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"DQ6n:=,<0,s6*p6_[1],s6*p6_[2],s 6*p6_[3]>:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "HG:=<1,0,0,0>,<0,x4,y4,z4>;" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I#HGG6\"6$-I'RTABLEGF$6%\"5u4H1:3ZnW=-I 'MATRIXGF$6#7&7#-I#mnG6$%*protectedG/I+modulenameGF$I,TypesettingG6$F2 I(_syslibGF$6#Q\"1F$7#-F06#Q\"0F$F:F:&I'VectorGF66#I'columnGF$-F'6%\"5 %4\"H1:3ZnW=-F+6#7&F:7#-F06#Q\"7F$7#-F06#Q+&uminus0;2F$7#-F06#Q#11F$F> " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 212 "" 0 "" {TEXT 212 0 "" }{TEXT 206 6 "Teil 1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "linksHG:=DQmult(DQkon(DQ1n),Given):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "rechtsHG:=DQmult(DQkdk(Given),DQdko n(DQ1n)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "finaleHG:=DQmu lt(DQmult(linksHG,HG),rechtsHG);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)f inaleHGG6\"6$X*I)anythingG%*protectedGF$F$[gl!#%!!!\"%\"%-I%mrowG6$F(/ 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F?6#Q#91F$FKFTFKF:FKFYFKFaqFKFHFa]lFho-F*6'-F?6#Q\"6F$FKFWFKFFFB-F*6'F ^qFKFRFKFFFB-F*6%FWFKF7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "lang:=factor(Norm(finale [2],2,conjugate=false)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%langG6 \",$*(,4**I#c2GF$\"\"\"I#c3GF$\"\"#I#s2GF$F*\"#5#F*F,\"$D$*,F)F*F+F*F- F*F.F/I#s3GF$F*\"$?&**F-F*F.F/F2F,F)F*!$f&*&F)F,F+F,!&v3\"*(F)F,F+F*F2 F*\"&+>\"*&F)F,F2F,!%vQ*&F-F,F+F,!%v$)*(F-F,F2F*F+F*\"%+&)*&F-F,F2F,!% vLF*,&*$F)F,F**$F-F,F*F*,&*$F+F,F**$F2F,F*F*#!\"#\"$D\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "langHG:=factor(Norm(finaleHG[2],2,c onjugate=false)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I'langHGG6\",$*& ,&*&\"\"##\"\"\"F)\"#:F*\"$x$\"&+,&F+F+,&*$I#c1GF$F)F+*$I#s1GF$F)F+F)# F+\"$]#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "eq1:=simplify(numer(finaleHG [2][2]-finale[2][2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$eq1G6\",0*& ,&*&,&*$I#c1GF$\"\"#\"$?$*$I#s1GF$F,F-\"\"\"\"\"$#F0F,F0*(I#s2GF$F0,(* $I#c3GF$F,F0*&F7F0I#s3GF$F0#!#M\"#D*$F9F,#F0\"\"&F0I#c2GF$F0!%+5F0\"#5 F2F0*&,(F6!%+NF8!%+KF=\"%S>F0F@F,F0*&F4F,F7F,!%+A*(F4F,F9F0F7F0!%?6*&F 4F,F9F,!$'HF*!$V%F.FN" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "eq2:=simplify(numer(finale HG[2][3]-finale[2][3]));" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$eq2G6\",2 *&,&*&,(*$I#c1GF$\"\"#!$x$*&F+\"\"\"I#s1GF$F/!%?>*$F0F,\"$x$F/\"\"$#F/ F,F/*(I#s2GF$F/,(*$I#c3GF$F,F/*&F:F/I#s3GF$F/#!#M\"#D*$F " 0 "" {MPLTEXT 1 0 50 "eq3:=simplify(numer(finaleHG[2][4]- finale[2][4]));" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$eq3G6\",2*&,&*&,(* $I#c1GF$\"\"#!$g**&F+\"\"\"I#s1GF$F/\"$a(*$F0F,\"$g*F/\"\"$#F/F,F/*(I# s2GF$F/I#c2GF$F/,(*$I#c3GF$F,F/*&F;F/I#s3GF$F/#\"\")\"\"&*$F=F,#!#V\"# DF/\"%+8F/\"#5F5F/*&,(F:!%+bF<\"%+oFA!%+:F/F8F,F/*&F7F,F;F,\"%+X*(F7F, F=F/F;F/!