\")-F-6$F/F2F6F8\"#:*(F,\"\"\"-F-6$F/-F46$F2F7F>F:F>!#5* (F,F8F?F8)F:F7F8FC-F-6$F/-F46$F2\"\"%F>*&FFF>F9F8F6*&FFF8)F:FJF8F>F8*$ ),&F>F>*$F9F8F>#\"\"*F6F8!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "DD:=f->diff(f,x)/sqrt(1+diff(u(x),x)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#DDGR6#%\"fG6\"6$%)operatorG%&arrowGF(*&-%%diffG6$9$% \"xG\"\"\"-%%sqrtG6#,&\"\"\"F7*$)-F.6$-%\"uG6#F1F1\"\"#F2F7!\"\"F(F(F( " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "factor(DD(II[11])-II[11 1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "factor(DD(II[111])-II[1111]+3*II[11]^3);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "dchange(tr,diff(v(y),y$5),[x,u(x)]):II[11111]:=factor (subs(frame,%));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>&%#IIG6#\"&66\"*& ,<-%%diffG6$-%\"uG6#%\"xG-%\"$G6$F0\"\"&\"\"\"*&)-F+6$F--F26$F0\"\"$\" \"#\"\"\")-F+6$F-F0F!#?*&F*F5)F@\"\"%F>F<*&F*F>)F@F=F>F<*&F7F>F@F5! #5*&F*F>)F@\"\"'F>F5*(-F+6$F--F26$F0F=F5-F+6$F--F26$F0FEF5)F@F4F>!#:*& )FNFEF>F?F>!$0\"*&F7F>FVF>FI*()FNF=F>F8F5FDF>\"$0\"*(FgnF>F8F>FGF>Fhn* (FNF>FRF>F@F>FW*(FNF>FRF>F?F>!#IF>*$),&F5F5*$FGF>F5\"\"'F>!\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "factor(DD(II[1111])-II[11111 ]+10*II[11]^2*II[111]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "9 0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 }