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\n \n RETURN([a[1]*b[1]-a[2]*b[2],a[1]*b[2]+a[2]*b[1]]); \n fi;\n " }{XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1219 "RI:=proc(F)\n local a,b,x,y,x2,y2,L,n;\n\n #print (type(F,functi on),evalb(op(0,F)=Sqrt));\n if type(F,list) then RETURN(F); fi;\n if t ype(F,`function`) and evalb(op(0,F)=Sqrt) then\n S:=RI(op(F));\n i f type(S,list) then x:=S[1];y:=S[2];RETURN ([sqrt((sqrt(x^2+y^2)+x)/2) ,signum(y)*sqrt((sqrt(x^2+y^2)-x)/2)])\n else RETUR N ('F'); \n fi; \n fi; \n if type(F,`^`) and type(o p(F)[2],integer) then\n n:= op(F)[2]; \n a:= RI(op(F)[1]);\n if \+ (n<0) then a:=[a[1]/(a[1]^2+a[2]^2),-a[2]/(a[1]^2+a[2]^2)]; n:=-n; fi; \n if (n=0) then a:=[1,0]; fi;\n b := a; \n while n>1 do \+ \n a := [a[1]*b[1]-a[2]*b[2],a[1]*b[2]+a[2]*b[1]];\n n:=n-1;\n od;\n RETURN (a);\n fi;\n if type(F,`*`) then\n L:=[op(F)];\n \+ a:=RI(L[1]);\n if(nops(L)>2) then b:=RI(`*`(op(L[2..nops(L)])));\n \+ else b:=RI(L[2]);\n\n fi;\n \n RETURN([a[1]*b[1] -a[2]*b[2],a[1]*b[2]+a[2]*b[1]]); \n fi;\n if type(F,`+`) then\n L:= map(RI,[op(F)]);\n RETURN(`+`(op(L)));\n fi;\n if type(F,`/`) then\n a:=RI(op(F)[1]); b:=RI(op(F)[2]);\n if type(a,integer) then a:=[a ,0]; fi; \n b:=[b[1],-b[2]];\n n := b[1]^2+b[2]^2;\n RETURN([(a[ 1]*b[1]-a[2]*b[2])/n,(a[1]*b[2]+a[2]*b[1])/n]); \n fi;\n\nRETURN('RI(F )');\n\n\nend;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 7 "" 1 "" {TEXT -1 60 "Warning, `S` is \+ implicitly declared local to procedure `RI`\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#RIGR6#%\"FG6+%\"aG%\"bG%\"xG%\"yG%#x2G%#y2G%\"LG%\"n G%\"SG6\"F2C)@$-%%typeG6$9$%%listG-%'RETURNG6#F8@$3-F66$F8%)functionG- %&evalbG6#/-%#opG6$\"\"!F8%%SqrtGC$>8,-F$6#-FGF<@%-F66$FMF9C%>8&&FM6# \"\"\">8'&FM6#\"\"#-F;6#7$-%%sqrtG6#,&-F]o6#,&*$)FVFhnFYFY*$)FenFhnFYF Y#FYFhn*&FgoFYFVFYFY*&-%'signumG6#FenFY-F]o6#,&F`oFgo*&#FYFhnFYFVFY!\" \"FY-F;6#.F8@$3-F66$F8%\"^G-F66$&FPFgn%(integerGC)>8+F]q>8$-F$6#&FPFX@ $2FaqFIC$>Fcq7$*&&FcqFXFY,&*$)F]rFhnFYFY*$)&FcqFgnFhnFYFYFbp,$*&FcrFYF ^rFbpFbp>Faq,$FaqFbp@$/FaqFI>Fcq7$FYFI>8%Fcq?(F2FYFYF22FYFaqC$>Fcq7$,& *&F]rFY&F]sFXFYFY*&FcrFY&F]sFgnFYFbp,&*&F]rFYFgsFYFY*&FcrFYFesFYFY>Faq ,&FaqFYFYFbp-F;6#Fcq@$-F66$F8%\"*GC&>8*7#FP>Fcq-F$6#&FetFX@%2Fhn-%%nop sG6#Fet>F]s-F$6#-Fbt6#-FG6#&Fet6#;FhnF]u>F]s-F$6#&FetFgn-F;6#Fbs@$-F66 $F8%\"+GC$>Fet-%$mapG6$F$Fft-F;6#-Fcv6#-FGF_u@$-F66$F8%\"/GC(>FcqFdq>F ]s-F$6#F]q@$-F66$FcqF^q>Fcq7$FcqFI>F]s7$Fes,$FgsFbp>Faq,&*$)FesFhnFYFY *$)FgsFhnFYFY-F;6#7$*&FcsFYFaqFbp*&FhsFYFaqFbp-F;6#.-F$F " 0 "" {MPLTEXT 1 0 36 "s1:=RI([-x,-y]+Sqrt([x,y]^2- [1,0]));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#s1G7$,&*$-%%sqrtG6#,**$ -F)6#,.*&)%\"xG\"\"#\"\"\")%\"yGF3F4F3*$)F2\"\"%F4F4*&F3F4F1F4!\"\"*$) F6F9F4F4*&F3F4F5F4F4F4F4F4F3F3F;*&F3F4F1F4F4*&F3F4F5F4F;F4#F4F3F2F;,&* &-%'signumG6#*&F2F4F6F4F4-F)6#,*F,F3F3F4*&F3F4F1F4F;*&F3F4F5F4F4F4FAF6 F;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "simplify(s1[1]^2+s1[2 ]^2):W:=subs(signum(x*y)^2=1,%);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>% \"WG,,*$-%%sqrtG6#,.*&)%\"xG\"\"#\"\"\")%\"yGF.F/F.*$)F-\"\"%F/F/*&F.F /F,F/!\"\"*$)F1F4F/F/*&F.F/F0F/F/F/F/F/F/*$F,F/F/*$F0F/F/*&-F(6#,*F&F. 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