%+o*&F7F,F=F,\"$+&F*\"%46F.\"%+uF2!%46" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "eq4:=simplify(numer(langHG-lang));" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$eq4G6\",4*&,&*&,&*$I#c1GF$\"\"#\"\"\"*$I#s1GF $F,F-F,\"\"$#F-F,\"$x$*,I#s2GF$F-,&*$I#c3GF$F,F-*$I#s3GF$F,F-F-I#c2GF$ F-,(F6F-*&F7F-F9F-#\"\")\"\"&F8#!#V\"#DF-,&*$F:F,F-*$F4F,F-F-\"%+8F-\" #5F1F-*(,(F6F-F<#!$w%\"$N%F8#\"#J\"#()F-F5F-F:\"\"%!&+N%**F4F,F5F-,(F6 F-F<#!$3%\"$&QF8#\"#H\"#xF-F:F,!&+q(*&F4FPF7FP!&+N$*(F4FPF7F0F9F-\"&+S $*(F4FPF7F,F9F,!&+q%*(F4FPF9F0F7F-Fhn*&F4FPF9FP!&+N\"*$F)F,\"&+,&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "s3:=2*t3/(1+t3^2):c3:=(1-t3^2)/(1+t3^2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "yes1:=numer(simplify(eq1,\{s2^2+c2^2=1,s1^2+c1^2=1\}) );" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%yes1G6\",F**\"#5#\"\"\"\"\"#I#c 2GF$F)I#s2GF$F)I#t3GF$\"\"%!%+5*(\"\"$F(F'F(F-F.\"$?$**F'F(F+F)F,F)F-F 1!%?F*&F+F*F-F.!%+8**F'F(F+F)F,F)F-F*\"%+7*&F+F*F-F1\"%gT*(F1F(F'F(F-F *\"$S'**F'F(F+F)F,F)F-F)\"%?F*&F+F*F-F*\"&W:\"*$F-F.!%VE*(F+F)F,F)F'F( F/*&F+F*F-F)!%gT*$F-F1\"%SA*&F'F(F1F(F2*$F+F*F6*$F-F*\"%IBF-!%SAFBF)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "yes2:=numer(simplify(eq2) ):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "yes3:=numer(simplify( eq3)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "yes4:=numer(simpl ify(eq4,\{s2^2+c2^2=1,s1^2+c1^2=1\}));" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%yes4G6\",F**\"#5#\"\"\"\"\"#I#c2GF$F)I#s2GF$F)I#t3GF$\"\"%\"%+8*( \"\"$F(F'F(F-F.\"$x$**F'F(F+F)F,F)F-F1!%gT*&F+F*F-F.!&++\"**F'F(F+F)F, F)F-F*!&W:\"*&F+F*F-F1!&+s#*(F1F(F'F(F-F*\"$a(**F'F(F+F)F,F)F-F)\"%gT* &F+F*F-F*\"&+?\"*$F-F.\"&+m\"*(F+F)F,F)F'F(F/*&F+F*F-F)\"&+s#*$F-F1!&+ !o*&F'F(F1F(F2*$F+F*F6*$F-F*\"'+K6F-\"&+!oFBF)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "d egree(yes1,t1);degree(yes4,t1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"! " }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "factor(simplify(resultant(yes1,yes4,t3)));" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*$,P*(\"\"$#\"\"\"\"\"#\"#5F'I#c2G6\"\"\"'\" (+7:$**F&F'F*F'F+\"\"%I#s2GF,F)F.*$F+\"\")\"*++Sx(*&F+F-F1F)\"+++![b\" *&F+F0F1F0F4*(F*F'F+\"\"&F1F(\"++#*ze6*(F*F'F+F&F1F&F:*(F&F'F+F9F1F(\" ++gNu9*(F&F'F+F&F1F&F=*(F&F'F*F'F+F0!*?F\"4s**F&F'F*F'F+F)F1F)!+SM2S9* $F+F-\",+S[1D#*&F+F0F1F)FD*(F*F'F+F&F1F(\"+gdP>5*(F&F'F+F&F1F(\"+O%Gbb )*(F&F'F*F'F+F)\"+SA)Q3\"*$F+F0\",%p9!*f7*&F1F)F+F)!,iO\"Qgv*(F+F(F1F( F*F'!,g&[?$\\\"*(F&F'F+F(F1F(\",/&)\\a)G*&F*F'F&F'\"+!GZa=$*$F+F)!,ojR ba\"!,^?b*p@F(F)\"/+%evioM'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 654 "T:=-25616084000*s2^6+777400000*s2^8-1272049725-80371685020*s2^2+3 551568000*2^(1/2)*3^(1/2)*5^(1/2)+1158799200*c2*s2^5*5^(1/2)*2^(1/2)-7 11459120*s2^4*2^(1/2)*3^(1/2)*5^(1/2)+1474356000*c2*s2^5*3^(1/2)+14743 56000*c2^3*s2^3*3^(1/2)-11504240436*c2*s2^3*3^(1/2)+38884382940*c2*s2* 3^(1/2)-12753873600*c2*s2*5^(1/2)*2^(1/2)-51542529662*c2^2*s2^2+847828 66694*s2^4+1158799200*c2^3*s2^3*5^(1/2)*2^(1/2)-1436922240*c2^2*s2^2*5 ^(1/2)*2^(1/2)*3^(1/2)-3151200*c2^2*s2^4*5^(1/2)*2^(1/2)*3^(1/2)-33369 74160*c2*s2^3*5^(1/2)*2^(1/2)+348489600*2^(1/2)*3^(1/2)*5^(1/2)*s2^2-3 151200*s2^6*2^(1/2)*3^(1/2)*5^(1/2)+777400000*c2^4*s2^4-25616084000*c2 ^2*s2^4+1554800000*c2^2*s2^6:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "degree(T,c2);degree(T,s2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\" %" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "hilf2:=c2^2+s2^2-1;" }}{PARA 11 "" 1 "" {XPPMATH 20 " >I&hilf2G6\",(*$I#c2GF$\"\"#\"\"\"*$I#s2GF$F(F)!\"\"F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "weg:=numer(factor(resultant(T,hilf2 ,s2)));" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$wegG6\",$*(,&\"46:>xs(H,oC \"\"\"*$\"#I#F)\"\"#\"2SZ;'=Pl\\RF),&*$I#c2GF$F-\"\"%!\"$F)F),0*$F1\" \"'!HCul5x=5GEAX_YD!=ex.()*&F1F2F+F,\"F+GeNQ=Uoji&)*GY-#R8*y*$F1F2\"H; N1@R!euoKlL$**z$oK5cn*&F1F-F+F,\"G+W@%4<:sRI\\t$G:?auQ$p(F)F)! \"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "# explizit loesbar, \+ da nur gerade exponenten" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Digits:=20:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "los:=solve(evalf(weg),c2);" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I$losG6\"6*$\"+QSDg')!#5$!+QSDg')F($!+N Xq`&*F($\"+NXq`&*F(^$$!+@'=vY)!#7$!+/Ca&3#F(^$$\"+@'=vY)F2$\"+/Ca&3#F( ^$F0F8^$F6F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "c2:=solve(- 3^(1/2)+2*c2,c2);" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 " >I#c2G6\",$*$\"\"$#\"\"\"\"\"#F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "evalf(2*arccos(c2)*180/Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 " $\"#g\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(T);" } }{PARA 11 "" 1 "" {XPPMATH 20 ",$*&,&!\"\"\"\"\"I#s2G6\"\"\"#F&,>*$F' \"\"(!*++Sx(*&F'\"\"&\"#I#F&F)\"(+7:$*$F'\"\"'!*++q)Q*&F'\"\"%F0F1!*+S #yd*$F'F/\",+SjbU#*&F'\"\"$F0F1\"*?0\"\\U*$F'F7\"++IG;***&F'F)F0F1\"+S ERY9*$F'F " 0 "" {MPLTEXT 1 0 14 "factor(hilf2);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&, &!\"\"\"\"\"I#s2G6\"\"\"#F&,&F'F)F&F&F&#F&\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "s2:=solve(-1 + 2*s2,s2);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#s2G6\"#\"\"\"\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "factor(yes1);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*(,& *$\"#I#\"\"\"\"\"#\"#N!%4=F(F(,**&I#t3G6\"F(F&F'\"'g7_*$F.F)\"(JdB$F. \"(U.)>!(JdB$F(F(,(F1F(F.!\"#!\"\"F(F(#F)F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "factor(yes4);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$* (,&*$\"#I#\"\"\"\"\"#\"#F\"$]$F(F(,**&I#t3G6\"F(F&F'\"%!y(*$F.F)\"&j+ \"F.!&Mc*!&j+\"F(F(,(F1F(F.!\"#!\"\"F(F(#\"#EF2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "t3:=solve(-t3+1+2^(1/2),t3);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#t3G6\",&\"\"\"F&*$\"\"##F&F(F&" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 27 "evalf(2*arctan(t3)*180/Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"$N\"\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "factor(yes2);" }} {PARA 11 "" 1 "" {XPPMATH 20 ",$*&,**&\"\"##\"\"\"F&\"#:F'\"%J6*$F)F' \"%3:*$F&F'\"%+u\"&+6\"F(F(,.**I#c1G6\"F(F&F'F)F'I#s1GF3F(\"('=SzF%!($ 4qR*$F2F&\"(IhU**&F2F(F4F(!)+=#*H*$F4F&!(IhU*\")+4'\\\"F(F(#!\"%\"(lIr %" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "factor(yes3);" }} {PARA 11 "" 1 "" {XPPMATH 20 ",$*&,**&\"\"##\"\"\"F&\"#:F'\"%!)G*$F)F' \"%SQ*$F&F'!%=A!%FLF(F(,.**I#c1G6\"F(F&F'F)F'I#s1GF3F(\"('=SzF%!($4qR* $F2F&!)>\"=k#*&F2F(F4F(\")+=#*H*$F4F&\")>\"=k#!)+4'\\\"F(F(#\"\")F<" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 121 "yo2:=7940186*c1*sqrt(2)*s qrt(15)*s1 - 3970093*sqrt(2)*sqrt(15) + 9426130*c1^2 - 29921800*c1*s1 \+ - 9426130*s1^2 + 14960900;" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$yo2G6\" ,.**I#c1GF$\"\"\"\"\"##F(F)\"#:F*I#s1GF$F(\"('=Sz*&F)F*F+F*!($4qR*$F'F )\"(IhU**&F'F(F,F(!)+=#*H*$F,F)!(IhU*\")+4'\\\"F(" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 123 "yo3:=7940186*c1*sqrt(2)*sqrt(15)*s1 - 39700 93*sqrt(2)*sqrt(15) - 26418119*c1^2 + 29921800*c1*s1 + 26418119*s1^2 - 14960900;" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$yo3G6\",.**I#c1GF$\"\" \"\"\"##F(F)\"#:F*I#s1GF$F(\"('=Sz*&F)F*F+F*!($4qR*$F'F)!)>\"=k#*&F'F( F,F(\")+=#*H*$F,F)\")>\"=k#!)+4'\\\"F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "hilf1:=c1^2+s1^2-1;" }}{PARA 11 "" 1 "" {XPPMATH 20 " >I&hilf1G6\",(*$I#c1GF$\"\"#\"\"\"*$I#s1GF$F(F)!\"\"F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "factor(resultant(yo2,hilf1,c1));" } }{PARA 11 "" 1 "" {XPPMATH 20 ",$*(,&!/PY%3'Hby\"\"\"*$\"#I#F&\"\"#\"/ SF(GBz=\"F&,(*$I#s1G6\"F*\"1-!GKg[-O%F'\"09.4/+h%G!1,Q:0Mpr;F&F&,&F-F* !\"\"F&F&#!#5\"1,Sh,V7!=#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "factor(resultant(yo3,hilf1,c1));" }}{PARA 11 "" 1 "" {XPPMATH 20 " ,$*(,&\"1Jw;$p%f%R\"\"\"\"*$\"#I#F&\"\"#\"0+usGBz=\"F&,(*$I#s1G6\"F*!1 -!GKg[-O%F'\"09.4/+h%G\"1,U2)>b&)o#F&F&,&F-F*!\"\"F&F&#F4\"1,Sh,V7!=#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "s1:=solve(2*s1-2^(1/2),s 1);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#s1G6\",$*$\"\"##\"\"\"F'F(" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "factor(yo2);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&,(I#c1G6\"\"(IhU**$\"#:#\"\"\"\"\"#\"('=Sz*$F,F *!)NyC5F+,&F%!\"#F.F+F+#!\"\"F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "factor(yo3);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&,&I#c1G6\"! \"#*$\"\"##\"\"\"F)F+F+,(F%!)Qi$G&*$\"#:F*\")s.)e\"F(\"(\"o.NF+#!\"\" \"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "c1:=solve(2*c1-2^( 1/2),c1);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#c1G6\",$*$\"\"##\"\"\"F' F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "#Probe" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "#theta1=Pi/2,theta2=Pi/3,theta3=-Pi /2," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "simplify(arccos(c1)* 180/Pi); #theta1/2" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#X" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "simplify(arccos(c2)*180/Pi*2); #the ta2/2" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#g" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "simplify(arccos(c3)*180/Pi); #theta3/2" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$N\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 213 "" 0 "" {TEXT 212 0 "" }{TEXT 206 6 "Teil 2 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "end4:=Qmult(Qkon(DQ4n[1]),Qmult(Qkon(DQ3n[1]),Q mult(Qkon(DQ2n[1]),Qmult(Qkon(DQ1n[1]),Given[1]))));" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibG F'6(-I%mrowGF$6#-I'mtableGF$68-I$mtrGF$6&-I$mtdGF$6(-F,6)-F,6%-I&mfrac GF$6)-I#mnGF$6&Q\"1F'/%+foregroundGQ([0,0,0]F'/%)readonlyGQ&falseF'/%, mathvariantGQ'normalF'-F?6&Q$260F'FBFEFH/%.linethicknessGFA/%+denomali gnGQ'centerF'/%)numalignGFR/%)bevelledGFGFB-I#moGF$6-Q1&InvisibleTimes ;F'FH/%&fenceGFG/%*separatorGFG/%)stretchyGFG/%*symmetricGFG/%(largeop GFG/%.movablelimitsGFG/%'accentGFG/%'lspaceGQ&0.0emF'/%'rspaceGFeo-F,6 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"" {MPLTEXT 1 0 40 "s6:=2*t6/(1+t6^2):c6:=(1-t6^ 2)/(1+t6^2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "bed1:=factor(numer(simplify(end4[1] -end56[1]))):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "bed2:=fact or(numer(simplify(end4[2]-end56[2]))):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "bed3:=factor(numer(simplify(end4[3]-end56[3]))):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "bed4:=factor(numer(simplify( end4[4]-end56[4]))):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "aha2:=factor(simplify(resul tant(bed1,bed2,t4)/((1+t5^2)^2*(1+t6^2)^2)));" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%aha2G6\",$*&,&*$\"#8#\"\"\"\"\"#\"\")\"#pF+F+,ho\"%HRF +*&I#t5GF$\"\"%I#t6GF$F3F0*&F2\"\"$F4F6!>)*&F2F6F4F+\">)*&F2F+F4F6 F9*&F2F3F4F,!&a+$*&F2F,F4F3!&q3(*(F)F*F2F6F4F+\"&Oj$*(F)F*F2F+F4F6F@*$ F4F6!%wr*$F2F3F0*$F4F3F0*(F)F*F2F+F4F,!%Cm*&F2F3F4F6FC*&F)F*F4F6\"$K)* (F)F*F2F3F4F,!&[c\"*(F)F*F2F6F4F6!&Oj$*(F)F*F2F,F4F3!&gX\"*(F)F*F2F3F4 F6FJ*(F)F*F2F3F4F+!$K)*(F)F*F2F6F4F,\"%Cm*(F)F*F2F,F4F,\"&'\\U*&F)F*F2 F,FP*&F)F*F4F,FL*&F2F,F4F,\"'+@:*(F)F*F2F,F4F6!%k;F4\"%wr*&F2F3F4F+Fhn *&F2F6F4F,!%%)***&F2F+F4F+F7*&F2F,F4F6\"&_V\"*&F2F,F4F+!&_V\"*&F2F+F4F ,\"%%)***(F2F+F4F+F)F*FN*$F2F,F>*$F4F,F<*&F4F+F)F*FS*(F)F*F2F,F4F+\"%k ;F+#\"(+!3aF0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "aha3:=fact or(simplify(resultant(bed1,bed3,t4)/((1+t5^2)^2*(1+t6^2)^2)));" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I%aha3G6\",$*&,&*$\"#8#\"\"\"\"\"#\"\"' !#BF+F+,hp\"$0$F+*&I#t5GF$\"\"%I#t6GF$F3F0*&F2\"\"$F4F6\"&)Ga*&F2F6F4F +!&)Ga*&F2F+F4F6F9*&F2F3F4F,\"&9<#*&F2F,F4F3\"&A@$*(F)F*F2F6F4F+!&WX\" *(F)F*F2F+F4F6F@F2!%cS*$F4F6\"%)e$*$F2F3F0*$F4F3F0*(F)F*F2F+F4F,\"%/d* &F2F3F4F6FD*&F2F6F4F3\"%cS*&F)F*F4F6\"$O**(F)F*F2F3F4F,\"%[i*(F)F*F2F6 F4F6\"&WX\"*(F)F*F2F,F4F3\"%[!**(F)F*F2F3F4F6FM*(F)F*F2F6F4F3\"%'>\"*( F)F*F2F3F4F+!$O**(F)F*F2F6F4F,!%/d*(F)F*F2F+F4F3!%'>\"*$F2F6FK*(F)F*F2 F,F4F,!&c1$*&F)F*F2F,FS*&F)F*F4F,FO*&F2F,F4F,!'go5*(F)F*F2F,F4F6!%;cF4 !%)e$*&F2F3F4F+F`o*&F2F6F4F,!&W$>*&F2F+F4F3FB*&F2F+F4F+F7*&F2F,F4F6!&G :#*&F2F,F4F+\"&G:#*&F)F*F2F6FV*&F2F+F)F*Ffn*&F2F+F4F,\"&W$>*(F2F+F4F+F )F*FQ*$F2F,F>*$F4F,F<*&F4F+F)F*FX*(F)F*F2F,F4F+\"%;cF+#!)+SEV\"#h" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "aha4:=factor(simplify(result ant(bed1,bed4,t4)/((1+t5^2)^2*(1+t6^2)^2)));" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%aha4G6\",$*&,&*$\"#8#\"\"\"\"\"#\"\"%!#@F+F+,N*&I#t5GF $F-I#t6GF$F-!$L#*(F)F*F1F-F2F,\"#;*(F)F*F1\"\"$F2F7\"$w\"*(F)F*F1F,F2F -F5*&F1F-F2F,\"$]&*&F1F7F2F7!%s=*&F1F,F2F-F;*(F)F*F1F7F2F+!$w\"*(F)F*F 1F,F2F,\"$7&*(F)F*F1F+F2F7F@*$F1F-F3*&F1F7F2F+\"%s=*&F1F,F2F,!%+d*&F1F +F2F7FF*$F2F-F3*&F)F*F1F,F5*(F1F+F2F+F)F*F8*&F)F*F2F,F5*$F1F,F;*&F1F+F 2F+F=*$F2F,F;F3F+F+#\")+SIq\"$L#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "fin34:=factor(simplify(resultant(aha3,aha4,t6)));" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I&fin34G6\",$*,,&\"-dr;Q.E\"\"\"*$\"#8#F)\"\"# \",cJC8a&F),(*$I#t5GF$F-F)F1F-!\"\"F)F-,2*&F+F,F1\"\"$\"#G*$F1\"\"%!$> %*&F+F,F1F-\"$7$*$F1F5F;*&F1F)F+F,!#GF0\"%-7F1!$7$F9F)F-,(F0F)F1!\"#F2 F)F-,B*&F+F,F1\"\"(\"*OO\"Hi*$F1\"\")!*R]M)R*&F+F,F1\"\"'!*/XN&p*$F1FE !+o4k/=*&F+F,F1\"\"&\"*+TGv(*$F1FK\"+!QbHD(*&F+F,F1F8!+;s!*QA*$F1FP!+% y>Ki&F4!*+TGv(F7!+u#\\Yp'F:FLF<\"+%y>Ki&F=!*OO\"HiF0FSF1\"+o4k/=FIF)F- #\"]o++++++++++++;ClUhkDW?#p(3'4Z`)Gqz0N\"8\"GQDK3ob.y&y#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "fin24:=factor(simplify(resultant(ah a2,aha4,t6)));" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I&fin24G6\",$*,,&!,h` c]J#\"\"\"*$\"#8#F)\"\"#\"))o1Y\"F),(*$I#t5GF$F-F)F1F-!\"\"F)F-,B*&F+F ,F1\"\"(\")%el'>*$F1\"\")!).=Db*&F+F,F1\"\"'\")%GxR%*$F1F5\")moTJ*&F+F ,F1\"\"&!)Ot;x*$F1F;\"*/.Se&*&F+F,F1\"\"%!*C+p-$*$F1F@!*=t$\\H*&F+F,F1 \"\"$\")Ot;x*$F1FE!+Ad+U7*&F+F,F1F-F<*$F1FJ\"*=t$\\H*&F1F)F+F,!)%el'>F 0FCF1!)moTJF9F)F-,(F0F)F1!\"#F2F)F-,2FI\"#GFL\"$>%FN!$7$FO\"$7$FQ!#GF0 !%-7F1FYFXF)F-#!\\o++++++++++++wd\"R)GgwFw![0N>M.VJ7\">#\"6\\)yne9H!f% f`" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "fin23:=factor(simplif y(resultant(aha2,aha3,t6)));" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I&fin23 G6\",$*,,&\"-,vcxal\"\"\"*$\"#8#F)\"\"#\",!)f=O=#F),(*$I#t5GF$F-F)F1F- !\"\"F)F-,(F0F)F1!\"#F2F)F-,.*&F+F,F1\"\"$\"\"%*$F1F8F+*&F+F,F1F-\"#C* &F1F)F+F,!\"%F0\"#]F+F)F-,B*&F+F,F1\"\"(\"-%)oWy6>*$F1\"\")\"-,\\/K2l* &F+F,F1\"\"'\"-cOmY#3%*$F1FA\"-;U:69H*&F+F,F1\"\"&!-%o%*4Bv%*$F1FG\"-O G#>s0&*&F+F,F1F8!._VV&\\1Q*$F1FL!.scvT<1\"F6\"-%o%*4Bv%F9!/mGN%R2C\"F: FH*$F1F7\".scvT<1\"FF0FOF1!-;U:69HFEF)F-#\"[o++++++++++++kkC H[2x1h\"=`fhZ<6OW2#\"9,)*4!3P5E%>_MU" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "gcd(gcd(fin34,fin24),fin23);" }}{PARA 11 "" 1 "" {XPPMATH 20 "*&,(*$I#t5G6\"\"\"#\"\"\"F%F'!\"\"F(F',(F$F(F%!\"#F)F(F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "solve(t5^2+2*t5-1,t5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,&*$\"\"##\"\"\"F%F'!\"\"F',&F(F'F$F (" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "arctan(2^(1/2)-1)*180/ Pi*2; arctan(-2^(1/2)-1)*180/Pi*2; #theta5/2" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#X" }}{PARA 11 "" 1 "" {XPPMATH 20 "!$N\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "solve(t5^2-2*t5-1,t5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,&\"\"\"F$*$\"\"##F$F&F$,&F$F$F%!\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "arctan(2^(1/2)+1)*180/Pi*2; \+ arctan(-2^(1/2)+1)*180/Pi*2; #theta5/2" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$N\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "!#X" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "# somit zwei Loesungen" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "t5: =2^(1/2)-1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#t5G,&*$)\"\"##\"\"\" \"\"#\"\"\"\"\"\"\"\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "factor(gcd(gcd(aha2,aha3),aha4));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(\"\"\"!\"\"*&\"\"#\"\"\"%#t6G\"\"\"!\"\"*$)%#t6G\"\"#\"\"\"\" \"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "solve(-1-2*t6+t6^2, t6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,&*$)\"\"##\"\"\"F&F(F(F(F(,&F (F(F$!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "t6:=1-2^(1/2) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#t6G,&\"\"\"\"\"\"*$)\"\"##\"\" \"\"\"#\"\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "facto r(gcd(gcd(bed1,bed2),gcd(bed3,bed4)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%#t4G\"\"\"\"\"#!\"\"*$)\"\"$#\"\"\"\"\"#\"\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "t4:=solve(t4-2-3^(1/2),t4);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#t4G,&\"\"#\"\"\"*$)\"\"$#\"\"\"\"\" #\"\"\"\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "arctan(t4) *180/Pi*2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$]\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "arctan(t5)*180/Pi*2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#X" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "arct an(t6)*180/Pi*2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!#X" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "# somit erhalten wir genau die Dreh winkel, mit welchen die Pose \"Given\" generiert wurde. " }}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }