{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 } {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 "Text Output" -1 6 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 2 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 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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 27 "currentdir(\"d:/prog/work\");" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#Q(d:\\prog6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "with(gfun);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7J%(La placeG%+ParametersG%.algebraicsubsG%.algeqtodiffeqG%.algeqtoseriesG%.a lgfuntoalgeqG%&borelG%.cauchyproductG%.diffeq*diffeqG%.diffeq+diffeqG% 2diffeqtohomdiffeqG%,diffeqtorecG%/gfunParametersG%)guesseqnG%(guessgf G%0hadamardproductG%0holexprtodiffeqG%)invborelG%,listtoalgeqG%-listto diffeqG%0listtohypergeomG%+listtolistG%.listtoratpolyG%*listtorecG%-li sttoseriesG%,poltodiffeqG%)poltorecG%/ratpolytocoeffG%(rec*recG%(rec+r ecG%,rectodiffeqG%,rectohomrecG%*rectoprocG%.seriestoalgeqG%/seriestod iffeqG%2seriestohypergeomG%-seriestolistG%0seriestoratpolyG%,seriestor ecG%/seriestoseriesG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "rea d \"wsolve.mpl\";" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%7_field_charact eristic_G\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "read \"km-sys-wu.mpl\";" }}{PARA 6 "" 1 "" {TEXT -1 75 "KernelMethod(K,A,B,x,y,[Extra Eqns])Please avoid \+ using the variables SubRes" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "Example 3.1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 131 "K0:=matrix([[1-x^2/(1-v^2)^2]]);\n A0:=map(simplify,matrix([[-x^2/(1+v)+x/(1-v^2)*(x-x*v/(1-v^2)),x-x/(1- v^2)]]));\nB0:=matrix([[x]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#K0 GK%'matrixG6#7#7#,&\"\"\"F+*&%\"xG\"\"#,&F+F+*$)%\"vGF.F+!\"\"!\"#F3Q( pprint06\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A0GK%'matrixG6#7#7$,$ *(%\"vG\"\"$%\"xG\"\"#,&\"\"\"!\"\"*$)F,F/F1F1!\"#F2*(F.F1F,F/F0F2Q(pp rint16\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#B0GK%'matrixG6#7#7#%\"x GQ(pprint26\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "K:=subs(v=v/x,evalm(K0)): A: =subs(v=v/x,evalm(A0)): B:=subs(v=v/x,evalm(B0)):" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 29 "res:=KernelMethod(K,A,B,v,x);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#%0A~New~ComponentG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%0A~New~ComponentG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%0A~New~Co mponentG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%0A~New~ComponentG" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%0A~New~ComponentG" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#%0A~New~ComponentG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #%0A~New~ComponentG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%0A~New~Compone ntG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%0A~New~ComponentG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%0A~New~ComponentG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$resG7$,,*(\"\"$\"\"\")%\"vG\"\"#F)%#g1GF)F)F-!\"\"*( F(F))F+F(F))F-F,F)F)*&)F+\"\"%F))F-F(F)F)F+F),2%#g2GF)*&F3F))F7F(F)F)* (F(F)F3F))F7F,F)F)*(F(F)F3F)F7F)F)*&F,F)F*F)F.*(F,F)F*F)F;F)F.*(F4F)F* F)F7F)F.*$F3F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "map(sor t,collect(res,g1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$,**&)%\"vG\" \"%\"\"\")%#g1G\"\"$F)F)*(F,F))F'F,F))F+\"\"#F)F)F'F)*&,&*&F,F))F'F0F) F)F)!\"\"F)F+F)F),2*&F&F))%#g2GF,F)F)*(F,F)F&F))F9F0F)F)*(F,F)F&F)F9F) F)*$F&F)F)*(F0F)F4F)F;F)F5*(F(F)F4F)F9F)F5*&F0F)F4F)F5F9F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "map(sort,collect(res,g2));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7$,,*&)%\"vG\"\"%\"\"\")%#g1G\"\"$F)F) *(F,F))F'F,F))F+\"\"#F)F)*(F,F))F'F0F)F+F)F)F'F)F+!\"\",,*&F&F))%#g2GF ,F)F)*$F&F)F)*&F0F)F2F)F3*&,&*&F,F)F&F)F)*&F0F)F2F)F3F))F7F0F)F)*&,(*& F,F)F&F)F)*&F(F)F2F)F3F)F)F)F7F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 123 "K0:=matrix([[1-x^3/(1-v^3)^3]]):\nA0:=matrix([[-x^ 3*v^5/(1-v^3)^3, -x^2*v^4/(1-v^3)^2, -x*v^3/(1-v^3)]]):\nB0:=matrix([[ x]]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "K:=map(factor,subs(v=v/x,evalm(K0))): A: =map(factor,subs(v=v/x,evalm(A0))): B:=map(factor,subs(v=v/x,evalm(B0) )):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 56 "#res:=KernelMethod(K,A,B,v,x,[[x=v,matrix([[ 1,0,0]])]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "Example 3.2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 172 "K 1:=matrix([[1-(x-x/(1-v^2))^2]]); A1:=matrix([[x*v^2/(1-v^2)*(x-x/(1-v ^2)),x-x*v/(1-v^2)+(x^2/(1+v)-x^2)*(x-x/(1-v^2))]]);\nB1:=matrix([[x-( x-x/(1-v^2))*(x^2-x^2/(1+v))]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% #K1GK%'matrixG6#7#7#,&\"\"\"F+*$),&%\"xGF+*&F/F+,&F+F+*$)%\"vG\"\"#F+! \"\"F6F6F5F+F6Q(pprint36\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A1GK% 'matrixG6#7#7$**%\"xG\"\"\"%\"vG\"\"#,&F,F,*$)F-F.F,!\"\"F2,&F+F,*&F+F ,F/F2F2F,,(F+F,*(F+F,F-F,F/F2F2*&,&*&F+F.,&F,F,F-F,F2F,*$)F+F.F,F2F,F3 F,F,Q(pprint46\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#B1GK%'matrixG6# 7#7#,&%\"xG\"\"\"*&,&F+F,*&F+F,,&F,F,*$)%\"vG\"\"#F,!\"\"F5F5F,,&*$)F+ F4F,F,*&F+F4,&F,F,F3F,F5F5F,F5Q(pprint56\"" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "K:=su bs(v=v/x,evalm(K1)): A:=subs(v=v/x,evalm(A1)): B:=subs(v=v/x,evalm(B1) ): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "read \"km-sys.mpl\"; " }}{PARA 6 "" 1 "" {TEXT -1 65 "Please avoid using the variables SubR es, Strict_Con, uu, bb and f" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "KernelMethod(K,A,B ,v,x,[[x=v,matrix([[1,0]])]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<#7$ ,$*&%\"vG\"\"\",&*$)F'\"\"#F(F(F(!\"\"F-F-,$*&F'F,F)F-F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 149 "K1:=matrix([[1,-x-x/(1-v^2) ],[-x-x/(1-v^2),1]]): A1:=matrix([[0,x-x*v/(1-v^2)],[-x*v^2/(1-v^2),-x ^2/(1+v)-x^2]]):\nB1:=matrix([[x],[-x^2-x^2/(1+v)]]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "K1:=matrix([[1-(x+x/(1-v^2))^2]]); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#K1GK%'matrixG6#7#7#,&\"\"\"F+*$ ),&%\"xGF+*&F/F+,&F+F+*$)%\"vG\"\"#F+!\"\"F6F+F5F+F6Q(pprint66\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "A1:=matrix([[(x+x/(1-v^2))*( -x*v^2/(1-v^2)),(x-x*v/(1-v^2))-(x+x/(1-v^2))*(x^2+x^2/(1+v))]]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A1GK%'matrixG6#7#7$,$**,&%\"xG\"\" \"*&F-F.,&F.F.*$)%\"vG\"\"#F.!\"\"F5F.F.F-F.F3F4F0F5F5,(F-F.*(F-F.F3F. F0F5F5*&F,F.,&*$)F-F4F.F.*&F-F4,&F.F.F3F.F5F.F.F5Q(pprint76\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "B1:=matrix([[x-(x+x/(1-v^2)) *(x^2+x^2/(1+v))]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#B1GK%'matri xG6#7#7#,&%\"xG\"\"\"*&,&F+F,*&F+F,,&F,F,*$)%\"vG\"\"#F,!\"\"F5F,F,,&* $)F+F4F,F,*&F+F4,&F,F,F3F,F5F,F,F5Q(pprint86\"" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 78 "K:=subs(v=v/x,evalm(K1)): A:=subs(v=v/x,evalm( A1)): B:=subs(v=v/x,evalm(B1)): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "read \"km-sys-wu.mpl\";" }}{PARA 6 "" 1 "" {TEXT -1 75 "KernelMethod(K,A,B,x,y,[Extra Eqns])Please avoid using the variabl es SubRes" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "res:=KernelMet hod(K,A,B,v,x,[[x=v,matrix([[1,0]])]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%0A~New~ComponentG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%0A~New~Co mponentG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%0A~New~ComponentG" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%0A~New~ComponentG" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#%0A~New~ComponentG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #%0A~New~ComponentG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%0A~New~Compone ntG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%0A~New~ComponentG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%0A~New~ComponentG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%0A~New~ComponentG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#% 0A~New~ComponentG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$resG7$,0*&)%\" vG\"\"$\"\"\")%#g1G\"\"#F+F+*(F*F+)F)F.F+)F-F*F+!\"\"*(F.F+F0F+F-F+F2F )F+*(\"\"%F+F)F+F,F+F+*$F1F+F+F-F2,0*$)%#g2GF*F+F2*(F*F+F0F+F9F+F+*&F. F+)F:F.F+F+*(\"\"(F+F0F+F=F+F+*(\"\"&F+F0F+F:F+F+F:F2*$F0F+F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "map(sort,collect(res,g1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$,**&,&*&\"\"$\"\"\")%\"vG\"\"#F)! \"\"F)F)F))%#g1GF(F)F)*&,&*$)F+F(F)F)*&\"\"%F)F+F)F)F))F/F,F)F)F+F)*&, &*&F,F)F*F)F-F)F-F)F/F)F),0*(F(F)F*F))%#g2GF(F)F)*(\"\"(F)F*F))F=F,F)F )*(\"\"&F)F*F)F=F)F)*$F " 0 "" {MPLTEXT 1 0 26 "map(sort,collect(res,g2));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#7$,0*&)%\"vG\"\"$\"\"\")%#g1G\"\"#F)F)*(F(F))F'F ,F))F+F(F)!\"\"*(F,F)F.F)F+F)F0*(\"\"%F)F'F)F*F)F)*$F/F)F)F'F)F+F0,**& ,&*&F(F)F.F)F)F)F0F))%#g2GF(F)F)*$F.F)F)*&,&*&\"\"(F)F.F)F)F,F)F))F:F, F)F)*&,&*&\"\"&F)F.F)F)F)F0F)F:F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "subs(g1 =2*sA-v/(1-v^2),v^3*g1^2-3*v^2*g1^3-2*v^2*g1+4*v*g1^2+v+g1^3-g1):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "numer(%);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#,>*&\"\"#\"\"\"%\"vGF&!\"\"*(\"#KF&)F'\"\"(F&)%#sAGF% F&F(*(\"#[F&)F'\"\"&F&F-F&F&*(\"#;F&)F'\"\"$F&F-F&F(*(\"#5F&)F'\"\"%F& F.F&F(*&\"\")F&)F.F6F&F(*&F%F&F.F&F&*(F:F&)F'\"\"*F&F-F&F&*(\"#!)F&F=F &)F'\"\"'F&F&*(\"#'*F&F=F&F9F&F(*(F0F&F=F&)F'F%F&F&*(F:F&F-F&F'F&F(*( \"#CF&)F'F " 0 "" {MPLTEXT 1 0 30 "res1:=map(sort,collect(%,sA));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%res1G,**&,,*&\"#C\"\"\")%\"vG\"\")F*!\"\"*&\"#!)F*)F ,\"\"'F*F**&\"#'*F*)F,\"\"%F*F.*&\"#[F*)F,\"\"#F*F*F-F.F*)%#sAG\"\"$F* F**&,,*&F6F*)F,\"\"*F*F**&\"#KF*)F,\"\"(F*F.*&F8F*)F,\"\"&F*F**&\"#;F* )F,F=F*F.*&F6F*F,F*F.F*)F " 0 "" {MPLTEXT 1 0 28 "algeqto series(res1,v,sA,15);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7$+C%\"vG-%'R ootOfG6#,&\"\"\"!\"\"*&\"\"%F*)%#_ZG\"\"#F*F*\"\"!#!\"$F-F*,$*&#\"#D\" \")F*F&F*F*F0#!\"(F0\"\"$,$*&#\"$6*\"$G\"F*F&F*F*F-#!#JF0\"\"&,$*&#\"% \"R'\"%C5F*F&F*F+\"\"'#!$\">F0\"\"(,$*&#\")d^s6\"&oF$F*F&F*F+F8#!%\"z \"F0\"\"*,$*&#\"+Pr0S9\"'W@EF*F&F*F+\"#5#!&J;#F0\"#6,$*&#\"-*)zJmCK\"( /V>%F*F&F*F+\"#7#!'F8HF0\"#8,$*&#\"/b#zryUk$\")KWbLF*F&F*F+\"#9-%\"OG6 #F*\"#:+5F%F*F*F0F;F`oFC\"$M\"FL\"%<;FT\"&16#Fgn\"'\\(*GF`o\"(1I7%FjoF go\"#;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "subs(g2=2*sA-v^2/(1-v^2),3*v^2*g2^3-g2^3+2*g2^2+7*v^2*g2^2-g2+5* v^2*g2+v^2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "res2:=map(s ort,collect(numer(%),sA));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%res2G ,0*&,,*&\"#C\"\"\")%\"vG\"\")F*F**&\"#!)F*)F,\"\"'F*!\"\"*&\"#'*F*)F, \"\"%F*F**&\"#[F*)F,\"\"#F*F2F-F*F*)%#sAG\"\"$F*F**&,,*&\"#kF*F+F*F**& \"$g\"F*F0F*F2*&\"$?\"F*F5F*F**&\"#;F*F9F*F2F-F2F*)F " 0 " " {MPLTEXT 1 0 28 "algeqtoseries(res2,v,sA,15);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7$+5%\"vG#\"\"\"\"\"#\"\"!-%'RootOfG6#,&\"\"%!\"\"*$)%# _ZGF(F'F'F'#\"\"(F(F(,$*&#\"#D\"\")F'F*F'F'\"\"$#\"# " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "Generating \+ Trees k=1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "K0:=matrix([[1 +x*v^2/(1-v)]]): A0:=matrix([[x*v^2/(1-v)]]): B0:=matrix([[v]]):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "K:=subs(v=v/x,evalm(K0)): A: =subs(v=v/x,evalm(A0)): B:=subs(v=v/x,evalm(B0)): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "read \"km-sys.mpl\";" }}{PARA 6 "" 1 "" {TEXT -1 65 "Please avoid using the variables SubRes, Strict_Con, uu, \+ bb and f" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "KernelMethod(K, A,B,x,v);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<#7#,$*(\"\"#!\"\",&\"\" \"F(*$,&F*F**&\"\"%F*%\"xGF*F(#F*F'F*F*F/F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "k=2" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "K0:=matrix([[(1+x*u^3/(1-u^2 ))*(1+x*u^2/(1+u))+(1-x*u^3/(1-u^2))*(1+x*u^2/(1-u))]]);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%#K0GK%'matrixG6#7#7#,&*&,&\"\"\"F-*(%\"xGF-%\" uG\"\"$,&F-F-*$)F0\"\"#F-!\"\"F6F-F-,&F-F-*(F/F-F0F5,&F-F-F0F-F6F-F-F- *&,&F-F-F.F6F-,&F-F-*(F/F-F0F5,&F-F-F0F6F6F-F-F-Q(pprint96\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 124 "A0:=matrix([[(1+x*u^2/(1+u) )*x*u/(1-u^2)-(1+x*u^2/(1-u))*x*u/(1-u^2),(1+x*u^2/(1+u))*x*u/(1-u)-(1 +x*u^2/(1-u))*x*u/(1+u)]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A0GK %'matrixG6#7#7$,&**,&\"\"\"F-*(%\"xGF-%\"uG\"\"#,&F-F-F0F-!\"\"F-F-F/F -F0F-,&F-F-*$)F0F1F-F3F3F-**,&F-F-*(F/F-F0F1,&F-F-F0F3F3F-F-F/F-F0F-F4 F3F3,&**F,F-F/F-F0F-F:F3F-**F8F-F/F-F0F-F2F3F3Q)pprint106\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "B0:=matrix([[1+x*u^2/(1+u)+1 +x*u^2/(1-u)]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#B0GK%'matrixG6# 7#7#,(\"\"#\"\"\"*(%\"xGF,%\"uGF+,&F,F,F/F,!\"\"F,*(F.F,F/F+,&F,F,F/F1 F1F,Q)pprint116\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "K:=sub s(u=u/x,evalm(K0)): A:=subs(u=u/x,evalm(A0)): B:=subs(u=u/x,evalm(B0)) : " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "read \"km-sys-wu.mpl \";" }}{PARA 6 "" 1 "" {TEXT -1 75 "KernelMethod(K,A,B,x,y,[Extra Eqns ])Please avoid using the variables SubRes" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 29 "res:=KernelMethod(K,A,B,x,u);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%0A~New~ComponentG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#% 0A~New~ComponentG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%0A~New~Component G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%0A~New~ComponentG" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#%0A~New~ComponentG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%0A~New~ComponentG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%0A~New~Co mponentG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$resG7$,,\"\"\"F'*&%\"xG F'%#g1GF'!\"\"F*F+*&F)F')F*\"\"#F'F'*&)F)F.F')F*\"\"$F'F',.*&F0F')%#g2 GF2F'F'*&)F6F.F'F0F'F'*(F.F'F8F'F)F'F+*&F)F'F6F'F+F)F+F6F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "map(sort,collect(res,g1));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7$,**&)%\"xG\"\"#\"\"\")%#g1G\"\"$F)F) *&F'F))F+F(F)F)*&,&F'!\"\"F)F1F)F+F)F)F)F),.*&F&F))%#g2GF,F)F)*&F&F))F 5F(F)F)*(F(F)F'F)F7F)F1*&F'F)F5F)F1F'F1F5F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "map(sort,collect(res,g2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$,,*&)%\"xG\"\"#\"\"\")%#g1G\"\"$F)F)*&F'F))F+F(F)F)*& F'F)F+F)!\"\"F+F0F)F),**&F&F))%#g2GF,F)F)*&,&*$F&F)F)*&F(F)F'F)F0F))F4 F(F)F)F'F0*&,&F'F0F)F)F)F4F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "algeqtoseries(x^ 2*g1^3+x*g1^2+(-x-1)*g1+1,x,g1,10);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6 #7$+9%\"xG-%'RootOfG6#,(\"\"\"!\"\"*$)%#_ZG\"\"#F*F*F.F*F+,&*&#F*\"\"& F*F&F*F*#F/F3F+\"\"!,&*&#\"\")\"#DF*F&F*F+#\"\"%F:F+F*,&*&#\"#<\"$D\"F *F&F*F+#\"#rFAF+F/,&*&#\"$.\"FAF*F&F*F+#\"$9\"FAF+\"\"$,&*&#\"%'*R\"%D JF*F&F*F+#\"%[#)FOF+F<,&*&#\"&cu'\"&Dc\"F*F&F*F+#\"&Gi*FVF+F3,&*&#\"'n dy\"&D\"yF*F&F*F+#\"(Y%p8FgnF+\"\"',&#\")WUV=\"'D1RF+*&#\"))[o=\"F^oF* F&F*F+\"\"(,&#\")4TV`F^oF+*&#\")V)eA$F^oF*F&F*F+F9-%\"OG6#F*\"\"*+7F%F *F5F*F/F*FJFF9\"$S&F\\pFio\"#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "algeqtoseries(x^2*g2^3+(-2*x+x^2)*g2^2+(-x+1)*g2-x,x, g2,10);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7$,0*&\"\"\"F&%\"xG!\"\"F&- %'RootOfG6#,(F&F(*$)%#_ZG\"\"#F&F&F/F&F&*&,&*&#F&\"\"&F&F)F&F&#F0F5F(F &F'F&F&*&,&*&#\"#<\"#DF&F)F&F&#\"\"%FF&F&-%\"OG6#*$)F'#\"\"*F0F&F&+9F'F&F&F&F0FIFI\"\"'F>F;F5\"#VFZ\"$B\" \"\"(\"$V$\"\")\"%/5FX\"%QH\"#5-FS6#F&\"#6" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "w:=(-1+sqrt(-3))/2:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 68 "u:='u': x:='x': v1:=[1+x*u^4/(1-u^3),1+x*u^4/(1-u^3 ),1+u^2*x/(1-u)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#v1G7%,&\"\"\"F '*(%\"xGF'%\"uG\"\"%,&F'F'*$)F*\"\"$F'!\"\"F0F'F&,&F'F'*(F)F'F*\"\"#,& F'F'F*F0F0F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "t:=map(expa nd,subs(u=u*w,[v1[1],v1[2]*w,v1[3]*w^2])):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 31 "assume(u,real): assume(x,real):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "v2:=simplify(map(Re,t)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "v3:=simplify(map(Im/sqrt(3),t)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "t:=map(expand,subs(u=u*w^2,[v1[1],v1[2]*w^2,v1[3]*w^4 ])):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "K0:=matrix([v1,v2,v 3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#K0GK%'matrixG6#7%7%,&\"\"\" F+*(%#x|irGF+%#u|irG\"\"%,&F+F+*$)F.\"\"$F+!\"\"F4F+F*,&F+F+*(F-F+F.\" \"#,&F+F+F.F4F4F+7%,$*(F7F4,(F7F4*&F7F+F2F+F+*&F-F+)F.F/F+F+F+,&F+F4F1 F+F4F+,$*(F7F4,(F+F+F1F4F>F+F+F@F4F+,$*(F7F4,,F+F+F.F+*$)F.F7F+F+*&F-F +FHF+F+*(F7F+F-F+F2F+F+F+,(F+F+F.F+FGF+F4F47%,$**F7F4F-F+F.F/F@F4F4,$* (F7F4,(F+F4F1F+F>F+F+F@F4F+,$*(F7F4,*F+F4F.F4FGF4FIF+F+FKF4F+Q)pprint1 56\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "u:='u': x:='x': v1:= [x*u/(1-u^3),x*u^2/(1-u^3),x*u/(1-u)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#v1G7%*(%\"xG\"\"\"%\"uGF(,&F(F(*$)F)\"\"$F(!\"\"F.*(F'F(F)\" \"#F*F.*(F'F(F)F(,&F(F(F)F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "t:=map(expand,subs(u=u*w,[v1[1],v1[2],v1[3]])):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "assume(u,real): assume(x,real):" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "v2:=simplify(map(Re,t)):" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "v3:=simplify(map(Im/sqrt(3 ),t)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "A0:=matrix([v1,v2 ,v3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A0GK%'matrixG6#7%7%*(%#x| irG\"\"\"%#u|irGF,,&F,F,*$)F-\"\"$F,!\"\"F2*(F+F,F-\"\"#F.F2*(F+F,F-F, ,&F,F,F-F2F27%,$**F4F2F+F,F-F,,&F,F2F/F,F2F,,$**F4F2F+F,F-F4F:F2F,,$*, F4F2F+F,F-F,,&F,F,*&F4F,F-F,F,F,,(F,F,F-F,*$)F-F4F,F,F2F27%,$**F4F2F+F ,F-F,F:F2F2F;,$**F4F2F+F,F-F,FAF2F,Q)pprint166\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "x:='x': u:='u':" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 465 "K0 := matrix([[1+x*u^4/(1-u ^3), 1+x*u^4/(1-u^3), 1+u^2*x/(1-u)], [1/2*(-2+2*u^3+x*u^4)/(-1+u^3), \+ 1/2*(1-u^3+x*u^4)/(-1+u^3), -1/2*(1+u+u^2+u^2*x+2*u^3*x)/(1+u+u^2)], [ -1/2*x*u^4/(-1+u^3), 1/2*(-1+u^3+x*u^4)/(-1+u^3), 1/2*(-1-u-u^2+u^2*x) /(1+u+u^2)]]):\n\nA0 := matrix([[x*u/(1-u^3), x*u^2/(1-u^3), x*u/(1-u) ], [1/2*x*u/(-1+u^3), 1/2*x*u^2/(-1+u^3), -1/2*x*u*(1+2*u)/(1+u+u^2)], [-1/2*x*u/(-1+u^3), 1/2*x*u^2/(-1+u^3), 1/2*x*u/(1+u+u^2)]]):\n\nB0:= matrix([[1],[1],[0]]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "K: =subs(u=u/x,evalm(K0)): A:=subs(u=u/x,evalm(A0)): B:=subs(u=u/x,evalm( B0)): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "read \"km-sys-wu. mpl\";" }}{PARA 6 "" 1 "" {TEXT -1 75 "KernelMethod(K,A,B,x,y,[Extra E qns])Please avoid using the variables SubRes" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "#KernelMethod(K,A,B,x,u);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "111" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }