{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 "" 0 1 0 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 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "T itle" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }{PSTYLE "Author" 0 19 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 8 8 0 0 0 0 0 0 -1 0 } } {SECT 0 {EXCHG {PARA 18 "" 1 "" {TEXT -1 41 "Elliptic Integrals and El liptic Functions" }}{PARA 19 "" 0 "" {TEXT -1 20 "by Ricardo Carretero " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 74 "Plotting the COMPLETE ELLIPTIC FUNCTIONS \+ of FIRST (K) and SECOND (E) kinds" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "plot(\{EllipticK(k),EllipticE(k)\},k=0..1,y=0..5, color=[red,blue] ,numpoints=100);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-%'CURVESG6$7`q7$$\"\"!F)$\"+Fjzq:!\"*7$$\"+<<$o0\"!#6$\"+mCvq:F, 7$$\"+V`Pw>F0$\"+DHkq:F,7$$\"+B$)\\5IF0$\"+f.Wq:F,7$$\"+ThZ^SF0$\"+M:: q:F,7$$\"+tj](3&F0$\"+@%z(p:F,7$$\"+?!R![gF0$\"+&*)e$p:F,7$$\"+R\\hUqF 0$\"+'yY)o:F,7$$\"+xn?r!)F0$\"+!)\\Bo:F,7$$\"+3**\\'4*F0$\"+G=an:F,7$$ \"+#*R6:5!#5$\"+#)=um:F,7$$\"+Tn+36Fhn$\"+)3kfc\"F,7$$\"+w>e77Fhn$\"+R i+l:F,7$$\"+1me<8Fhn$\"+#ecRc\"F,7$$\"+C!y(=9Fhn$\"+x9'Gc\"F,7$$\"+E&p 1^\"Fhn$\"+Odzh:F,7$$\"+5u$*>;Fhn$\"+h)R/c\"F,7$$\"+S;]7Fhn$\"+\">(Gc:F,7$$\"+Xe0??Fhn$ \"+3qka:F,7$$\"+%HJ'>@Fhn$\"+<:+`:F,7$$\"+Gy_BAFhn$\"+#>(>^:F,7$$\"+!G P*=BFhn$\"+:7Y\\:F,7$$\"+i#\\=U#Fhn$\"+JM]Z:F,7$$\"+!*euGDFhn$\"+rbPX: F,7$$\"+=(*z@EFhn$\"+&eWMa\"F,7$$\"+-/IAFFhn$\"+,jFT:F,7$$\"+Uu7EGFhn$ \"+2a%*Q:F,7$$\"+X>qFHFhn$\"+C^dO:F,7$$\"++0)f-$Fhn$\"+hk>M:F,7$$\"+y? 5NJFhn$\"+QjXJ:F,7$$\"+qE:LKFhn$\"+WY!*G:F,7$$\"+1E%yL$Fhn$\"++e3E:F,7 $$\"+ZsqKMFhn$\"+]mWB:F,7$$\"+d$>k`$Fhn$\"+V#o/_\"F,7$$\"+qV+MOFhn$\"+ %>wv^\"F,7$$\"+F)3gt$Fhn$\"+P%fW^\"F,7$$\"+GotNQFhn$\"+F(=8^\"F,7$$\"+ .G9SRFhn$\"+H1$z]\"F,7$$\"+l\")pSSFhn$\"+6(pX]\"F,7$$\"+Z0`VTFhn$\"+yB .,:F,7$$\"+D9^XUFhn$\"+MIU(\\\"F,7$$\"+g7ARVFhn$\"+sk,%\\\"F,7$$\"+2Li YWFhn$\"+a\\+!\\\"F,7$$\"+x\\oUXFhn$\"+:)=j[\"F,7$$\"+an5XYFhn$\"+!=&G #[\"F,7$$\"+ju8VZFhn$\"+&>B$y9F,7$$\"+nz)>&[Fhn$\"+Oi!QZ\"F,7$$\"+1XCY \\Fhn$\"+MMzp9F,7$$\"+?lA`]Fhn$\"+xI7l9F,7$$\"+7!H2:&Fhn$\"+Fxvg9F,7$$ \"+:9Qd_Fhn$\"+n>'eX\"F,7$$\"+,WS\\`Fhn$\"+jZ`^9F,7$$\"+Uy?aaFhn$\"+P% )[Y9F,7$$\"+\"zUab&Fhn$\"+WC\\T9F,7$$\"+2;hccFhn$\"+'GyjV\"F,7$$\"+S#3 uv&Fhn$\"+#**f6V\"F,7$$\"+\\ACaeFhn$\"+(3HgU\"F,7$$\"+xB#*efFhn$\"+z+N ?9F,7$$\"+I,pegFhn$\"+zp![T\"F,7$$\"+\"*4pjhFhn$\"+&[K)39F,7$$\"+c?uei Fhn$\"+TqH.9F,7$$\"+w7zjjFhn$\"+Cc.(R\"F,7$$\"+C,TkkFhn$\"+sM*3R\"F,7$ $\"+iSyklFhn$\"+/;i%Q\"F,7$$\"+I]ipmFhn$\"+kB\"zP\"F,7$$\"+)Q(=mnFhn$ \"+*3'er8F,7$$\"+_/3loFhn$\"+BZ(Fhn$\"+I9l?8F,7$$\"+F0IsvFhn$ \"+#\\3FJ\"F,7$$\"+)*)[#zwFhn$\"+-)))RI\"F,7$$\"+.iitxFhn$\"+IY4'H\"F, 7$$\"+@!=D)yFhn$\"+]Qu'G\"F,7$$\"+#\\%y!)zFhn$\"+mB2y7F,7$$\"+GS,y!)Fh n$\"+ZUEp7F,7$$\"+:qc#=)Fhn$\"+tn_f7F,7$$\"+THa(G)Fhn$\"+dvX\\7F,7$$\" +*[bIQ)Fhn$\"+yo-S7F,7$$\"+tb[%[)Fhn$\"+/SrH7F,7$$\"+@9Z$e)Fhn$\"+n[L> 7F,7$$\"+DJx!p)Fhn$\"+ttq27F,7$$\"+K*=Oy)Fhn$\"+*f1t>\"F,7$$\"+nV g6F,7$$\"+X28*=*Fhn$\"+snZZ6F,7$$\"+jkY!H*Fhn$\"+]RlL6F,7$$\"+E1)yR*Fh n$\"+7pB=6F,7$$\"+'*)oj\\*Fhn$\"+([*G.6F,7$$\"+l%*e$f*Fhn$\"+:oh(3\"F, 7$$\"+`m^(p*Fhn$\"+iifp5F,7$$\"++w@,)*Fhn$\"+2s%)\\5F,7$$\"+f`H%*)*Fhn $\"+j%4)H5F,7$$\"\"\"F)Fdjl-%'COLOURG6&%$RGBG$\"*++++\"!\")F(F(-F$6$7d rF'7$F.$\"+!>S3d\"F,7$F4$\"+^(\\4d\"F,7$F9$\"+:C:r:F,7$F>$\"+<:Wr:F,7$ FC$\"+@U\"=d\"F,7$FH$\"+NdBs:F,7$FM$\"+0&\\Fd\"F,7$FR$\"+dROt:F,7$FW$ \"+z41u:F,7$Ffn$\"+Wl'[d\"F,7$F\\o$\"+!*4lv:F,7$Fao$\"+Z'=md\"F,7$Ffo$ \"+06ox:F,7$F[p$\"+j=zy:F,7$F`p$\"+*4v)z:F,7$Fep$\"+qkD\"e\"F,7$Fjp$\" ++o]#e\"F,7$F_q$\"+'yaSe\"F,7$Fdq$\"+g*4be\"F,7$Fiq$\"+([*>(e\"F,7$F^r $\"+]***))e\"F,7$Fcr$\"+')3x!f\"F,7$Fhr$\"+Wsd#f\"F,7$F]s$\"+b=i%f\"F, 7$Fbs$\"+5J&of\"F,7$Fgs$\"+>h)))f\"F,7$F\\t$\"+H$y6g\"F,7$Fat$\"+\"e`O g\"F,7$Fft$\"+&f#=1;F,7$F[u$\"+cFt3;F,7$F`u$\"+Ldo6;F,7$Feu$\"+60X9;F, 7$Fju$\"+)e@vh\"F,7$F_v$\"+vIT?;F,7$Fdv$\"+e_pB;F,7$Fiv$\"+n=x\"F,7$F`_l$\"+nx)4y\"F, 7$Fe_l$\"+@88!z\"F,7$Fj_l$\"+$*fi*z\"F,7$F_`l$\"+,a'*4=F,7$Fd`l$\"+OM* )>=F,7$Fi`l$\"+@\"*[I=F,7$F^al$\"+lXsU=F,7$Fcal$\"+n@Ka=F,7$Fhal$\"+?/ tm=F,7$F]bl$\"+$**e*z=F,7$Fbbl$\"+0=q#*=F,7$Fgbl$\"+6&[p!>F,7$F\\cl$\" +(3==#>F,7$Facl$\"+;8gQ>F,7$Ffcl$\"+2GBa>F,7$F[dl$\"+#oF,7$F`dl$\" +>5g\"*>F,7$Fedl$\"+yey5?F,7$Fjdl$\"+!HjF.#F,7$F_el$\"+J3Sc?F,7$Fdel$ \"+=eWz?F,7$Fiel$\"+HSt0@F,7$F^fl$\"+o%RM8#F,7$Fcfl$\"+/G6m@F,7$Fhfl$ \"+2v&p>#F,7$F]gl$\"+)4feB#F,7$Fbgl$\"+([okF#F,7$Fggl$\"+d/Q@BF,7$F\\h l$\"+p,6sBF,7$Fahl$\"+n!49V#F,7$Ffhl$\"+_tE0DF,7$F[il$\"+@6p'e#F,7$F`i l$\"+D#\\do#F,7$$\"+eIbX'*Fhn$\"+1\"z&\\FF,7$Feil$\"+MZ5CGF,7$$\"+ErO \\(*Fhn$\"+SP>8HF,7$Fjil$\"+%)*3R-$F,7$$\"+Sq[C)*Fhn$\"+M#RP3$F,7$$\"+ ![cx%)*Fhn$\"+`YO_JF,7$$\"+?f-r)*Fhn$\"+!*esKKF,7$F_jl$\"+ST`HLF,7$$\" +S%3v!**Fhn$\"+L$HZR$F,7$$\"+?:s?**Fhn$\"+p*)=qMF,7$$\"++Y$R$**Fhn$\"+ l4ofNF,7$$\"+!oZr%**Fhn$\"+t(>&pOF,7$$\"+?Uv`**Fhn$\"+++RNPF,7$$\"+g2O g**Fhn$\"+Boa6QF,7$$\"++t'p'**Fhn$\"+x?w,RF,7$$\"+SQdt**Fhn$\"+WdN7SF, 7$$\"+5r(o(**Fhn$\"+,xhySF,7$$\"+!Q!=!)**Fhn$\"+Vw!4!***Fhn$\"+q06+XF, 7$$\"+gMR$***Fhn$\"+F\"\\Aq%F,7$$\"+Inp'***Fhn$\"+Kd=[]F,7$%%FAILGF[dn -Fgjl6&FijlF(F(Fjjl-%+AXESLABELSG6$Q\"k6\"Q\"yFbdn-%%VIEWG6$;F(Fdjl;F( $\"\"&F)" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Cur ve 1" "Curve 2" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 103 "Plot the rati o of the true period (T) to the harmonic period (T_H) for a simple pe ndulum with IC theta" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "g:=9.8;L:=0.1;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "T_H := 2* Pi*sqrt(g/L):;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "T := theta -> 4*s qrt(g/L)*EllipticK(sin(theta/2));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "Tapprox := theta -> (1+sin(theta/2)^2/4)*T_H;" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 86 "plot(\{T(theta)/T_H,Tapprox(theta)/T_H\},theta=0..3 *Pi/4,y=0.99..1.3, color=[red,blue]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG$\"#)*!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG$\"\"\"! \"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"TGf*6#%&thetaG6\"6$%)opera torG%&arrowGF(,$*&-%%sqrtG6#*&%\"gG\"\"\"%\"LG!\"\"F3-%*EllipticKG6#-% $sinG6#,$9$#F3\"\"#F3\"\"%F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% (TapproxGf*6#%&thetaG6\"6$%)operatorG%&arrowGF(*&,&\"\"\"F.*&#F.\"\"%F .)-%$sinG6#,$9$#F.\"\"#F9F.F.F.%$T_HGF.F(F(F(" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-%'CURVESG6$7S7$$\"\"!F)$\"\"\"F) 7$$\"3TSdmWM$e8&!#>$\"3]>Vn=[;+5!#<7$$\"3S(>F;$\"3dNt5z\\T -5F27$$\"3Y(R?zg]BZ#F;$\"3ijJB.4!Q+\"F27$$\"3E@Ykjf8RHF;$\"3&oL%>?.O05 F27$$\"3$o0MA;lCU$F;$\"3]q377'\\s+\"F27$$\"3$[\"[#3\"\\KARF;$\"3w5bW^F \\45F27$$\"3IAC'Gg\"e?WF;$\"3O>e,je,75F27$$\"3@Gb:a)*4L\\F;$\"3D#\\)4< P!\\,\"F27$$\"3d&*R')3i_%Q&F;$\"3$zW7y4(o<5F27$$\"3s8WAk`s#*eF;$\"3!\\ &H0^=3@5F27$$\"3#>^VTB6IS'F;$\"3Ye5]80wC5F27$$\"3ALH[Biw%*oF;$\"3LQUm< EbG5F27$$\"3lNIxkoKTtF;$\"3BHra*[)>K5F27$$\"37Hp`f1LsyF;$\"3-'fh])RxO5 F27$$\"3OtVeD0;A$)F;$\"3@c:!)[^%3/\"F27$$\"3H(yJuf>a%))F;$\"3y2@45XzX5 F27$$\"34\"Qa)QDf3$*F;$\"3TV:82\"F27$$\"3ifco\\U$p<\"F2$\"3i=x( [HIq2\"F27$$\"3VW!)>\"G#))G7F2$\"30NEbI')3$3\"F27$$\"3!\\=S`>.TF\"F2$ \"3'QGZ>2b%)3\"F27$$\"3UA6[@I%HK\"F2$\"3s0Q/rXL%4\"F27$$\"3EP^'3M*Rt8F 2$\"3Yb%4$3`[+6F27$$\"39?1n05wA9F2$\"3E%RUl4jl5\"F27$$\"3@S%*\\a4_q9F2 $\"3'R5?Qd'[76F27$$\"3N#[D[B]N_\"F2$\"3Qj?RNk4>6F27$$\"3'\\&4x,%*>r:F2 $\"3)HkqVQ]]7\"F27$$\"3r*G'*z0v?i\"F2$\"33\\wkKqSJ6F27$$\"3)4uXT'fL0&*pb\"=F2$\"3:0V\"y3#Hb6F27$$\"3TikxzU.k=F 2$\"3;95m$oJ6;\"F27$$\"3$**)Q0T>x9>F2$\"3^M>YfS:n6F27$$\"3eP\"y\"R$QO' >F2$\"3')4()*[$>&G<\"F27$$\"3=Z/>*G6O,#F2$\"3:LZ+x0cy6F27$$\"3'o&e%zVq J1#F2$\"33h/_9**3%=\"F27$$\"3b**zj[,r3@F2$\"3]c*HE>V!*=\"F27$$\"396\\C 'z.4;#F2$\"3m'oa+HcX>\"F27$$\"3^A&poT'e2AF2$\"3Q\"\\bU@F$*>\"F27$$\"31 cBF2$\"36-=BZ$)Q87F2-%'COLOURG6&%$RGBG$\"*++++\"!\")F(F(-F$ 6$7S7$F($\"+,+++5!\"*7$$\"+VM$e8&!#6$\"+!)[;+5Ff[l7$$\"+hY\\/'*Fj[l$\" +Xod+5Ff[l7$$\"+cr*HY\"!#5$\"+o$R8+\"Ff[l7$$\"+fg()o>Fe\\l$\"+\">GC+\" Ff[l7$$\"+21NsCFe\\l$\"+dP$Q+\"Ff[l7$$\"+jf8RHFe\\l$\"+[fU05Ff[l7$$\"+ h^YAMFe\\l$\"+,.P25Ff[l7$$\"+5\\KARFe\\l$\"+65q45Ff[l7$$\"+-;e?WFe\\l$ \"+z>N75Ff[l7$$\"+`)*4L\\Fe\\l$\"+s^U:5Ff[l7$$\"+2i_%Q&Fe\\l$\"+VvU=5F f[l7$$\"+j`s#*eFe\\l$\"+rW9A5Ff[l7$$\"+K7,.kFe\\l$\"+_ECE5Ff[l7$$\"+@i w%*oFe\\l$\"+WkaI5Ff[l7$$\"+joKTtFe\\l$\"+xFwM5Ff[l7$$\"+d1LsyFe\\l$\" +*Hn,/\"Ff[l7$$\"+B0;A$)Fe\\l$\"+Hi3X5Ff[l7$$\"+&f>a%))Fe\\l$\"+dA@^5F f[l7$$\"+ODf3$*Fe\\l$\"+Ty+d5Ff[l7$$\"+imw;)*Fe\\l$\"+0Ayj5Ff[l7$$\"+g o1I5Ff[l$\"+#Q]12\"Ff[l7$$\"+^pb!3\"Ff[l$\"+5fEy5Ff[l7$$\"+;E#p7\"Ff[l $\"+uzn&3\"Ff[l7$$\"+\\U$p<\"Ff[l$\"+#HRT4\"Ff[l7$$\"+\"G#))G7Ff[l$\"+ 19Y.6Ff[l7$$\"+&>.TF\"Ff[l$\"+^r.76Ff[l7$$\"+@I%HK\"Ff[l$\"+e=!=7\"Ff[ l7$$\"+S$*Rt8Ff[l$\"+dDYK6Ff[l7$$\"+05wA9Ff[l$\"+AC[V6Ff[l7$$\"+a4_q9F f[l$\"+)GGZ:\"Ff[l7$$\"+M-bB:Ff[l$\"+,I#z;\"Ff[l7$$\"+,%*>r:Ff[l$\"+B$ \\/=\"Ff[l7$$\"+e]2A;Ff[l$\"+%*\\c%>\"Ff[l7$$\"+kfb!37Ff[ l7$$\"+Jkd=x9>Ff[l$\"+CR J$H\"Ff[l7$$\"+R$QO'>Ff[l$\"+MjF88Ff[l7$$\"+*G6O,#Ff[l$\"+&oL\\L\"Ff[l 7$$\"+P/cBFf[l$\"+%eZz_\" Ff[l-Fjz6&F\\[lF(F(F][l-%+AXESLABELSG6$Q&theta6\"Q\"yF_[m-%%VIEWG6$;F( $\"+!\\%>cBFf[l;$\"#**!\"#$\"#8!\"\"" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 18 "" 0 " " {TEXT -1 18 "Elliptic Functions" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 "R" }{MPLTEXT 1 0 0 "" }{TEXT -1 20 "escaled SN f unction:" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "SN : = (x,k) -> JacobiSN(x*(4*EllipticK(k)),k);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "plot(\{SN(x,0),SN(x,0.9),SN(x,0.999),SN(x,0.9999999) \},x=-1..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#SNGf*6$%\"xG%\"kG6 \"6$%)operatorG%&arrowGF)-%)JacobiSNG6$,$*&9$\"\"\"-%*EllipticKG6#9%F3 \"\"%F7F)F)F)" }}{PARA 13 "" 1 "" {GLPLOT2D 635 298 298 {PLOTDATA 2 "6 (-%'CURVESG6$7fq7$$!\"\"\"\"!$\"+7.]+5!#<7$$!+HU,\"*)*!#5$\"+fk8N>F17$ $!+e%G?y*F1$\"+*p12t$F17$$!+(oUIn*F1$\"+P%*p%G&F17$$!+s%HaF1$\"+?Gh$['F17$$!+#)*G;K&F1$\" +!)pE:_F17$$!+rdy8_F1$\"+r6slOF17$$!+hD%f5&F1$\"++US#)=F17$$!+]$*4)*\\ F1$!+I)4yT$!#77$$!+DL\")*)[F1$!+n\\\"f&>F17$$!++t_\"y%F1$!+6IYQPF17$$! +v7CtYF1$!+@T7#G&F17$$!+]_&\\c%F1$!+F9OTlF17$$!+]zCcVF1$!+%fK[?)F17$$! +]1aZTF1$!+(4%[7\"*F17$$!+FW,eRF1$!+lXBV&*F17$$!+/#)[oPF1$!+S3lo(*F17$ $!+%>BJa$F1$!+1;8**)*F17$$!+$=exJ$F1$!+vmmd**F17$$!+L2$f$HF1$!+2k\\#** *F17$$!+PYx\"\\#F1$!+9y******F17$$!+L7i)4#F1$!+^l#Q***F17$$!+P'psm\"F1 $!+-*p]&**F17$$!+u_*=Y\"F1$!+hC,,**F17$$!+74_c7F1$!+qvu)y*F17$$!+6wP\\ 6F1$!+t>x)o*F17$$!+5VBU5F1$!+=xjV&*F17$$!+!454N*!#6$!+S=:M$*F17$$!*3x% z#)F1$!+QNEM!*F17$$!+Srl6jFiy$!+(\\D$H\")F17$$!*?PQM%F1$!+(\\]X`'F17$$ !+ytb#G$Fiy$!+@I^,`F17$$!+bvF@AFiy$!+.N([z$F17$$!+Lx**f6Fiy$!+\"oWi0#F 17$$!(\"zr)*F1$!+hs*\\x\"Fiy7$$\"+nNl.5Fiy$\"+;M[&y\"F17$$\"+X]-1@Fiy$ \"+0#fgh$F17$$\"+AlR3KFiy$\"+n?#\\?&F17$$\")!o2J%!\"*$\"+\\'=.]'F17$$ \"++K+IiFiy$\"+\"*H$)y!)F17$$\")%Q#\\\")Fa]l$\"+Cl4!**)F17$$\"++l?A5F1 $\"+#>^+^*F17$$\"*;*[H7Fa]l$\"+5q%pw*F17$$\"+ICjV9F1$\"+!R.S*)*F17$$\" *qvxl\"Fa]l$\"+i$\\L&**F17$$\"+:JFn=F1$\"+%zX/)**F17$$\"*`qn2#Fa]l$\"+ Pm+$***F17$$\"*cp@[#Fa]l$\"+=(*)*****F17$$\"*3'HKHFa]l$\"+K]k#***F17$$ \"*xanL$Fa]l$\"+NxMa**F17$$\"+gxn_NF1$\"+jkX&*)*F17$$\"*v+'oPFa]l$\"+] jbo(*F17$$\"+v!fU'RF1$\"+9'**H`*F17$$\"*S<*fTFa]l$\"+(=pP2*F17$$\"+DO# QP%F1$\"+\"f:')4)F17$$\"*&)Hxe%Fa]l$\"+@bd+jF17$$\"+&Rk$)o%F1$\"++(oJ3 &F17$$\"+S*)**)y%F1$\"+f$)GAOF17$$\"+&[L'*)[F1$\"+%4D!f>F17$$\"*.o-*\\ Fa]l$\"+rA')\\D&**p\"F17$$\"+?Al+_F1$!+,u]fMF17$ $\"+:V%eI&F1$!+n7]0]F17$$\"*TO5T&Fa]l$!+T%prG'F17$$\"+:as;cF1$!+M*3#R! )F17$$\"*U9C#eFa]l$!+%>Ed,*F17$$\"+!3$3IfF1$!+$*=QA$*F17$$\"+Sj`*F17$$\"++/UXhF1$!+5YJ%o*F17$$\"*1*3`iFa]l$!+\"G$4'y*F17$$\"+&\\ %[gkF1$!+?r[+**F17$$\"*$*zym'Fa]l$!+)\\y^&**F17$$\"*^j?4(Fa]l$!+Qze$** *F17$$\"*jMF^(Fa]l$!+bZ******F17$$\"*q(G**yFa]l$!+I8!R***F17$$\"*9@BM) Fa]l$!+/:L`**F17$$\"+N$[/a)F1$!+*HQ,!**F17$$\"*`v&Q()Fa]l$!+N\\[#z*F17 $$\"+()z>W))F1$!+d)yep*F17$$\"+X/#)\\*)F1$!+IiLc&*F17$$\"+-HWb!*F1$!+? m'eN*F17$$\"*Ol5;*Fa]l$!+G%)4q!*F17$$\"++PDj$*F1$!+5&[J;)F17$$\"*/Uac* Fa]l$!+9pMOlF17$$\"+I:3u'*F1$!+^r@r_F17$$\"+?5s#y*F1$!+5&z*>PF17$$\"+5 0O\"*)*F1$!+s<9H>F17$$\"\"\"F*$!+7.]+5F--%'COLOURG6&%$RGBG$\"#5F)$F*F* F_]m-F$6$7es7$F($\"+]+++5F-7$$!+9r]X**F1$\"+WDnd>F17$F/$\"+K%G3x$F17$$ !+V8_O)*F1$\"+:9pM`F17$F5$\"+4cz-mF17$F:$\"+8hn0$)F17$F?$\"+9BH'>*F17$ $!+!)*G#p%*F1$\"+AFu)e*F17$FD$\"+u(R;z*F17$$!+wq)pK*F1$\"+;R+_)*F17$$! +3Jdz#*F1$\"+xF(\\*)*F17$$!+S\"f@B*F1$\"+7I^D**F17$FI$\"+Li>Z**F17$FN$ \"+hyz))**F17$FS$\"+8xi(***F17$Fgn$\"+,j*)****F17$F\\o$\"+We******F17$ Fao$\"+)*********F17$Ffo$\"+9d******F17$F[p$\"+Re*)****F17$Fep$\"+Qos( ***F17$F_q$\"+U+$*))**F17$Fiq$\"+u+>Y**F17$$!+gpvkdF1$\"+l%GQ#**F17$$! +O\"for&F1$\"+/WA#*)*F17$$!+78'*ocF1$\"+'*zgZ)*F17$F^r$\"+![@Zy*F17$$! +SyEDbF1$\"+8PHs&*F17$Fcr$\"+p,;f\"*F17$Fhr$\"+f>bW#)F17$F]s$\"+BR+;lF 17$$!+mT')f^F1$\"+#f>*R_F17$Fbs$\"+*F17$$!++;ggWF1$!+ !*4H8'*F17$Fau$!+lY><)*F17$$!+D62/VF1$!+H*)fu)*F17$$!++V*=D%F1$!+:a09* *F17$$!+vur*>%F1$!+TS8T**F17$Ffu$!+*G)pf**F17$F[v$!+\"fT)*)**F17$F`v$! +^EW(***F17$Fjv$!+FV!*****F17$F_w$!+7X******F17$Fdw$!+++++5Fa]l7$Fiw$! +We******F17$F^x$!+[K*)****F17$Fhx$!+>$oy***F17$Fby$!+f*f)*)**F17$F]z$ !+8^%=&**F17$$!+&4Avy(Fiy$!+%o!=J**F17$$!+5rc&H(Fiy$!+PCp,**F17$$!+D@h .oFiy$!+Bzlf)*F17$Fbz$!+!3J)*z*F17$$!+qruF`Fiy$!+cmd%f*F17$Fgz$!+_/\\( =*F17$F\\[l$!+!fv-K)F17$Fa[l$!+&)RE(o'F17$$!+Wwj!p\"Fiy$!+mM`yaF17$Ff[ l$!+p5n()RF17$$!+:#yNH'F[t$!+aoJ^AF17$F[\\l$!++2I\"f$Fiy7$$\"+&GyY_%F[ t$\"+1T.K;F17$F`\\l$\"+'>n&)\\$F17$$\"+1$R[b\"Fiy$\"+UwIB^F17$Fe\\l$\" +6[$)[kF17$Fj\\l$\"+>%H`B)F17$F_]l$\"+/\"=&o\"*F17$$\"++cQq_Fiy$\"+Lal x&*F17$Fe]l$\"+UKq(y*F17$$\"++?\")4nFiy$\"+%\\:)\\)*F17$$\"++3i*=(Fiy$ \"+8H&Q*)*F17$$\"++'H%pwFiy$\"+0k-D**F17$Fj]l$\"+-#pq%**F17$F_^l$\"+)Q p#))**F17$Fd^l$\"+>ZS(***F17$F^_l$\"+tb))****F17$Fh_l$\"+Y]******F17$F ]`lFcam7$Fb`l$\"+wY******F17$Fg`l$\"+g+*)****F17$Faal$\"+b0W(***F17$Ff al$\"+8%p$*)**F17$F[bl$\"+]s!f&**F17$$\"+cRR8UF1$\"+0A*\\$**F17$$\"+70 (oE%F1$\"+LS?/**F17$$\"+oqM?VF1$\"+Gw$*e)*F17$F`bl$\"+IY]#z*F17$$\"+Pn x![%F1$\"+@Y[`&*F17$Febl$\"+-WJ_!*F17$Fjbl$\"+*))=X7)F17$F_cl$\"+?**Hd kF17$$\"+7iJR[F1$\"+^b_h_F17$Fdcl$\"+BK&Q\"QF17$$\"+d2&*R\\F1$\"+0IN^@ F17$Ficl$\"+OxZSNFiy7$$\"+xS'G/&F1$!+bv]Z:F17$F^dl$!+nY#4M$F17$$\"+sh0 [^F1$!++:=@\\F17$Fcdl$!+0uLKiF17$Fhdl$!+!pM;0)F17$F]el$!+(*RdF1$!+\\!>V*)*F17$$\"+p@*4x&F1$!+Wg>F**F17$Fgel$!+G4()\\**F17$Fa fl$!+-Q_*)**F17$F[gl$!+#Q9y***F17$Fegl$!+@P*)****F17$Fjgl$!+/c******F1 7$F_hl$!+)*********F17$Fdhl$!+7f******F17$Fihl$!+#\\&))****F17$Fcil$!+ qI%z***F17$F]jl$!+8&H/***F17$Fgjl$!+)3Qb&**F17$$\"+XCh6#*F1$!+uq#e$**F 17$$\"+I&f@E*F1$!+\"R=u!**F17$$\"+:mq7$*F1$!+Px^m)*F17$F\\[m$!+iEs2)*F 17$$\"+qyMk%*F1$!+xH\"Gg*F17$Fa[m$!+`&y%)=*F17$Ff[m$!+3D\"RH)F17$F[\\m $!+;\\b)e'F17$$\"+l2/P)*F1$!+JK:@`F17$F`\\m$!+AC,gPF17$$\"+b-oX**F1$!+ 7:h^>F17$Fe\\m$!+]+++5F--Fj\\m6&F\\]mF_]mF]]mF_]m-F$6$7[s7$F($\"3$\\q% H)f$H\\C!#L7$$!3!RLL$e%G?y*!#=$\"3H60Q#=y_O\"Fh]o7$$!3pmmm;p0k&*Fh]o$ \"3hH:>$3))\\q#Fh]o7$$!3F++vV5Su$*Fh]o$\"3@!\\'[P4JIQFh]o7$$!3vKL$3na'y)>-'Fh]o7$$!3 nmmmT%p\"e()Fh]o$\"3L`=**Fh]o7$$!3in m\"zHmPl(Fh]o$\"3Z%3p/wkL&**Fh]o7$$!3RMLLL)QUg(Fh]o$\"3n>#ffcf&y**Fh]o 7$$!3/++vo8ravFh]o$\"3g0(3w(>4%***Fh]o7$$!3\"ommT!R=0vFh]o$\"3ivE9bp%* ****Fh]o7$$!37MLL$3,RX(Fh]o$\"3qu(HS\\0e***Fh]o7$$!3K++]i#=ES(Fh]o$\"3 jP$Htu'G\")**Fh]o7$$!3`mmmTaL^tFh]o$\"3Mh<)yy0k&**Fh]o7$$!3tKL$3i_+I(F h]o$\"3UiQ?Y%)=@**Fh]o7$$!3Cmm;zp[(>(Fh]o$\"3=T\"oXb,*>)*Fh]o7$$!3w*** *\\P8#\\4(Fh]o$\"3!H+#)GdYyn*Fh]o7$$!3$RLL3FuF)oFh]o$\"33\"y:\"Q!ytD*F h]o7$$!3*pmmT?F1n'Fh]o$\"3dwp41'pEn)Fh]o7$$!3tLL$e\\g\"fkFh]o$\"32Qt\\ &>'pOzFh]o7$$!3\\++](y$pZiFh]o$\"3&[a/(fT\"31(Fh]o7$$!3MnmT&Gu,.'Fh]o$ \"3pL`b>!p,.'Fh]o7$$!33LLL$yaE\"eFh]o$\"31YnYA41()[Fh]o7$$!3&)****\\([ j5i&Fh]o$\"3wv\\:b:(R!QFh]o7$$!3hmmm\">s%HaFh]o$\"3768tKP#em#Fh]o7$$!3 ]LL$3x&y8_Fh]o$\"3$)\\Kf$y>#R8Fh]o7$$!3S+++]$*4)*\\Fh]o$!33<^bJL@%>\"! #?7$$!3E++++t_\"y%Fh]o$!3P[9TdMp(3()Fh]o7$$!3!QLL$eW%o7$Fh]o$!31CW_ vTNM#*Fh]o7$$!3*RLLLtIf$HFh]o$!3684k'3Csi*Fh]o7$$!3M+]P4<*[#GFh]o$!3G* >n?1mBz*Fh]o7$$!3CnmT&o_Qr#Fh]o$!3sa2%GZi)4**Fh]o7$$!3U+vVtJLeEFh]o$!3 d5VR*zb0&**Fh]o7$$!3:M$e9m8Gg#Fh]o$!3!*=][I;9z**Fh]o7$$!3Kn\"z%\\THZDF h]o$!3?`F&Q=&e&***Fh]o7$$!3]++]PYx\"\\#Fh]o$!3'3,X:Xm)****Fh]o7$$!3An \"z>YIEW#Fh]o$!3WS+!*3S]$***Fh]o7$$!3'RLekG'[$R#Fh]o$!3(3fBq)Qhx**Fh]o 7$$!3n+v$46UVM#Fh]o$!3'R9b`B6A&**Fh]o7$$!3SnmTNz>&H#Fh]o$!3gI(eCF?t\"* *Fh]o7$$!3%3+vVe4p>#Fh]o$!3Zr%)p&[:#>)*Fh]o7$$!3GMLLL7i)4#Fh]o$!3m-$z \\ctOo*Fh]o7$$!3#pm;aVXH)=Fh]o$!3f(pAlo%yd#*Fh]o7$$!3d****\\P'psm\"Fh] o$!38ZC-0x9i')Fh]o7$$!3r*****\\F&*=Y\"Fh]o$!3M>^I5y8ZzFh]o7$$!3()**** \\74_c7Fh]o$!3;jjII+)**4(Fh]o7$$!3ZmmT5VBU5Fh]o$!3G]-[&[V/4'Fh]o7$$!3) 3LLL3x%z#)!#>$!3[Xsg*4m1(\\Fh]o7$$!3fKL$e9d;J'F\\`p$!30uB!G\"pfiQFh]o7 $$!3JMLL3s$QM%F\\`p$!3/&\\+/Gabp#Fh]o7$$!3T,+]ivF@AF\\`p$!3u;9IOK9\"R \"Fh]o7$$!3\\^omm;zr)*!#@$!3HUStj)*e-iFfgo7$$\"3@CL$3-Dg5#F\\`p$\"32rh oAiR>8Fh]o7$$\"3%pJL$ezw5VF\\`p$\"3yEYga&Rbn#Fh]o7$$\"3L`mmmJ+IiF\\`p$ \"3$[mE,Zf#Fh]o$\"3:mhE xCI#)**Fh]o7$$\"3N)\\(o/q'4l#Fh]o$\"3hCSg=g/b**Fh]o7$$\"3L)**\\(=GB2FF h]o$\"3FG\"Qxz[`\"**Fh]o7$$\"3F)*\\(oWk(>GFh]o$\"3+G_2#*f%))z*Fh]o7$$ \"3B)****\\2'HKHFh]o$\"3\\zI!)\\iPL'*Fh]o7$$\"3uJL$3UDX8$Fh]o$\"3'*)Hv rREd@*Fh]o7$$\"3ElmmmZvOLFh]o$\"3/k&\\\\G&[\\')Fh]o7$$\"3h******\\2goP Fh]o$\"3we=NBe%z)pFh]o7$$\"3,mm\"H2fU'RFh]o$\"3gHzE>O.egFh]o7$$\"3UKL$ eR<*fTFh]o$\"3k6(Fh]o$!3.jgp)*yf>)*Fh]o7$$\"3c***\\(o!*R -tFh]o$!3*4aP$))\\-B**Fh]o7$$\"3)f;a)eH)\\N(Fh]o$!3[4q)*ps^e**Fh]o7$$ \"3^L$e*[oc2uFh]o$!3#e%R:#yRJ)**Fh]o7$$\"3$**\\i!R2:guFh]o$!3?IzC\\c'o ***Fh]o7$$\"3Mmm;HYt7vFh]o$!33L!>%*))z'****Fh]o7$$\"3*H$3-jP0hvFh]o$!3 Ulw%)*)Hk#***Fh]o7$$\"3j**\\(o*GP4wFh]o$!3Iug')*R'Rw**Fh]o7$$\"3Em\"H2 .#pdwFh]o$!3=nn4$4b4&**Fh]o7$$\"3\"HL$ek6,1xFh]o$!3O*GYu^Uj\"**Fh]o7$$ \"3>m;HK%\\E!yFh]o$!3=kO4&eR(>)*Fh]o7$$\"3Y*******p(G**yFh]o$!3d\"Q**f lVpo*Fh]o7$$\"3)HLL3U/37)Fh]o$!3r(zx(f8&)[#*Fh]o7$$\"3]mmmT6KU$)Fh]o$! 32P0$Q1!)=j)Fh]o7$$\"3a****\\P$[/a)Fh]o$!3ovGOR6>QzFh]o7$$\"3fKLLLbdQ( )Fh]o$!3vDPpqFk@rFh]o7$$\"3`mm\"zW?)\\*)Fh]o$!3\"4@A!=>'*HhFh]o7$$\"3[ ++]i`1h\"*Fh]o$!3u\">Cu*yWI]Fh]o7$$\"3X++++PDj$*Fh]o$!3O,C5^c\"\\*QFh] o7$$\"3W++]P?Wl&*Fh]o$!3=:t.L&3mp#Fh]o7$$\"3B++v=5s#y*Fh]o$!3%)z\")49t '4O\"Fh]o7$Fe\\m$!3$\\q%H)f$H\\CFd]o-Fj\\m6&F\\]mF]]mF]]mF_]m-F$6$7eq7 $F($!+(ohL0\"Fh]o7$F5$\"+ff*\\'>F17$F?$\"+Q2A(z$F17$FD$\"+s8u/_F17$FI$ \"+e(\\5S'F17$FN$\"+TZl'[(F17$FS$\"+$\\%)zJ)F17$FX$\"+g/-O*)F17$Fgn$\" +qwkw$*F17$$!+c[3:\")F1$\"+6sqw'*F17$F\\o$\"+L6Eo)*F17$$!+iPH.xF1$\"+1 C/n**F17$Fao$\"+e(y*****F17$$!+?E0+tF1$\"+Pv7o**F17$Ffo$\"+dcvl)*F17$$ !+qUx#)oF1$\"+q5Gu'*F17$F[p$\"+k^hv$*F17$F`p$\"+!*GSU*)F17$Fep$\"+2ieP $)F17$F_q$\"+[#QR\\(F17$Fiq$\"+qW8'Q'F17$F^r$\"+(3oM<&F17$Fcr$\"+5rzXP F17$F]s$\"+\">A\"G>F17$Fgs$!+)e3Qt\"F[t7$Fbt$!+(\\2%p>F17$F\\u$!+_T4!z $F17$Fau$!+$G'oG`F17$Ffu$!+QG'*4mF17$F[v$!+([>ia(F17$F`v$!+i$)3$G)F17$ Fev$!+?(eo$*)F17$Fjv$!+F%*=&R*F17$$!+eW%o7$F1$!+)[YKm*F17$F_w$!+&G%pV) *F17$$!+3<*[#GF1$!+cco9**F17$$!+%o_Qr#F1$!+Hh\\j**F17$$!+gO\"Gg#F1$!+5 [i\"***F17$Fdw$!+7l%*****F17$$!+Mz>&H#F1$!+;sam**F17$Fiw$!+#)zFo)*F17$ $!+Ma%H)=F1$!+OaZu'*F17$F^x$!+u6))p$*F17$Fcx$!+)*e,\\*)F17$Fhx$!+1%*ym $)F17$Fby$!+8@JZvF17$F]z$!+42FtkF17$Fbz$!+M'eHC&F17$Fgz$!+/w%[y$F17$Fa [l$!+<)f:+#F17$F[\\l$!+(\\@]+*F[t7$F`\\l$\"+nJWK\"*Fiy7$Fe\\l$\"+Lo/+> F17$Fj\\l$\"+B$)Q`GF17$F_]l$\"+K\"o&ePF17$Fe]l$\"+)*z$o=&F17$Fj]l$\"+, L:*R'F17$F_^l$\"+&yF#euF17$Fd^l$\"+\\#)=w#)F17$Fi^l$\"+!z3V!*)F17$F^_l $\"+6F[`$*F17$Fc_l$\"+^$*Qc'*F17$Fh_l$\"+k/+`)*F17$$\"+X+ZzAF1$\"+1t:h **F17$F]`l$\"+b'[(****F17$$\"+!>,Zf#F1$\"+en*G***F17$$\"+?GB2FF1$\"+27 ul**F17$$\"+]Ww>GF1$\"+tST<**F17$Fb`l$\"+a'*QY)*F17$$\"+Da_MJF1$\"+-iF a'*F17$Fg`l$\"+WM'HO*F17$F\\al$\"+b_W8*)F17$Faal$\"+P\\q#G)F17$Ffal$\" +Bbn=vF17$F[bl$\"+4*)RTlF17$F`bl$\"+cSr3_F17$Febl$\"+6]43OF17$F_cl$\"+ ,Nc.>F17$Ficl$\"+-L[x))F[t7$Fcdl$!+6%4@\"=F17$F]el$!+$*Q;)f$F17$Fbel$! +\")=WV^F17$Fgel$!+wx!>W'F17$Fafl$!+9'ov_(F17$F[gl$!+p$zaN)F17$F`gl$!+ Q!3c%*)F17$Fegl$!+bf#4P*F17$$\"+?<(*zoF1$!+)o)3r'*F17$Fjgl$!+c%*yj)*F1 7$$\"+!HJs>(F1$!+#)H7E**F17$$\"+q!*R-tF1$!+Et()o**F17$$\"+]oc2uF1$!+FN B$***F17$F_hl$!+&zr)****F17$$\"+l6,1xF1$!+?v9m**F17$Fdhl$!+d>pp)*F17$$ \"+?W!37)F1$!+%H,-n*F17$Fihl$!+NSJ`$*F17$F^il$!+G0NV*)F17$Fcil$!+QM&GQ )F17$F]jl$!+_?.#e(F17$Fgjl$!+gB*\\`'F17$F\\[m$!+6c3\"G&F17$Fa[m$!+H2B' y$F17$F[\\m$!+m$)*)e>F17$Fe\\m$\"+(ohL0\"Fh]o-Fj\\m6&F\\]mF_]mF_]mF]]m -%+AXESLABELSG6$Q\"x6\"Q!F]\\s-%%VIEWG6$;F(Fe\\m%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "C urve 3" "Curve 4" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 "R" }{MPLTEXT 1 0 0 "" }{TEXT -1 20 "escaled CN function:" }{MPLTEXT 1 0 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "CN := (x,k) -> JacobiCN(x*(4*Ellipt icK(k)),k);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "plot(\{CN(x,0),CN(x, 0.9),CN(x,0.999),CN(x,0.9999999)\},x=-1..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#CNGf*6$%\"xG%\"kG6\"6$%)operatorG%&arrowGF)-%)Jacobi CNG6$,$*&9$\"\"\"-%*EllipticKG6#9%F3\"\"%F7F)F)F)" }}{PARA 13 "" 1 "" {GLPLOT2D 635 298 298 {PLOTDATA 2 "6(-%'CURVESG6$7ar7$$!\"\"\"\"!$\"++ +++5!\"*7$$!+HU,\"*)*!#5$\"+T`zh#*F17$$!+e%G?y*F1$\"+t!*>5vF17$$!+(oUI n*F1$\"+j!y\"pbF17$$!+t %FR7$$!+vL\"['))F1$\"+zhq5KFR7$$!+U%p\"e()F1$\"+4e2y@FR7$$!+nxYV&)F1$ \"+N6Nn**!#77$$!+#4m(G$)F1$\"+)R&4aXFao7$$!+@OS,zF1$\"+*Qt$=\"*!#87$$! +/R=0vF1$\"+v[,Q%)!#:7$$!+P8#\\4(F1$!+VM.b#*F\\p7$$!+/siqmF1$!+i2@kXFa o7$$!+'\\g\"fkF1$!+K4Ps)*Fao7$$!+(y$pZiF1$!+,04K@FR7$$!+PS$*QhF1$!+]7B nJFR7$$!+'Gu,.'F1$!+IY+/ZFR7$$!+NXT@fF1$!+6:y$)pFR7$$!+$yaE\"eF1$!+rL+ O5F17$$!+)[j5i&F1$!+9\"*yj?F17$$!+\">s%HaF1$!+g'*p8SF17$$!+#)*G;K&F1$! +'Hs#fcF17$$!+rdy8_F1$!+\"4Cce(F17$$!+hD%f5&F1$!+ut1+$*F17$$!+]$*4)*\\ F1$!+V2w****F17$$!+DL\")*)[F1$!+&ynkC*F17$$!++t_\"y%F1$!+vF:,vF17$$!+v 7CtYF1$!++=_sbF17$$!+]_&\\c%F1$!+5.qRRF17$$!++;ggWF1$!+^=-aFF17$$!+]zC cVF1$!+CiL.>F17$$!++V*=D%F1$!+5^C38F17$$!+]1aZTF1$!+_**))o*)FR7$$!+FW, eRF1$!+*Gti]%FR7$$!+/#)[oPF1$!+WcUhAFR7$$!+%>BJa$F1$!+dr%[&**Fao7$$!+$ =exJ$F1$!+eMPuVFao7$$!+L2$f$HF1$!+#\\/q/\"Fao7$$!+PYx\"\\#F1$\"+-2**Q8 !#97$$!+L7i)4#F1$\"++[X<\"*F\\p7$$!+P'psm\"F1$\"+^Nf?YFao7$$!+u_*=Y\"F 1$\"+&3+Xx*Fao7$$!+74_c7F1$\"+RAok?FR7$$!+6wP\\6F1$\"+a'\\\"\\IFR7$$!+ 5VBU5F1$\"+?'*>-XFR7$$!+!454N*FR$\"+!yIak'FR7$$!*3x%z#)F1$\"+BR$>!)*FR 7$$!+Srl6jFR$\"+kl!3*>F17$$!*?PQM%F1$\"+J)>%[RF17$$!+ytb#G$FR$\"+xHMZb F17$$!+bvF@AFR$\"+pd3NuF17$$!+Lx**f6FR$\"+5B_q\"*F17$$!(\"zr)*F1$\"+.# \\N***F17$$\"+nNl.5FR$\"+7A.o$*F17$$\"+X]-1@FR$\"+7!4Gk(F17$$\"+AlR3KF R$\"+.XoscF17$$\")!o2J%F-$\"+5qF#*RF17$$\"++K+IiFR$\"+)>,'\\?F17$$\")% Q#\\\")F-$\"+K#Gv-\"F17$$\"++dF1$!+eH)*\\9F17$$\"*U9C#eF- $!+5V.+5F17$$\"+!3$3IfF1$!+]&)QnnFR7$$\"+SuWi$*F\\p7$$\"*jMF^(F-$\"+q\"yM 2#F_y7$$\"*q(G**yF-$\"+NCVS!*F\\p7$$\"*9@BM)F-$\"+![yay%Fao7$$\"+N$[/a )F1$\"+4AJe)*Fao7$$\"*`v&Q()F-$\"+61;G?FR7$$\"+()z>W))F1$\"+rjqyHFR7$$ \"+X/#)\\*)F1$\"+*)H*RP%FR7$$\"+-HWb!*F1$\"++%\\3U'FR7$$\"*Ol5;*F-$\"+ !*fX>%*FR7$$\"+I&f@E*F1$\"+FQfd8F17$$\"++PDj$*F1$\"+Lub^>F17$$\"+qyMk% *F1$\"+BuL!z#F17$$\"*/Uac*F-$\"+X)>h%RF17$$\"+I:3u'*F1$\"+[>o'e&F17$$ \"+?5s#y*F1$\"+l_pAvF17$$\"+50O\"*)*F1$\"+)e\">m#*F17$$\"\"\"F*F+-%'CO LOURG6&%$RGBG$\"#5F)$F*F*Ff`m-F$6$7hqF'7$F?$\"+Zh+^#*F17$FD$\"+SVxQ&)F 17$FI$\"+)euGo(F17$FT$\"+s'z%HmF17$Fhn$\"+#zx2b&F17$F]o$\"+N4g)[%F17$F co$\"+[0TvMF17$$!+c[3:\")F1$\"+<#p@_#F17$Fho$\"+\")\\%yh\"F17$F^p$\"+y &o71#Fao7$Fdp$!+.S0L;F17$$!+qUx#)oF1$!+M#f9`#F17$Fip$!+a\\>yMF17$F^q$! +K?(eZ%F17$Fcq$!+p6H@bF17$F]r$!+B`C@mF17$Fgr$!+)*oF&p(F17$F\\s$!+U$exb )F17$Fas$!+^r%>F*F17$Ffs$!+Y#zAe*F17$F[t$!+OnN7)*F17$$!+mT')f^F1$!+C!f W*)*F17$F`t$!+NVX`**F17$$!+b4-_]F1$!+)G\\())**F17$Fet$!+d\\)*****F17$$ !+Pj&R%\\F1$!+pO%p)**F17$Fjt$!+%)Qm\\**F17$$!+7.nN[F1$!+Mv_)))*F17$F_u $!+=R:/)*F17$Fdu$!+!*eDp&*F17$Fiu$!+Y\"GRD*F17$F]w$!+Z<*Q](F17$Fbw$!+X #)fhlF17$Fgw$!+Pyr-cF17$F\\x$!+3<$p[%F17$Fax$!+E%p\\U$F17$$!+eW%o7$F1$ !+b+EtDF17$Ffx$!+X&f6w\"F17$F[y$\"+a$[1F$Fao7$Fay$\"+k@u<;F17$$!+Ma%H) =F1$\"+4jrIDF17$Ffy$\"+(G7O\\$F17$F[z$\"+l`jiWF17$F`z$\"+_m$pZ&F17$Fjz $\"+X9MglF17$Fd[l$\"+zM7AwF17$Fi[l$\"+#ph`^)F17$F^\\l$\"+F_2c#*F17$Fc \\l$\"+M6Ul&*F17$Fh\\l$\"+Q/k(z*F17$$!+Wwj!p\"FR$\"+xl1#))*F17$F]]l$\" +:TBW**F17$$!+:#yNH'Fao$\"+4*QN)**F17$Fb]l$\"+XXf****F17$$\"+&GyY_%Fao $\"+!*p[\"***F17$Fg]l$\"+>>@e**F17$$\"+1$R[b\"FR$\"+OJ7+**F17$F\\^l$\" +J=$y\")*F17$Fa^l$\"+]qE%e*F17$Ff^l$\"+:vxm#*F17$F[_l$\"+&[h'\\&)F17$F `_l$\"+]UX%o(F17$Fj_l$\"+iTWhmF17$Fd`l$\"+'\\0Hh&F17$Fi`l$\"+=]=^XF17$ F^al$\"+E;GPNF17$$\"+:JFn=F1$\"+XP())f#F17$Fcal$\"+7sK3s%HaFggn$!3jn$ *o%Q@\"Q'*Fggn7$$!3]***\\7)*G;K&Fggn$!3%y3b>K,lz*Fggn7$$!3]LL$3x&y8_Fg gn$!3P1xJ(y=*4**Fggn7$$!30,]ilT')f^Fggn$!3(=jW&*y&f\\**Fggn7$$!3]nmTgD %f5&Fggn$!3#\\#\\xMK&y(**Fggn7$$!3%RL3_&4-_]Fggn$!3)p)ey!peY***Fggn7$$ !3S+++]$*4)*\\Fggn$!270q#pG******!#<7$$!3j++]Pj&R%\\Fggn$!3wyC5o2!Q*** Fggn7$$!3L+++DL\")*)[Fggn$!3?\"yXN*R/w**Fggn7$$!3,++]7.nN[Fggn$!3+yyY$ 4Vn%**Fggn7$$!3E++++t_\"y%Fggn$!3bo@Uu>$f!**Fggn7$$!3>+++v7CtYFggn$!3b )RQ#[7)**y*Fggn7$$!38+++]_&\\c%Fggn$!3`q[Nl$G(G'*Fggn7$$!34+++]zCcVFgg n$!3ga)pVMmI>*Fggn7$$!30+++]1aZTFggn$!3c^n(y+W&*f)Fggn7$$!3RLL3FW,eRFg gn$!3[k%G(RMJKzFggn7$$!3vmm;/#)[oPFggn$!3ALsV-)HF:(Fggn7$$!3<++v$>BJa$ Fggn$!3/zFq:A([4'Fggn7$$!3hLLL$=exJ$Fggn$!3VzH0T8,:\\Fggn7$$!3!QLL$eW% o7$Fggn$!3'zk:#f'Qv$QFggn7$$!3*RLLLtIf$HFggn$!3V(Hw&yL\"\\q#Fggn7$$!3C nmT&o_Qr#Fggn$!3#[H\"zJkjR8Fggn7$$!3]++]PYx\"\\#Fggn$\"3y=s*RnC\"o^Fe \\o7$$!3SnmTNz>&H#Fggn$\"3jpghH4E$G\"Fggn7$$!3GMLLL7i)4#Fggn$\"3YwwL=) )G&\\#Fggn7$$!3#pm;aVXH)=Fggn$\"3]5Zm>Vm!y$Fggn7$$!3d****\\P'psm\"Fggn $\"3'p0.pj=n*\\Fggn7$$!3r*****\\F&*=Y\"Fggn$\"3=j>(>aV)pgFggn7$$!3()** **\\74_c7Fggn$\"3*)[#[1*o.UqFggn7$$!3ZmmT5VBU5Fggn$\"3f9wA$oh8$zFggn7$ $!3)3LLL3x%z#)!#>$\"3!3TgD'Q7x')Fggn7$$!3fKL$e9d;J'F]io$\"3Lh.N_2!RA*F ggn7$$!3JMLL3s$QM%F]io$\"3.A/,f([)H'*Fggn7$$!3'ym;aQdDG$F]io$\"3Am\\%3 Kf!)y*Fggn7$$!3T,+]ivF@AF]io$\"3FnxxvKw-**Fggn7$$!3?o;/^wj!p\"F]io$\"3 &Q[ywKLO%**Fggn7$$!3'\\L$eRx**f6F]io$\"3$o@'fV#*Fggn7$$\" 3r*)***\\PQ#\\\")F]io$\"3m?()GP&3vr)Fggn7$$\"3ilm\"z\\1A-\"Fggn$\"3E!p k=*GP2!)Fggn7$$\"3GKLLe\"*[H7Fggn$\"3MT:\">P0;;(Fggn7$$\"3ylm;HCjV9Fgg n$\"3XK))4;WjghFggn7$$\"3I*******pvxl\"Fggn$\"3i,K6>5I[]Fggn7$$\"3h)** *\\7JFn=Fggn$\"3nkXG0HkrQFggn7$$\"3$z****\\_qn2#Fggn$\"3L'R9Zh)*zi#Fgg n7$$\"3=)**\\P/q%zAFggn$\"3**>&[?)3?\"Q\"Fggn7$$\"3V)***\\i&p@[#Fggn$ \"3MOg%Q*fH?6F]io7$$\"3L)**\\(=GB2FFggn$!3gGVI'f?)QFggn7$$ \"3ElmmmZvOLFggn$!3unm\"H\"eg=]Fggn7$$\"3VKLLexn_NFggn$!3eG>I'4cB9'Fgg n7$$\"3h******\\2goPFggn$!3'RnV.(RA`rFggn7$$\"3,mm\"H2fU'RFggn$!3\">;( *G3Wh&zFggn7$$\"3UKL$eR<*fTFggn$!3f\"*[9rF(*Q')Fggn7$$\"3/mm\"HiBQP%Fg gn$!3=;0=PU'fB*Fggn7$$\"3m******\\)Hxe%Fggn$!3m3I&*\\5Pm'*Fggn7$$\"3!f m\"z%Rk$)o%Fggn$!3[E)oF#4\"*3)*Fggn7$$\"37KLeR*)**)y%Fggn$!3^=/+IoC7** Fggn7$$\"3^l\"z>@;$R[Fggn$!355N!31y!\\**Fggn7$$\"3M)*\\P%[L'*)[Fggn$!3 s!eW*3o'R$*\\Fgg n7$$\"3ILL$3sr*zoFggn$!3G=!Q`Kbzz$Fggn7$$\"3wKLL3N1#4(Fggn$!3==!>Gbn^` #Fggn7$$\"3c***\\(o!*R-tFggn$!3rzQC&)fPQ7Fggn7$$\"3Mmm;HYt7vFggn$\"3\\ jyD4\"=8+)Fe\\o7$$\"3\"HL$ek6,1xFggn$\"3GM%\\hu%z!H\"Fggn7$$\"3Y****** *p(G**yFggn$\"3i>3I;Pc#[#Fggn7$$\"3)HLL3U/37)Fggn$\"3jKa#46mC!QFggn7$$ \"3]mmmT6KU$)Fggn$\"3$fjOgDE)[]Fggn7$$\"3a****\\P$[/a)Fggn$\"3_i!4oRR: 3'Fggn7$$\"3fKLLLbdQ()Fggn$\"3t59F17$Fcq$!+GDLx?F17$F]r$!+<;[\\IF17$Fgr$!+S AW&R%F17$F\\s$!+z&\\+\"fF17$Fas$!+2\"GLh(F17$F[t$!+5k*QI*F17$Fet$!+%fT *****F17$F_u$!+0n!\\F*F17$Fiu$!+#HoPc(F17$Fcv$!+Mbq;dF17$F]w$!+$zr&=TF 17$Fbw$!+DSv()HF17$Fgw$!+=^cQ@F17$F\\x$!+zWv;9F17$Fax$!+(e/<>*FR7$Ffx$ !+gT=tQFR7$F[y$\"+DuR8mF\\p7$Fay$\"+'ysK^$FR7$Ffy$\"+T$3)o%*FR7$F[z$\" +f)\\NS\"F17$F`z$\"+)y2Y/#F17$Fjz$\"+))fY')HF17$Fd[l$\"+sIV(G%F17$Fi[l $\"+W&yN#eF17$F^\\l$\"+CKlpvF17$Fh\\l$\"+l#p>D*F17$Fb]l$\"+qXU)***F17$ F\\^l$\"+\\.JB$*F17$Ff^l$\"+<&p!*f(F17$F[_l$\"+Q\\U$*eF17$F`_l$\"+R\") GzVF17$Fj_l$\"+S8v\"4$F17$Fd`l$\"+uJLY@F17$Fi`l$\"+)HN@X\"F17$F^al$\"+ #[()zk*FR7$Fcal$\"+w'G#RPFR7$Fhal$\"+!H/QV\"Fao7$F]bl$!+9*[Y$QFR7$Fbbl $!+7&GWa*FR7$Fgbl$!+'=+AW\"F17$F\\cl$!+zm**Q@F17$Facl$!+k8D?IF17$Ffcl$ !+'*)yJ?%F17$F`dl$!+!\\5i'eF17$Fjdl$!+9W[lxF17$Fdel$!+h>*3K*F17$F^fl$! +t)o%)***F17$Fhfl$!+mn_#Q*F17$Fbgl$!+eBMwxF17$F\\hl$!+?COZfF17$Ffhl$!+ (*zFEVF17$F`il$!+%H`(4IF17$Fjil$!+#[us0#F17$F_jl$!+A3D29F17$Fdjl$!+oJQ d%*FR7$Fijl$!+iR]!e$FR7$F^[m$\"+,s%R-\"Fao7$Fc[m$\"+$=P>\\$FR7$Fh[m$\" +s\"H)\\'*FR7$F]\\m$\"+/Fq49F17$Fb\\m$\"+JBjE?F17$F\\]m$\"+\"Rzb%HF17$ Ff]m$\"+6U46UF17$F`^m$\"+\")=2wdF17$Fj^m$\"+#3-\"ovF17$Fd_m$\"+8bL#G*F 1F]`m-Fa`m6&Fc`mFf`mFf`mFd`m-%+AXESLABELSG6$Q\"x6\"Q!F]_r-%%VIEWG6$;F( F^`m%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 "R" }{MPLTEXT 1 0 0 "" }{TEXT -1 20 "escaled DN function:" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "DN := (x,k) -> JacobiDN(x*(2*EllipticK(k)),k);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "plot(\{DN(x,0),DN(x,0.9),DN(x,0.999),DN(x,0.9999999)\},x=-1..1);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#DNGf*6$%\"xG%\"kG6\"6$%)operatorG%& arrowGF)-%)JacobiDNG6$,$*&9$\"\"\"-%*EllipticKG6#9%F3\"\"#F7F)F)F)" }} {PARA 13 "" 1 "" {GLPLOT2D 635 298 298 {PLOTDATA 2 "6(-%'CURVESG6$7S7$ $!\"\"\"\"!$\"\"\"F*7$$!3pmmm;p0k&*!#=F+7$$!3vKL$3s%HaF0F+7$$!3S+++]$*4)*\\F0F+7$$!38+++]_&\\c% F0F+7$$!30+++]1aZTF0F+7$$!3vmm;/#)[oPF0F+7$$!3hLLL$=exJ$F0F+7$$!3*RLLL tIf$HF0F+7$$!3]++]PYx\"\\#F0F+7$$!3GMLLL7i)4#F0F+7$$!3d****\\P'psm\"F0 F+7$$!3()****\\74_c7F0F+7$$!3)3LLL3x%z#)!#>F+7$$!3JMLL3s$QM%FjoF+7$$!3 \\^omm;zr)*!#@F+7$$\"3%pJL$ezw5VFjoF+7$$\"3r*)***\\PQ#\\\")FjoF+7$$\"3 GKLLe\"*[H7F0F+7$$\"3I*******pvxl\"F0F+7$$\"3$z****\\_qn2#F0F+7$$\"3V) ***\\i&p@[#F0F+7$$\"3B)****\\2'HKHF0F+7$$\"3ElmmmZvOLF0F+7$$\"3h****** \\2goPF0F+7$$\"3UKL$eR<*fTF0F+7$$\"3m******\\)Hxe%F0F+7$$\"3ckm;H!o-* \\F0F+7$$\"3y)***\\7k.6aF0F+7$$\"3#emmmT9C#eF0F+7$$\"32****\\i!*3`iF0F +7$$\"3%QLLL$*zym'F0F+7$$\"3wKLL3N1#4(F0F+7$$\"3Mmm;HYt7vF0F+7$$\"3Y** *****p(G**yF0F+7$$\"3]mmmT6KU$)F0F+7$$\"3fKLLLbdQ()F0F+7$$\"3[++]i`1h \"*F0F+7$$\"3W++]P?Wl&*F0F+7$F+F+-%'COLOURG6&%$RGBG$\"#5F)$F*F*F^u-F$6 $7aq7$F($\"+++++5!\"*7$$!+HU,\"*)*!#5$\"+jR]1)*Fiu7$$!+e%G?y*Fiu$\"+Ib zh#*Fiu7$$!+(oUIn*Fiu$\"+`d>e%)Fiu7$$!+5vFiu7$$!+!)*G #p%*Fiu$\"+vQ`\\mFiu7$$!+W5Su$*Fiu$\"+zaB5eFiu7$$!+3Jdz#*Fiu$\"+sb%e-& Fiu7$$!+r^u%=*Fiu$\"+dJd9VFiu7$$!+S75y!*Fiu$\"+w$G.h$Fiu7$$!+2tXr*)Fiu $\"+w341IFiu7$$!+vL\"['))Fiu$\"+lYQ%\\#Fiu7$$!+U%p\"e()Fiu$\"+#H$)[1#F iu7$$!+nxYV&)Fiu$\"+I?F09Fiu7$$!+#4m(G$)Fiu$\"+v+ZL&*!#67$$!+c[3:\")Fi u$\"+9G:qkF]z7$$!+@OS,zFiu$\"+93E)Q%F]z7$$!+iPH.xFiu$\"+[B'31$F]z7$$!+ /R=0vFiu$\"+`rxM@F]z7$$!+?E0+tFiu$\"+g)*)*p9F]z7$$!+P8#\\4(Fiu$\"+^wK7 5F]z7$$!+/siqmFiu$\"+\"oJeo%!#77$$!+(y$pZiFiu$\"+?'R&)=#Fa\\l7$$!+$yaE \"eFiu$\"+Bg5K5Fa\\l7$$!+\">s%HaFiu$\"+$oi)3f!#87$$!+]$*4)*\\Fiu$\"+!e i@Z%Fa]l7$$!+]_&\\c%Fiu$\"+!**H$[fFa]l7$$!+]1aZTFiu$\"+e6D-6Fa\\l7$$!+ /#)[oPFiu$\"+4IRE@Fa\\l7$$!+$=exJ$Fiu$\"+z4Z&y%Fa\\l7$$!+L2$f$HFiu$\"+ \"*\\;r&*Fa\\l7$$!+%o_Qr#Fiu$\"+A1GL9F]z7$$!+PYx\"\\#Fiu$\"+k*>m9#F]z7 $$!+Mz>&H#Fiu$\"+W.FpIF]z7$$!+L7i)4#Fiu$\"+sD1)Q%F]z7$$!+Ma%H)=Fiu$\"+ +lL$\\'F]z7$$!+P'psm\"Fiu$\"+\"eu@g*F]z7$$!+u_*=Y\"Fiu$\"+[wv\"R\"Fiu7 $$!+74_c7Fiu$\"+&*Ha6?Fiu7$$!+6wP\\6Fiu$\"+N&HFV#Fiu7$$!+5VBU5Fiu$\"+C $=a$HFiu7$$!+!454N*F]z$\"+C(p-`$Fiu7$$!*3x%z#)Fiu$\"+9?RDUFiu7$$!+5rc& H(F]z$\"+cG+a\\Fiu7$$!+Srl6jF]z$\"+%4HCw&Fiu7$$!+qruF`F]z$\"+*GI9j'Fiu 7$$!*?PQM%Fiu$\"+jsECvFiu7$$!+ytb#G$F]z$\"+NT_Z%)Fiu7$$!+bvF@AF]z$\"+I D>N#*Fiu7$$!+Lx**f6F]z$\"+VeE\"y*Fiu7$$!(\"zr)*Fiu$\"+bmQ)***Fiu7$$\"+ nNl.5F]z$\"+%))*\\N)*Fiu7$$\"+X]-1@F]z$\"+\"=F!3$*Fiu7$$\"+AlR3KF]z$\" +3&)Fiu7$$\")!o2J%Feu$\"+_K2avFiu7$$\"++cQq_F]z$\"+HSG$o'Fiu7$$\"+ +K+IiF]z$\"+!y=E$eFiu7$$\"++3i*=(F]z$\"++kVP]Fiu7$$\")%Q#\\\")Feu$\"+# 3=pJ%Fiu7$$\"++`W=#F]z7 $$\"+?GB2FFiu$\"+l3k]9F]z7$$\"*3'HKHFeu$\"+*33Yj*Fa\\l7$$\"*xanL$Feu$ \"++TfBYFa\\l7$$\"*v+'oPFeu$\"+.t'f7#Fa\\l7$$\"*S<*fTFeu$\"+#QQ)z5Fa\\ l7$$\"*&)Hxe%Feu$\"+vd%3z&Fa]l7$$\"*.o-*\\Feu$\"+ir$GZ%Fa]l7$$\"*TO5T& Feu$\"+!)4g#y&Fa]l7$$\"*U9C#eFeu$\"+v)*y[5Fa\\l7$$\"*1*3`iFeu$\"+I#z'4 AFa\\l7$$\"*$*zym'Feu$\"+o6diYFa\\l7$$\"*^j?4(Feu$\"+s?325F]z7$$\"+q!* R-tFiu$\"+\"\\wiZ\"F]z7$$\"*jMF^(Feu$\"+<\"*Hk@F]z7$$\"+l6,1xFiu$\"+$3 Fg2$F]z7$$\"*q(G**yFeu$\"+`NTrVF]z7$$\"+?W!37)Fiu$\"+c9qPlF]z7$$\"*9@B M)Feu$\"+&GF/x*F]z7$$\"+N$[/a)Fiu$\"+#eZwR\"Fiu7$$\"*`v&Q()Feu$\"+6Q.% *>Fiu7$$\"+()z>W))Fiu$\"+E&*G0CFiu7$$\"+X/#)\\*)Fiu$\"+)*)*4&*GFiu7$$ \"+-HWb!*Fiu$\"+;bwtMFiu7$$\"*Ol5;*Feu$\"+\\pO\\TFiu7$$\"+I&f@E*Fiu$\" +)))>%*)[Fiu7$$\"++PDj$*Fiu$\"+^Kq9dFiu7$$\"+qyMk%*Fiu$\"+e7X0mFiu7$$ \"*/Uac*Feu$\"+UdpAvFiu7$$\"+I:3u'*Fiu$\"+/#>nY)Fiu7$$\"+?5s#y*Fiu$\"+ 5=>m#*Fiu7$$\"+50O\"*)*Fiu$\"+8>r2)*Fiu7$F+Fcu-Fit6&F[uF^uF\\uF^u-F$6$ 7_pFbu7$F]v$\"+]tN6)*Fiu7$Fgv$\"+e&G&z#*Fiu7$Faw$\"+Tqa0')Fiu7$F[x$\"+ [:I6yFiu7$F`x$\"+R\">%QtFiu7$Fex$\"+-)G.'oFiu7$Fjx$\"+G$>fQ'Fiu7$F_y$ \"+CAJAfFiu7$Fdy$\"+=t?U]Fiu7$Fiy$\"+c^O`UFiu7$F_z$\"+&**G\"oNFiu7$Fdz $\"+-<'3)HFiu7$Fiz$\"+h!\\u^#Fiu7$F^[l$\"+^R\"R7#Fiu7$Fh[l$\"+J$Q_\\\" Fiu7$F]\\l$\"+Gfl]5Fiu7$Fc\\l$\"+St_\"e(F]z7$Fh\\l$\"+GbX:dF]z7$F]]l$ \"+>wz2[F]z7$$!+rdy8_Fiu$\"+`?q`XF]z7$Fc]l$\"+*HC5Z%F]z7$$!++t_\"y%Fiu $\"+2*ytb%F]z7$Fh]l$\"++Zq;[F]z7$F]^l$\"++8MYeF]z7$Fb^l$\"+-1\\$\\(F]z 7$Fg^l$\"+yheg5Fiu7$F\\_l$\"+,*\\mX\"Fiu7$Ff_l$\"+M'p%H@Fiu7$F[`l$\"+R Eq?DFiu7$F``l$\"+W))z!)HFiu7$Fe`l$\"+t)*)Rd$Fiu7$Fj`l$\"+Ks-nUFiu7$F_a l$\"+&RA8-&Fiu7$Fdal$\"+8)='feFiu7$Fial$\"+C'pMK'Fiu7$F^bl$\"+E![!*z'F iu7$Fcbl$\"+&fi$zsFiu7$Fhbl$\"+E^ibxFiu7$Fbcl$\"+5he$e)Fiu7$F\\dl$\"+' HlVG*Fiu7$Ffdl$\"+yN@/)*Fiu7$F`el$\"+()og****Fiu7$$\"+&GyY_%Fa\\l$\"+7 qu\"***Fiu7$Feel$\"+1@]f**Fiu7$$\"+1$R[b\"F]z$\"+%okK!**Fiu7$Fjel$\"+; @rB)*Fiu7$F_fl$\"+J*p')f*Fiu7$Fdfl$\"+e)yXH*Fiu7$F^gl$\"+YMw:')Fiu7$Fh gl$\"+<0v7yFiu7$Fbhl$\"+f1r))oFiu7$F\\il$\"+g:AvfFiu7$Fail$\"+0'yE4&Fi u7$Ffil$\"+5n))*H%Fiu7$F[jl$\"+.9#4i$Fiu7$F`jl$\"+Y?aOIFiu7$Fejl$\"+S< ([b#Fiu7$Fjjl$\"+s,6Z@Fiu7$Fd[m$\"+v&R6Y\"Fiu7$Fi[m$\"+>HSW5Fiu7$F^\\m $\"+AQ)G\\(F]z7$Fc\\m$\"+AM&[!eF]z7$Fh\\m$\"+\"eg5y%F]z7$F]]m$\"+0')=r WF]z7$Fb]m$\"+3p=zZF]z7$Fg]m$\"+hm'ou&F]z7$F\\^m$\"+aBB6wF]z7$Fa^m$\"+ ANK[5Fiu7$Ff^m$\"+%*zh\"\\\"Fiu7$F`_m$\"+*>Lx8#Fiu7$Fe_m$\"+=PJBDFiu7$ Fj_m$\"+2U^vHFiu7$F_`m$\"+(pq^e$Fiu7$Fd`m$\"+!*GA+VFiu7$Fi`m$\"+3=WI]F iu7$F^am$\"+!Hj(QeFiu7$Fham$\"+.B_jnFiu7$Fbbm$\"+%4nsq(Fiu7$F\\cm$\"+c )o9c)Fiu7$Ffcm$\"+.b#QG*Fiu7$F`dm$\"+^a`7)*FiuFidm-Fit6&F[uF\\uF\\uF^u -F$6$7_rFbu7$$!+9r]X**Fiu$\"+(p)\\(***Fiu7$Fgu$\"+=A+!***Fiu7$$!+V8_O) *Fiu$\"+'zKv(**Fiu7$F]v$\"+,t7g**Fiu7$Fbv$\"+Kts5**Fiu7$Fgv$\"+1)yB%)* Fiu7$Faw$\"+qCq!o*Fiu7$F[x$\"+Pacp%*Fiu7$Fex$\"+=_\\\"=*Fiu7$F_y$\"+sP P]))Fiu7$Fdy$\"+'>7_[)Fiu7$Fiy$\"+U_k*4)Fiu7$F_z$\"+=CQ1xFiu7$Fdz$\"+U \"pJJ(Fiu7$Fiz$\"+Jt\"e&pFiu7$F^[l$\"+dw+6mFiu7$Fc[l$\"+e)4>F'Fiu7$Fh[ l$\"+rX([&fFiu7$$!+qUx#)oFiu$\"+C#=Ll&Fiu7$F]\\l$\"++k&3Q&Fiu7$$!+'\\g \"fkFiu$\"+D=&)R^Fiu7$Fc\\l$\"+Y,XI\\Fiu7$Fh\\l$\"+Yj],YFiu7$$!+)[j5i& Fiu$\"+.2f+XFiu7$F]]l$\"+YvkEWFiu7$$!+#)*G;K&Fiu$\"+3J*oR%Fiu7$Fihm$\" +_[ovVFiu7$$!+hD%f5&Fiu$\"+=5-jVFiu7$Fc]l$\"+r-!*eVFiu7$$!+DL\")*)[Fiu $\"+-zNjVFiu7$Faim$\"+k*GkP%Fiu7$$!+v7CtYFiu$\"+D[6)R%Fiu7$Fh]l$\"+$G< %GWFiu7$$!+]zCcVFiu$\"+WP86XFiu7$F]^l$\"+xL&ei%Fiu7$Fb^l$\"+]([d\"\\Fi u7$Fg^l$\"+X+*\\R&Fiu7$$!+eW%o7$Fiu$\"++/KScFiu7$F\\_l$\"+3PH4fFiu7$Fa _l$\"+@So\\iFiu7$Ff_l$\"+CJ=;mFiu7$F[`l$\"+#*o\\epFiu7$F``l$\"+NP78tFi u7$Fe`l$\"+^4-5xFiu7$Fj`l$\"+aH)o5)Fiu7$F_al$\"+#f#yv%)Fiu7$Fdal$\"+** RFE))Fiu7$F^bl$\"+A9Th\"*Fiu7$Fhbl$\"+(eHQX*Fiu7$Fbcl$\"+[%z^n*Fiu7$F \\dl$\"+Cp[V)*Fiu7$Fadl$\"+BK-5**Fiu7$Ffdl$\"+J&)fe**Fiu7$$!+Wwj!p\"F] z$\"+O^(f(**Fiu7$F[el$\"+Qan))**Fiu7$$!+:#yNH'Fa\\l$\"+PQm'***Fiu7$F`e l$\"+#)y\"*****Fiu7$Fb]n$\"+n`F)***Fiu7$Feel$\"+r*>:***Fiu7$Fj]n$\"++A nz**Fiu7$Fjel$\"+Dzwi**Fiu7$F_fl$\"+;'3S\"**Fiu7$Fdfl$\"+]X#e%)*Fiu7$F ^gl$\"+*3mKo*Fiu7$Fhgl$\"+IK(*p%*Fiu7$Fbhl$\"+V'H2>*Fiu7$F\\il$\"+PX]q ))Fiu7$Fail$\"+)*4%y])Fiu7$Ffil$\"+,G?C\")Fiu7$F[jl$\"+l6(*QxFiu7$F`jl $\"+z:3`tFiu7$Fejl$\"+_6[')pFiu7$Fjjl$\"+=PbKmFiu7$F_[m$\"+qADgiFiu7$F d[m$\"+9Qj9fFiu7$$\"+Da_MJFiu$\"+ZU)*HcFiu7$Fi[m$\"+B8#>P&Fiu7$F^\\m$ \"+prk:\\Fiu7$Fc\\m$\"+j%e\"=YFiu7$$\"+DO#QP%Fiu$\"+nN$H]%Fiu7$Fh\\m$ \"+u%G8U%Fiu7$$\"+&Rk$)o%Fiu$\"+w&oXR%Fiu7$$\"+S*)**)y%Fiu$\"+*Q]_P%Fi u7$$\"+&[L'*)[Fiu$\"+qCPjVFiu7$F]]m$\"+EP$*eVFiu7$$\"+D,Y&4&Fiu$\"+`cC iVFiu7$$\"+?Al+_Fiu$\"+8dotVFiu7$$\"+:V%eI&Fiu$\"+q]D$R%Fiu7$Fb]m$\"+X `&4U%Fiu7$$\"+:as;cFiu$\"+Tzh)\\%Fiu7$Fg]m$\"+4%otg%Fiu7$F\\^m$\"+.QRN \\Fiu7$$\"+&\\%[gkFiu$\"+CLET^Fiu7$Fa^m$\"+ln_x`Fiu7$$\"+?<(*zoFiu$\"+ U\\_\\cFiu7$Ff^m$\"+f%G1&fFiu7$F[_m$\"+>/nviFiu7$F`_m$\"+IO'Qi'Fiu7$Fe _m$\"+IakgpFiu7$Fj_m$\"+6VI4tFiu7$F_`m$\"+^y%pr(Fiu7$Fd`m$\"+l$zV7)Fiu 7$Fi`m$\"+3[!*z%)Fiu7$F^am$\"+rp>=))Fiu7$Fham$\"+cln\\\"*Fiu7$Fbbm$\"+ >d0S%*Fiu7$F\\cm$\"+&***fp'*Fiu7$Ffcm$\"+vKOV)*Fiu7$F[dm$\"+U()G6**Fiu 7$F`dm$\"+u#z.'**Fiu7$$\"+l2/P)*Fiu$\"+D]nx**Fiu7$Fedm$\"+ub1!***Fiu7$ $\"+b-oX**Fiu$\"+iX^(***FiuFidm-Fit6&F[uF^uF^uF\\u-%+AXESLABELSG6$Q\"x 6\"Q!F\\^p-%%VIEWG6$;F(F+%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" }}}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "Orbits of a pendulum" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "g:=9.8:;L:=0.1:;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "k := t0 -> sin(t0/2);" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 30 "T := t0 -> 4*EllipticK(k(t0));" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 70 "sol := (t,t0) -> 2*arcsin(k(t0)*JacobiSN(sqrt(g/L)* t+T(t0)/4,k(t0))); " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "solresc := ( t,t0) -> sol(t*T(t0)/sqrt(g/L),t0)/t0:;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "plot(\{sol(t,0.1),sol(t,0.5),sol(t,1),sol(t,Pi/2),sol(t,Pi-0.1 )\},t=0..1);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "plot(\{solresc(t,0. 1),solresc(t,0.5),solresc(t,1),solresc(t,Pi/2),solresc(t,Pi-0.1)\},t=0 ..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"kGf*6#%#t0G6\"6$%)operato rG%&arrowGF(-%$sinG6#,$9$#\"\"\"\"\"#F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"TGf*6#%#t0G6\"6$%)operatorG%&arrowGF(,$-%*EllipticK G6#-%\"kG6#9$\"\"%F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$solGf*6 $%\"tG%#t0G6\"6$%)operatorG%&arrowGF),$-%'arcsinG6#*&-%\"kG6#9%\"\"\"- %)JacobiSNG6$,&*&-%%sqrtG6#*&%\"gGF6%\"LG!\"\"F69$F6F6*&#F6\"\"%F6-%\" TGF4F6F6F2F6\"\"#F)F)F)" }}{PARA 13 "" 1 "" {GLPLOT2D 630 298 298 {PLOTDATA 2 "6)-%'CURVESG6$7]p7$$\"\"!F)$\"+++++5!\"*7$$\"+S&)G\\a!#7$ \"+ayv()**!#57$$\"+3x&)*3\"!#6$\"+s10^**F37$$\"+ilyM;F7$\"+'[O**))*F37 $$\"+;arz@F7$\"+uE^/)*F37$$\"+!y%*z7$F7$\"+a7L)f*F37$$\"+XTFwSF7$\"+_5 +?$*F37$$\"+\"z_\"4iF7$\"+/)*\\Q%)F37$$\"+S&phN)F7$\"+)oMf@(F37$$\"+*= )H\\5F3$\"+m%4Tq&F37$$\"+[!3uC\"F3$\"+S0M'3%F37$$\"+!pt*\\8F3$\"+k_>&= $F37$$\"+J$RDX\"F3$\"+7U\"=D#F37$$\"+kGhe:F3$\"+3.Xi7F37$$\"+)R'ok;F3$ \"+I(pAf#F77$$\"+_(>/x\"F3$!+S7IOuF77$$\"+1J:w=F3$!+@F3$!+#QBY2aF3$\"+_ [T!4$F37$$\"+yXu9cF3$\"+Qdxx[F37$$\"+\\y))GeF3$\"+]C\\.$o F3$\"++!))R)**F37$$\"+u.I%)oF3$\"+A8EW**F37$$\"+N&H@)pF3$\"+y[K6)*F37$ $\"+(pe*zqF3$\"+-\"F37$$\"+ee)*R%)F3$\"+%>Y$**=F77$$\"+`<.Y&)F3$!+' y*oc\")F77$$\"+K&*>^')F3$!+UG7/=F37$$\"+8tOc()F3$!+q.;tFF37$$\"+!e0I&) )F3$!+o'>xj$F37$$\"+\\Qk\\*)F3$!+E!e(pWF37$$\"+p0;r\"*F3$!+YybdF37$F\\p$\"+seX%*GF37$Ffp$!+WUycXF07$F`q$!+Y!4k1$F37 $Fjq$!+3hk;cF37$F_r$!+-rec#)F37$Fdr$!+&[qs0\"F,7$Fir$!+i.&GC\"F,7$Fcs$ !+z]`w8F,7$Fgt$!+(**p0\\\"F,7$Fau$!+-y%R_\"F,7$F[v$!+plS[:F,7$F`v$!+ee il:F,7$Fev$!+NCwq:F,7$$\"+K5S_QF3$!+8xAl:F,7$Fjv$!+!)eA]:F,7$$\"+#GF&e SF3$!+Hx(G_\"F,7$F_w$!+#zZT[\"F,7$Fdw$!+pu/z8F,7$Fiw$!+$)\\BE7F,7$Fcx$ !+wUm[5F,7$F]y$!+w_a0#)F37$Fgy$!+=E\"y\\&F37$Faz$!+qy%e$HF37$Ffz$!+/nB IbF07$F[[l$\"+qYg@HF37$F`[l$\"+Wy%3r&F37$Fe[l$\"+Iz>\">)F37$F_\\l$\"+x J/g5F,7$Fi\\l$\"+F]%*R7F,7$F]^l$\"+(fy-R\"F,7$Fg^l$\"+@%)y([\"F,7$F\\_ l$\"+]CJD:F,7$Fa_l$\"+F$R;b\"F,7$$\"+o%*\\%R(F3$\"+@qK;_ \"F,7$F``l$\"+\\/a%[\"F,7$Fe`l$\"+HF]t8F,7$F_al$\"+?,^C7F,7$Fial$\"+/d IJ5F,7$Fcbl$\"+?#Ha-)F37$F]cl$\"+!f%f[cF37$Fbcl$\"+]h>!p#F37$Fgcl$!+?& y]r'F07$F\\dl$!+!))y;+$F37$Fadl$!+IV3#p&F37$Ffdl$!+?\"\\BM)F3-F[el6&F] elF(F^elF(-F$6$7S7$F($\"+aEfTIF,7$F@$\"+y%f#RIF,7$FJ$\"+SSNLIF,7$FO$\" +%zM@-$F,7$FT$\"+OSX0IF,7$FY$\"+YSu#)HF,7$Fhn$\"+Q&p`&HF,7$Fbo$\"+E?[> HF,7$F\\p$\"+w.wsGF,7$Ffp$\"+#y$\\9GF,7$F`q$\"+O[zRFF,7$Fjq$\"+Op0fEF, 7$F_r$\"+'o/![DF,7$Fdr$\"+aUy5CF,7$Fir$\"+s4b\\AF,7$Fcs$\"+=\\[u?F,7$F gt$\"+>#4g#=F,7$F[v$\"++[8y:F,7$Fev$\"+![u^C\"F,7$Fjv$\"+_GmC\"*F37$F_ w$\"+elDP^F37$Fdw$\"+%*[6L6F37$Fiw$!+#))>74$F37$Fcx$!+wS6coF37$F]y$!+y 6&[1\"F,7$Fgy$!+=+J=9F,7$Faz$!+DH3)o\"F,7$Ffz$!+L9UR>F,7$F[[l$!+%[0!e@ F,7$F`[l$!+gWlNBF,7$Fe[l$!+YR%zZ#F,7$F_\\l$!+W'3qg#F,7$Fi\\l$!+Sp@,FF, 7$F]^l$!+iL(Hy#F,7$Fg^l$!+-J3VGF,7$Fa_l$!+_^?'*GF,7$Ff_l$!+#\\sh$HF,7$ F[`l$!+exGpHF,7$F``l$!+i/W%*HF,7$Fe`l$!+M9D9IF,7$F_al$!+;v%y-$F,7$Fial $!+7%*yOIF,7$Fcbl$!+wa3TIF,7$F]cl$!+IG=TIF,7$Fbcl$!+A9wOIF,7$Fgcl$!+_$ Q&GIF,7$F\\dl$!+]X'\\,$F,7$Fadl$!+y9z'*HF,7$Ffdl$!+A?xqHF,-F[el6&F]elF ^elF^elF(-F$6$7dp7$F($F+F37$F.$\"+;tZ&)**F77$F5$\"+;8&>%**F77$F;$\"+'* zap)*F77$F@$\"+wpZo(*F77$FE$\"+i\"f^_*F77$FJ$\"+k\"*3)>*F77$FO$\"+=6Rs \")F77$FT$\"+c\\#Qx'F77$FY$\"+%oQ$z]F77$$\"+=JN[6F3$\"+!)>17UF77$Fhn$ \"+_#GVI$F77$F]o$\"+'*[3JBF77$Fbo$\"+hE$QL\"F77$Fgo$\"+uOobF77$$\"+iB0pUF3$!+]=<(p%F77$Fdw$!+i@]xPF77$$\"+WG))yWF3$!+Uq ]wFF77$Fiw$!+^&4Vu\"F77$F^x$!+31!))y(F07$Fcx$\"+t(G$R>F07$Fhx$\"+)364C \"F77$F]y$\"+K`?uAF77$Fby$\"+#[-3K$F77$Fgy$\"+7$)*yK%F77$F\\z$\"+Ir2j^ F77$Faz$\"+7xr^fF77$Ffz$\"+iiXjuF77$F[[l$\"+kc.'p)F77$F`[l$\"+'p\")e_* F77$$\"+@]tRhF3$\"+Qsc#y*F77$Fe[l$\"+Ss,T**F77$$\"+%f]tH'F3$\"+!G_f)** F77$Fj[l$\"+s]'*****F77$$\"+AA))4kF3$\"+'R7I)**F77$F_\\l$\"+Il9N**F77$ Fd\\l$\"+KJ'>x*F77$Fi\\l$\"+YY56&*F77$F]^l$\"+'>2.k)F77$Fg^l$\"+1We5vF 77$Fa_l$\"+a/>cfF77$Fj]m$\"+Wv?G^F77$Ff_l$\"+%*HR\\UF77$Fb^m$\"+mI*eG$ F77$F[`l$\"+-&*z'G#F77$Fj^m$\"+)GtfG\"F77$F``l$\"+;KH=FF07$$\"+pe()=!) F3$!+S7QF77$Fdal$! +ww\\fZF77$Fial$!+M>TacF77$Fcbl$!+k:VOsF77$F]cl$!+3k<;%)F77$Fbcl$!+a6# *)Q*F77$$\"+mTAq#*F3$!+[Rj!o*F77$Fgcl$!+=WYz)*F77$$\"+$**)4A%*F3$!+MF \"o%**F77$$\"+A-\"\\Z*F3$!+I\\-()**F77$$\"+^9sF&*F3$!+w;******F77$F\\d l$!+1xn&)**F77$$\"+[oi\"o*F3$!+')eQ#))*F77$Fadl$!+?)e.o*F77$$\"+30O\"* )*F3$!+Y&3bN*F77$Ffdl$!++%4F#*)F7-F[el6&F]elF(F(F^el-F$6$7dp7$F($\"+++ ++]F37$F.$\"+Uc-$*\\F37$F5$\"+s.7s\\F37$F;$\"+MwLP\\F37$F@$\"+skw))[F3 7$FE$\"+[(eTF37$FT$\"+cmVTMF37$FY$\"+% eIgh#F37$Fhn$\"+yq'pu\"F37$F]o$\"+w!z'o7F37$Fbo$\"+')egtxF77$Fgo$\"+!G s)3EF77$F\\p$!+7@f%e#F77$Fap$!+E\\8LxF77$Ffp$!+wLrz7F37$F[q$!+yA)fy\"F 37$F`q$!+g:orAF37$Feq$!+'Ge!yEF37$Fjq$!+WwlgIF37$F_r$!+gZQ=QF37$Fdr$!+ UQ#*3WF37$Ff_n$!+9]!\\i%F37$Fir$!+s)4Lz%F37$F^s$!+_^m.\\F37$Fcs$!+!)=g s\\F37$Fhs$!+kCs$*\\F37$F]t$!+o$\\***\\F37$Fbt$!+'el7*\\F37$Fgt$!+Y[pn \\F37$Fau$!+9G)R*[F37$F[v$!+o-KyZF37$Fev$!+oai_VF37$Fjv$!+#zIc!QF37$F_ w$!+=_0XIF37$F_bn$!+5=$Gj#F37$Fdw$!+95u$>#F37$Fgbn$!+qzr6ux F77$Fby$\"+aI-08F37$Fgy$\"+Ow9<=F37$F\\z$\"+qnlXAF37$Faz$\"+)f(3aEF37$ Ffz$\"+#))=7X$F37$F[[l$\"+#)[PDTF37$F`[l$\"+qzM6YF37$F`en$\"+Mn')yZF37 $Fe[l$\"+E`7+\\F37$Fhen$\"+s$fq%\\F37$Fj[l$\"+QoEz\\F37$F`fn$\"+o)fm* \\F37$F_\\l$\"+s5>**\\F37$$\"+s`q;lF3$\"+UBy))\\F37$Fd\\l$\"+Y7Rm\\F37 $$\"+X+#yh'F3$\"+]q1K\\F37$Fi\\l$\"+Aa)e)[F37$Fc]l$\"+=w2[ZF37$F]^l$\" +3\\4eXF37$Fg^l$\"+7CY(3%F37$Fa_l$\"+7/d.MF37$Ff_l$\"++MLBEF37$F[`l$\" +3zl)p\"F37$Fj^m$\"+8A[<7F37$F``l$\"+gAJPsF77$Fihn$\"+V*R)))>F77$Fe`l$ !+Q')>#G$F77$Fj`l$!+3ZKC$)F77$F_al$!+qB*yK\"F37$Fdal$!+;x6?=F37$Fial$! +yiT#H#F37$Fcbl$!+!4Y0:$F37$F]cl$!+;p%=#QF37$Fbcl$!+eLqAWF37$Ffjn$!+g* *HEYF37$Fgcl$!+[h+(y%F37$Fc[o$!+!4l&4\\F37$F\\dl$!+_,i!)\\F37$$\"+k(z5 j*F3$!+3Q='*\\F37$F`\\o$!+sOv**\\F37$$\"+KRK\"*\\F37$Fadl$! +Sq!4(\\F37$Fh\\o$!+_3s')[F37$Ffdl$!+G@G[ZF3-F[el6&F]elF^elF(F^el-%+AX ESLABELSG6$Q\"t6\"Q!Fj^p-%%VIEWG6$;F(Ffdl%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" " Curve 4" "Curve 5" }}}{PARA 13 "" 1 "" {GLPLOT2D 637 298 298 {PLOTDATA 2 "6)-%'CURVESG6$7hn7$$\"\"!F)$\"+++++5!\"*7$$\"+;arz@!#6$\" +YUsv**!#57$$\"+XTFwSF0$\"+U&4D\"**F37$$\"+\"z_\"4iF0$\"+!>1by*F37$$\" +S&phN)F0$\"+c8J!e*F37$$\"+*=)H\\5F3$\"+r(Q0F*F37$$\"+[!3uC\"F3$\"+$*R s_))F37$$\"+J$RDX\"F3$\"+l=cO#)F37$$\"+)R'ok;F3$\"+$G77L(F37$$\"+1J:w= F3$\"+x?^rgF37$$\"+3En$4#F3$\"+MWrFVF37$$\"+c#o%*=#F3$\"+$\\.>T$F37$$ \"+/RE&G#F3$\"+^2#oT#F37$$\"+9r5$R#F3$\"+Rz-C7F37$$\"+D.&4]#F3$!+5'oX4 \"!#77$$\"+]jB4EF3$!+A>a]7F37$$\"+vB_Y2aF3$!+ONe7**F37$$\"+yXu9cF3$!+Vz9!z*F37$$\"+\\y))GeF3$!+(pu\")e*F3 7$$\"+i_QQgF3$!+5+^*G*F37$$\"+!y%3TiF3$!+#>a%o))F37$$\"+O![hY'F3$!+c^` (=)F37$$\"+#Qx$omF3$!+A)RDJ(F37$$\"+u.I%)oF3$!+[Pr9gF37$$\"+N&H@)pF3$! +1[K\"G&F37$$\"+(pe*zqF3$!+5!f;X%F37$$\"+5=\"p=(F3$!+xOVPMF37$$\"+C\\' QH(F3$!+'zSTK#F37$$\"+o%*\\%R(F3$!+3`E37F37$$\"+8S8&\\(F3$!+-6]/cF_p7$ $\"+3hK+wF3$\"+Y[i\\6F37$$\"+0#=bq(F3$\"+W[Z!R $F37$$\"+2s?6zF3$\"+&RH?P%F37$$\"+pe()=!)F3$\"+f-N*G&F37$$\"+IXaE\")F3 $\"++go\"**F37$F5$\"+K^64(*F37$F :$\"+K`FD$*F37$F?$\"+_u-z()F37$FD$\"+W(R#y!)F37$FI$\"+G4E#H(F37$FN$\"+ o+\"pM'F37$FS$\"+w8kR_F37$FX$\"+?1R@SF37$Fgn$\"+S7asEF37$Fao$\"+A$exU \"F37$F[p$!+3\\KXj!#87$Ffp$!+\")[7Y9F37$F`q$!+))=C*z#F37$Fjq$!+D3zsRF3 7$F_r$!+[Hdr_F37$Fdr$!+GDnqiF37$Fir$!+s'z()H(F37$F^s$!+)[%>y!)F37$Fcs$ !+[*)z%y)F37$Fhs$!+?*H#4$*F37$F]t$!+g#))**p*F37$Fbt$!+gMT<**F37$$\"+Ah $*))[F3$!+WTSy**F37$Fgt$!+St&*****F37$$\"+]7I0^F3$!+Sqe!)**F37$F\\u$!+ +hm=**F37$$\"+d,]6`F3$!+sW7I)*F37$Fau$!+k7N4(*F37$Ffu$!+;*4'Q$*F37$F[v $!+Wgc)z)F37$F`v$!+O6x<\")F37$Fev$!+wxJ>tF37$Fjv$!+;-pziF37$F_w$!+k8I> _F37$Fdw$!+YBXsRF37$F^x$!+:z!*fFF37$Fhx$!+ZW-r8F37$Fby$!+II-\\KF_p7$F \\z$\"+/L&pO\"F37$Ffz$\"+a+m.FF37$F`[l$\"+wVcPSF37$Fe[l$\"+3d2K_F37$Fj [l$\"+?v()RjF37$F_\\l$\"+%yI%3tF37$Fd\\l$\"+chQu!)F37$Fi\\l$\"+wgq)z)F 37$F^]l$\"+cA$QI*F37$Fc]l$\"+7V(>p*F37$$\"+[oi\"o*F3$\"+OeaA)*F37$Fh]l $\"+%=Zt\"**F37$$\"+30O\"*)*F3$\"+omLz**F37$F]^lF\\_l-Fb^l6&Fd^lF(Fe^l F(-F$6$7enF'7$$\"+3x&)*3\"F0$\"+iGdw**F37$F.$\"+[3S1**F37$$\"+!y%*z7$F 0$\"+oMc2)*F37$F5$\"+#[JRn*F37$F:$\"+!Gl)[#*F37$F?$\"+OS_`')F37$FD$\"+ G-([!zF37$FI$\"+=*4L3(F37$FN$\"+aPD3#QF3 7$Fgn$\"+#>ze_#F37$Fao$\"+&=7aM\"F37$F[p$!+7XIsfFbal7$Ffp$!+Z6wi8F37$F `q$!+'>&pYEF37$Fjq$!+WNytPF37$F_r$!+m\"*4V]F37$Fdr$!+=#*GSgF37$Fir$!+y 80!4(F37$F^s$!+%RA[!zF37$Fcs$!+K#e(f')F37$Fhs$!+A3AJ#*F37$F]t$!+Cnvj'* F37$$\"+UrT%o%F3$!+oZ8/)*F37$Fbt$!+M#oq!**F37$Fecl$!+;8nv**F37$Fgt$!+E >&*****F37$F]dl$!+W&H\"y**F37$F\\u$!+gcZ3**F37$Fedl$!+yP:4)*F37$Fau$!+ cZ>u'*F37$Ffu$!+9i`j#*F37$F[v$!+iPju')F37$F`v$!+a#ym%zF37$Fev$!+'p)H6r F37$Fjv$!+=gQ\\gF37$F_w$!+%pp9*\\F37$Fdw$!+[gXtPF37$F^x$!+=C<4EF37$Fhx $!+i:$=H\"F37$Fby$!+W1-eIF_p7$F\\z$\"+gs)zG\"F37$Ffz$\"+;#Rbb#F37$F`[l $\"+e.[OQF37$Fe[l$\"+cC3/]F37$Fj[l$\"++'[,6'F37$F_\\l$\"+YV.+rF37$Fd\\ l$\"+=tz+zF37$Fi\\l$\"+'4&yu')F37$F^]l$\"+7uGD#*F37$Fc]l$\"+Ma#[l*F37$ Fihl$\"+]um+)*F37$Fh]l$\"+#y$*p!**F37$Fail$\"+[9sw**F37$F]^lF*-Fb^l6&F d^lFe^lFe^lF(-F$6$7enF'7$F\\jl$\"+%)>dx**F37$F.$\"+kFN5**F37$Fdjl$\"+_ Ld:)*F37$F5$\"+q9C(o*F37$F:$\"+oNjx#*F37$F?$\"+aFZ+()F37$FD$\"+o/BpzF3 7$FI$\"+mwFgrF37$FN$\"+#G_6?'F37$FS$\"+g3?%4&F37$FX$\"+M$yH*QF37$Fgn$ \"+5MMyDF37$Fao$\"+!yuZP\"F37$F[p$!+gT90hFbal7$Ffp$!+#e([#R\"F37$F`q$! +C$)G,FF37$Fjq$!+o>OXQF37$F_r$!+qP!f7&F37$Fdr$!+)f,W7'F37$Fir$!+)yTp;( F37$F^s$!+#e$=pzF37$Fcs$!+Sp`1()F37$Fhs$!+Aaeg#*F37$F]t$!+Q:Yx'*F37$Fh ^m$!+#H$G7)*F37$Fbt$!+QB*4\"**F37$Fecl$!+_(3n(**F37$Fgt$!+%*R&*****F37 $F]dl$!+)[i!z**F37$F\\u$!+96M7**F37$Fedl$!+%H*4<)*F37$Fau$!+;X\\(o*F37 $Ffu$!+kf!=H*F37$F[v$!+)305s)F37$F`v$!+C'>-,)F37$Fev$!+_E%z=(F37$Fjv$! +3cZLhF37$F_w$!+)z7S2&F37$Fdw$!+5/.XQF37$F^x$!+I*4Jm#F37$Fhx$!+mp1?8F3 7$Fby$!+s$Qg7$F_p7$F\\z$\"+*eThJ\"F37$Ffz$\"+m3`3EF37$F`[l$\"+i%H)3RF3 7$Fe[l$\"+Q6p'3&F37$Fj[l$\"+9)oS>'F37$F_\\l$\"+'[4o<(F37$Fd\\l$\"+'QO_ 'zF37$Fi\\l$\"+kA:@()F37$F^]l$\"+U<&[D*F37$Fc]l$\"+1e()o'*F37$Fihl$\"+ gg&*3)*F37$Fh]l$\"+))4#4\"**F37$Fail$\"+_Urx**F3Ffdm-Fb^l6&Fd^lF(F(Fe^ l-F$6$7enF'7$F\\jl$\"+W&3o(**F37$F.$\"+sEL2**F37$Fdjl$\"+_5X4)*F37$F5$ \"+?d1x'*F37$F:$\"+KRib#*F37$F?$\"+K)>Xm)F37$FD$\"++%*))>zF37$FI$\"+)3 175(F37$FN$\"+;woOhF37$FS$\"+?tiI]F37$FX$\"++*>u$QF37$Fgn$\"+v%=z`#F37 $Fao$\"+,39_8F37$F[p$!+g'GF+'Fbal7$Ffp$!+EKdp8F37$F`q$!+!QD#fEF37$Fjq$ !+e$[-z$F37$F_r$!+O3@i]F37$Fdr$!+wrwfgF37$Fir$!+!3Iz5(F37$F^s$!+)yT)>z F37$Fcs$!+gXrq')F37$Fhs$!+3*=\"Q#*F37$F]t$!+_P)pm*F37$Fh^m$!+!)\\01)*F 37$Fbt$!+'\\$*z!**F37$Fecl$!+?g\"f(**F37$Fgt$!+;C&*****F37$F]dl$!+3'\\ $y**F37$F\\u$!+'4(Q4**F37$Fedl$!+/i-6)*F37$Fau$!+%eEtn*F37$Ffu$!+o#y,F *F37$F[v$!+wa\\&o)F37$F`v$!+7#4:'zF37$Fev$!+3<7HrF37$Fjv$!+K$f)ogF37$F _w$!+[!=0,&F37$Fdw$!+[*>**y$F37$F^x$!++9b@EF37$Fhx$!+(f,$)H\"F37$Fby$! +;PgtIF_p7$F\\z$\"+&pQWH\"F37$Ffz$\"+!4+xc#F37$F`[l$\"+))[7`QF37$Fe[l$ \"+cm9B]F37$Fj[l$\"+_peHhF37$F_\\l$\"+wp)y6(F37$Fd\\l$\"+'fMe\"zF37$Fi \\l$\"+?ek&o)F37$F^]l$\"++ABK#*F37$Fc]l$\"+cO8e'*F37$Fihl$\"+S1i-)*F37 $Fh]l$\"+o(>z!**F37$Fail$\"+Cc&p(**F3Ffdm-Fb^l6&Fd^lFe^lF(Fe^l-%+AXESL ABELSG6$Q\"t6\"Q!Fajn-%%VIEWG6$;F(F]^l%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Cu rve 4" "Curve 5" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "0 1 0" 20 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }