{VERSION 5 0 "IBM INTEL NT" "5.0" } {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 "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 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "phi0:=1; alpha0:=in t(phi0^2,X=-1..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%phi0G\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'alpha0G\"\"#" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 38 "phi1:=X; alpha1:=int(phi1^2,X=-1..1);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%phi1G%\"XG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'alpha1G#\"\"#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "phi2:=X^2+c;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ph i2G,&*$)%\"XG\"\"#\"\"\"F*%\"cGF*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "int(phi2*phi0,X=-1..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&#\"\"#\"\"$\"\"\"*&F%F'%\"cGF'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "solve(%,c);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##!\"\" \"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "phi2:=X^2-1/3; alp ha2:=int(phi2^2,X=-1..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%phi2G, &*$)%\"XG\"\"#\"\"\"F*#F*\"\"$!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%'alpha2G#\"\")\"#X" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "ph i3:=X^3+c*X;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%phi3G,&*$)%\"XG\"\" $\"\"\"F**&%\"cGF*F(F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "int(phi3*phi1,X=-1..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&#\"\"#\" \"&\"\"\"*(F%F'\"\"$!\"\"%\"cGF'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "solve(%,c);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##!\"$ \"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "phi3:=X^3-3/5*X; a lpha3:=int(phi3^2,X=-1..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%phi3 G,&*$)%\"XG\"\"$\"\"\"F**&#F)\"\"&F*F(F*!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'alpha3G#\"\")\"$v\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "phi4:=X^4-c2*X^2+c0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%phi4G,(*$)%\"XG\"\"%\"\"\"F**&%#c2GF*)F(\"\"#F*!\"\"%#c0GF*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "solve(\{int(phi4*phi2,X=-1.. 1),int(phi4*phi0,X=-1..1)\},\{c0,c2\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%#c0G#\"\"$\"#N/%#c2G#\"\"'\"\"(" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 52 "phi4:=X^4-6/7*X^2+3/35; alpha4:=int(phi4^2,X=-1..1) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%phi4G,(*$)%\"XG\"\"%\"\"\"F**& #\"\"'\"\"(F**$)F(\"\"#F*F*!\"\"#\"\"$\"#NF*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'alpha4G#\"$G\"\"&D5\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "plot(\{phi0,phi1,phi2,phi3,phi4\},X=-1..1);" }}{PARA 13 "" 1 "" {GLPLOT2D 494 494 494 {PLOTDATA 2 "6)-%'CURVESG6$7S7$$!\"\" \"\"!$\"\"\"F*7$$!3ommm;p0k&*!#=F+7$$!3wKL$3s%HaF0F+7$$!3Q+++]$*4)*\\F0F+7$$!39+++]_&\\c%F0F+7$$! 31+++]1aZTF0F+7$$!3umm;/#)[oPF0F+7$$!3hLLL$=exJ$F0F+7$$!3*RLLLtIf$HF0F +7$$!3]++]PYx\"\\#F0F+7$$!3EMLLL7i)4#F0F+7$$!3c****\\P'psm\"F0F+7$$!3' )****\\74_c7F0F+7$$!3)3LLL3x%z#)!#>F+7$$!3KMLL3s$QM%FjoF+7$$!3]^omm;zr )*!#@F+7$$\"3%pJL$ezw5VFjoF+7$$\"3s*)***\\PQ#\\\")FjoF+7$$\"3GKLLe\"*[ H7F0F+7$$\"3I*******pvxl\"F0F+7$$\"3#z****\\_qn2#F0F+7$$\"3U)***\\i&p@ [#F0F+7$$\"3B)****\\2'HKHF0F+7$$\"3ElmmmZvOLF0F+7$$\"3i******\\2goPF0F +7$$\"3UKL$eR<*fTF0F+7$$\"3m******\\)Hxe%F0F+7$$\"3ckm;H!o-*\\F0F+7$$ \"3y)***\\7k.6aF0F+7$$\"3#emmmT9C#eF0F+7$$\"33****\\i!*3`iF0F+7$$\"3%Q LLL$*zym'F0F+7$$\"3wKLL3N1#4(F0F+7$$\"3Nmm;HYt7vF0F+7$$\"3Y*******p(G* *yF0F+7$$\"3]mmmT6KU$)F0F+7$$\"3fKLLLbdQ()F0F+7$$\"3[++]i`1h\"*F0F+7$$ \"3W++]P?Wl&*F0F+7$F+F+-%'COLOURG6&%$RGBG$\"#5F)$F*F*F^u-F$6$7ep7$F($ \"3?'G9dG9dG#F07$$!3%pmm\"HU,\"*)*F0$\"3\\xA(f%4mU?F07$$!3!RLL$e%G?y*F 0$\"3[bJ#H;;:\"=F07$$!3u****\\(oUIn*F0$\"3[wENIV(>f\"F07$F.$\"3!**zt!G Kt$Q\"F07$$!3#HL3-)*G#p%*F0$\"3JJgt>^]67F07$$!3E++vV5Su$*F0$\"3C_E*[M6 u/\"F07$$!3_m;H2Jdz#*F0$\"3VA=tB3f7*)Fjo7$F2$\"3K&o$)p^u&GuFjo7$$!39** *\\iId9(*)F0$\"3-$4vp)yH(3;7m\"Fjo7$$!3&emmmwnMa)F0$! 3GP`r.W?br!#?7$F8$!3'\\$4q$=![nFFjo7$$!3)****\\i&[3:\")F0$!3-m4)R*p32X Fjo7$F;$!3-G@?(*y4kfFjo7$$!3'3++Dw$H.xF0$!31*G0oLI)yqFjo7$F>$!3Q=bk_iL \")zFjo7$$!3tKL$3i_+I(F0$!3\\-#Ga(HJ2()Fjo7$FA$!3^eiiy(*HO#*Fjo7$$!3%o mmT!y%)))pF0$!3:acgXX\\P%*Fjo7$$!3#RLL3FuF)oF0$!3Kz.B\"\\E?f*Fjo7$$!3- ,+]P2qwnF0$!3%[h!>.B)=q*Fjo7$FD$!3)e!ec&G=!p(*Fjo7$$!3#)******\\Q*[c'F 0$!3EJdEe!R`z*Fjo7$$!3uLL$e\\g\"fkF0$!3M'Qn!yX+$y*Fjo7$$!3mnmmTrU`jF0$ !3&[]Hj@1!)Fjo7$FP$!3]P#*\\+DN+mFjo7$FS$! 3yQv!GQ^y%\\Fjo7$FV$!3U-B8jF59KFjo7$FY$!3E=c\")3;Y%e\"Fjo7$Ffn$\"3?Fjo7$F\\o$\"3'Hl\\0u))\\j$Fjo7$F_o$\"3mN >Ya7O!*\\Fjo7$Fbo$\"3%o![t?`-miFjo7$Feo$\"3=ycmM01VsFjo7$Fho$\"3!oFjo7$Fhq$\"3mL8YpY-xEFfx7$F[r$!3o))e$[vZ\\e\"Fjo7$F^r$!3_JG$ys`nE$F jo7$Far$!3tVi$Hs5#R]Fjo7$Fdr$!3g([+p6DBd'Fjo7$Fgr$!3KpCv*GWB&zFjo7$Fjr $!3#ffw8e0P**)Fjo7$$\"3WKLeRC]T[l*Fj o7$$\"3AK$3-y'ycjF0$!3fv#z@^rft*Fjo7$$\"3Ymm\"z\\%[gkF0$!3E[f.D/R$y*Fj o7$$\"3q+]i:A=klF0$!3YLd&3;$Q&z*Fjo7$F`s$!3mJR!z)o?q(*Fjo7$$\"3eLL3Fe# Rx'F0$!30*H(o.VeY(Ffx7$F_t$\"3b[V8.oII9Fjo7$$\"3a mm\"zW?)\\*)F0$\"3QaleGR&Q2%Fjo7$Fbt$\"3'Q?(4Hz')pqFjo7$$\"3Y++DJ&f@E* F0$\"3'o)p`NCKM')Fjo7$$\"3Y++++PDj$*F0$\"3mn(>3#pkG5F07$$\"3Y++voyMk%* F0$\"39=\")zY<'G?\"F07$Fet$\"3'[sb.:5jQ\"F07$$\"3K+]7G:3u'*F0$\"3A<\"[ n:8Sf\"F07$$\"3A++v=5s#y*F0$\"3T/`uS![H\"=F07$$\"35+]P40O\"*)*F0$\"3/# z(exTTV?F07$F+Fcu-Fit6&F[uF^uF\\uF^u-F$6$7X7$F($!3A+++++++SF07$F[v$!3# GGTh@=5\\$F07$F.$!3s+%ev,A*4IF07$F]w$!3a(3@#*GENh#F07$F2$!3;w))oF?OPAF 07$F5$!3=#*=(fz)4j9F07$F8$!3&zyG?4vE!yFjo7$F;$!3*Q'zRPHw@>Fjo7$F>$\"3a SkJkX1cFFjo7$FA$\"3SgbR7xNS8F07$F_o$\"3#pO$4 J]um6F07$Fbo$\"3=aP`/A:S&*Fjo7$Feo$\"3#fwuOKS2M(Fjo7$Fho$\"3&Hy>#\\1$4 \"\\Fjo7$F\\p$\"3!*)4(esf5)f#Fjo7$F_p$\"3?r\\rz`1BfFap7$Fcp$!3GYhV&>]% yDFjo7$Ffp$!3tGFziQUN[Fjo7$Fip$!3%eiE%4+3\">(Fjo7$F\\q$!3#pCk:#41\"\\* Fjo7$F_q$!3!)pYb/<\\c6F07$Fbq$!3_q4)o:rjL\"F07$Feq$!3r1cCk#[s]\"F07$Fh q$!3$fsI3%3aI;F07$F[r$!3)>f)f?0$fs\"F07$F^r$!37R%)3i.3w:F 07$F]s$!3^ea!HSDoI\"F07$F`s$!3H(3FP,Zh.\"F07$Fcs$!3C[$Q#*\\q6)oFjo7$Ff s$!3I%**Qq\"ektEFjo7$Fis$\"3+6Q`4'Q[*=Fjo7$F\\t$\"3*Rbl;b\"*Q+)Fjo7$F_ t$\"38,TI/r')H9F07$Fchl$\"3#RW$y7+&))z\"F07$Fbt$\"3eQF!3v&z\">#F07$F`i l$\"3iSrrt4'3f#F07$Fet$\"3=c*o[X#*G,$F07$Fbjl$\"3[vD'R\"4f#\\$F07$F+$ \"3A+++++++SF0-Fit6&F[uF\\uF\\uF^u-F$6$7S7$F($\"3SnmmmmmmmF07$F.$\"3&o h!>P^y8eF07$F2$\"3o)G\")>0@E5&F07$F5$\"3hZ5cj)>sL%F07$F8$\"3#*4jjF6].O F07$F;$\"3Ky%)f%e%))4HF07$F>$\"3#y!H?5_W*H#F07$FA$\"3!f%z>XvX+F07$Ffn$!3%H!e-(R\"eKAF07$Fin$!3O7-C1WOrCF07$F\\o$!3] 2X#*[#RCr#F07$F_o$!3O!eL_A7H*GF07$Fbo$!3Q&R?*GXNbIF07$Feo$!3y\\$yH&)[a <$F07$Fho$!39\"*)fDf$ykKF07$F\\p$!3GK3k6WY9LF07$F_p$!3Gii5)eBLL$F07$Fc p$!34SF%Hh]ZJ$F07$Ffp$!3cg2CZK#pE$F07$Fip$!3k7uGu*o@=$F07$F\\q$!3S%G#= 18^eIF07$F_q$!3McC)>vN?!HF07$Fbq$!3w*=L'fn@1Yg4S*>AF07$F[r$!3:xK/s\")48>F07$F^r$!3nbwJf?%Gg\"F07$Far$!36 J_n:ogG7F07$Fdr$!3F%Q5/Le0V)Fjo7$Fgr$!3+vC$fF=S0%Fjo7$Fjr$\"3[;]ugIwrc Ffx7$F]s$\"3u%yB-\\*yndFjo7$F`s$\"34,;?Z*GF6\"F07$Fcs$\"33(***GZJS'p\" F07$Ffs$\"3'zm%\\F[y5BF07$Fis$\"3e%z.MGTl!HF07$F\\t$\"3%)Hltp))4EOF07$ F_t$\"3ogQ%=!p$HI%F07$Fbt$\"3[%RmU_y\"f]F07$Fet$\"3z\")Q%R![V;eF07$F+F iem-Fit6&F[uF^uF^uF\\u-F$6$7S7$F(F(7$F.F.7$F2F27$F5F57$F8F87$F;F;7$F>F >7$FAFA7$FDFD7$FGFG7$FJFJ7$FMFM7$FPFP7$FSFS7$FVFV7$FYFY7$FfnFfn7$FinFi n7$F\\oF\\o7$F_oF_o7$FboFbo7$FeoFeo7$FhoFho7$F\\pF\\p7$F_pF_p7$FcpFcp7 $FfpFfp7$FipFip7$F\\qF\\q7$F_qF_q7$FbqFbq7$FeqFeq7$FhqFhq7$F[rF[r7$F^r F^r7$FarFar7$FdrFdr7$FgrFgr7$FjrFjr7$F]sF]s7$F`sF`s7$FcsFcs7$FfsFfs7$F isFis7$F\\tF\\t7$F_tF_t7$FbtFbt7$FetFetFgt-Fit6&F[uF\\uF^uF\\u-%+AXESL ABELSG6$Q\"X6\"Q!Fdbn-%%VIEWG6$;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" "Curv e 4" "Curve 5" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "plot(\{ph i3*phi4,phi2*phi4\},X=-1..1);" }}{PARA 13 "" 1 "" {GLPLOT2D 494 494 494 {PLOTDATA 2 "6&-%'CURVESG6$7[p7$$!\"\"\"\"!$!3jXr&G9dG9*!#>7$$!3%p mm\"HU,\"*)*!#=$!3,?*f-v0Ok(F-7$$!3!RLL$e%G?y*F1$!3*e4*fBf.CjF-7$$!3u* ***\\(oUIn*F1$!3IA )F1$\"3kjUdz8l&H#FR7$$!3)****\\i&[3:\")F1$\"3\"\\`2hzV89#FR7$$!3Mm;aQU C3!)F1$\"3L4U>MzuV#FR7$$!3u****\\P8# \\4(F1$!3CxUuQwkJjFR7$$!3+nm;/siqmF1$!3!eouW+V-,\"F-7$$!3uLL$e\\g\"fkF 1$!33%o#zua1b6F-7$$!3[++](y$pZiF1$!3)o#zCz#HSE\"F-7$$!3MnmT&Gu,.'F1$!3 z'[uxu]hL\"F-7$$!33LLL$yaE\"eF1$!3#>+s$[$GsO\"F-7$$!3%)****\\([j5i&F1$ !3/VL*GwZ:O\"F-7$$!3hmmm\">s%HaF1$!3e\"=drU_0HFR7$$!3]++]PYx\"\\#F1$\"3eg8u; V;s[FR7$$!3EMLLL7i)4#F1$\"3^CV+(>zC#eFR7$$!3c****\\P'psm\"F1$\"3))[ssF N)y(fFR7$$!3')****\\74_c7F1$\"3slPO`E%pJ&FR7$$!3)3LLL3x%z#)F-$\"3tE4cW c7BRFR7$$!3KMLL3s$QM%F-$\"3q)f+:P?]=#FR7$$!3]^omm;zr)*Fgn$\"3O*H(*pqjo 2&!#A7$$\"3%pJL$ezw5VF-$!3IB`YK&>\"p@FR7$$\"3s*)***\\PQ#\\\")F-$!3qv2`*e-`+*FR7$$\"3ckm;H!o-*\\ F1$\"3[>Jc*)p5^6F-7$$\"3y)***\\7k.6aF1$\"3\"\\O?X6C>K\"F-7$$\"3IKLe9as ;cF1$\"37o,mhO2h8F-7$$\"3#emmmT9C#eF1$\"3KivtF>qm8F-7$$\"3WKLeR'4gH#FR7$$\"3]mmmT6KU$)F1$!3n6I/X3v=@FR7$$\"3-LLeRZQT%) F1$!3ibj/6dJW;FR7$$\"3a****\\P$[/a)F1$!3u%Q,>1e-D)Fgn7$$\"32mmTN>^R')F 1$\"3Gt*>*p)fZ(QFgn7$$\"3fKLLLbdQ()F1$\"3%p;kok[^/#FR7$$\"3amm\"zW?)\\ *)F1$\"3?1e^\">_#GtFR7$$\"3[++]i`1h\"*F1$\"3)3=t&[1d\\:F-7$$\"3Y++++PD j$*F1$\"3qTi)G;\"3lEF-7$$\"3W++]P?Wl&*F1$\"3w6]6#R.o<%F-7$$\"3K+]7G:3u '*F1$\"3=jQ#)oHXz^F-7$$\"3A++v=5s#y*F1$\"3n-Lfae)=L'F-7$$\"35+]P40O\"* )*F1$\"39v_#4hw![wF-7$$\"\"\"F*$\"3jXr&G9dG9*F--%'COLOURG6&%$RGBG$\"#5 F)$F*F*Fhdl-F$6$7dp7$F($\"3AC&4Q_4Q_\"F17$$!3/MLe9r]X**F1$\"3DfG(*H1G= 9F17$F/$\"3!oc?OR#\\<8F17$$!3()***\\PM@l$)*F1$\"3**o[)*47I@7F17$F5$\"3 %R^xzKm&H6F17$F:$\"3!['=I$Gl\"*e*F-7$F?$\"3_^A@vwsW!)F-7$$!3#HL3-)*G#p %*F1$\"3sPHJZuwCoF-7$FD$\"3%o'yXtj@8dF-7$$!3_m;H2Jdz#*F1$\"36LwBo3\"Qq %F-7$FI$\"3Koslr+_!z$F-7$FN$\"3?'o@(4>(y0#F-7$FT$\"3'4qp9Tf]?(FR7$Fin$ !34O#>$pddPGFR7$Fco$!3mhunizhs**FR7$F]p$!3!*Q]X!)=wl9F-7$Fgp$!39n/@`O[ N5%=F-7$$!3RMLLL)Q Ug(F1$!3k#4DI5z/&=F-7$Faq$!3TckrTXEN=F-7$$!3tKL$3i_+I(F1$!3!=>O:Kcxt\" F-7$Ffq$!3#R^F[c$fq:F-7$F[r$!3%>+'H]ng!4\"F-7$Fer$!3Q\"=Xo3y1]&FR7$F_s $!3AaAPa'f/2%Fgn7$Fis$\"3ydRf=zs&3$FR7$$!3]LL$3x&y8_F1$\"3&fquQ%f]8XFR 7$F^t$\"3W#GQgKOG^&FR7$$!3E++++t_\"y%F1$\"3qPV9$)=(42'FR7$Fct$\"3+)>R: F,@='FR7$$!33+++]zCcVF1$\"3Y`Gm_!ek(eFR7$Fht$\"3K&p(Hqiu%=&FR7$F]u$\"3 kM\"*H7]OJIFR7$Fbu$!3w&or8iu3x(Fgn7$Fgu$!3c&HvxOH,w%FR7$F\\v$!3=UbEHho f)*FR7$Fav$!3-#\\O\"3xmV9F-7$Ffv$!3l'p.U)G\\9>F-7$F[w$!3%zo&oEo***H#F- 7$F`w$!3XL8i\\943EF-7$Few$!3#H\\!or9[(y#F-7$$!3T,+]ivF@AF-$!3q9\"pnEX) QGF-7$Fjw$!3!QA)pgm5dGF-7$$\"3@CL$3-Dg5#F-$!3F,)4E9#pSGF-7$F`x$!3_J\"G [xJ&)y#F-7$Fex$!3YDm$3*yp:EF-7$Fjx$!3x[)3!))H`ABF-7$F_y$!3>Y=9XH@C>F-7 $Fdy$!31!>fg/2'o9F-7$Fiy$!37Qr'*3VEs**FR7$F^z$!3()H7#zGu.![FR7$Fcz$!3L q;%=SMG%fFgn7$Fhz$\"3wM1c_1;KIFR7$$\"3-mm\"H2fU'RF1$\"3'o\"=Eh4nzUFR7$ F][l$\"3$Q?.CF!4O_FR7$$\"3/mm\"HiBQP%F1$\"3&fbg![2S'FR7$$\"37KLeR*)**)y%F1$\"3ycJs>=>fgFR7$Fg[l$\"3A\"3Xk-P3a&FR7$$ \"3nJL$3A_1?&F1$\"3QLcPt*>oe%FR7$F\\\\l$\"3hwjr3\\*QA$FR7$Ff\\l$!3C1oc 4n,,^Fgn7$F`]l$!3CFMuM$4(obFR7$Fj]l$!3G<>V-#fr3\"F-7$F_^l$!3o2P,^](yc \"F-7$$\"3c***\\(o!*R-tF1$!3nrK)e/3$Rm;HK%\\E!yF1$!3- XE6zNi.=F-7$F^_l$!3uLjy73HPX:'FR7$F[bl$\"3!yq')>gw ^!>F-7$F`bl$\"3KI)G'*Rsnd$F-7$$\"3Y++DJ&f@E*F1$\"3OAdfW/2HXF-7$Febl$\" 35TepfzP*e&F-7$$\"3Y++voyMk%*F1$\"3Q\"['G!Hg\\w'F-7$Fjbl$\"399(*e2EQj! )F-7$F_cl$\"34OG-w(\\Yg*F-7$Fdcl$\"3ITd3A[qI6F17$$\"3;+D1k2/P)*F1$\"34 U')eOo>A7F17$Ficl$\"3XEx1)>=\"=8F17$$\"31+voa-oX**F1$\"3E@r`U$3'=9F17$ F^dlF]el-Fcdl6&FedlFhdlFfdlFhdl-%+AXESLABELSG6$Q\"X6\"Q!Ffhm-%%VIEWG6$ ;F(F^dl%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "int(phi2*phi4,X=-1..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "plot(sin(x), x=0..Pi/2);" }}{PARA 13 "" 1 "" {GLPLOT2D 494 494 494 {PLOTDATA 2 "6%- %'CURVESG6$7S7$$\"\"!F)F(7$$\"3NGK5j*))QU$!#>$\"3QsLeI+ABMF-7$$\"3DXXY Uk*HS'F-$\"3]DS+L@i)R'F-7$$\"3=N68yVJ`(*F-$\"3_b&ehJeyt*F-7$$\"3%3h%eR Se78!#=$\"3<&Q%f]#=)38F=7$$\"3k+,hQPB[;F=$\"3V-yj65yS;F=7$$\"3'H#*ed(R Uf>F=$\"3q)*)ys&)4p%>F=7$$\"3kHX[TMk\"G#F=$\"3G3RBS#)*=E#F=7$$\"3Saq%HF=$\"3=7dd?+e/HF=7$$\"3)pq'4O Kt)G$F=$\"3c0jx$Rp(HKF=7$$\"3#f/N#RTo*e$F=$\"3ML>uye38NF=7$$\"3Ut79wN[ GRF=$\"3V3zj5M@GQF=7$$\"3/VrOc6q%F=7$$\"31\\,oR/A[_F=$ \"3SMGBr+f5]F=7$$\"3uvW/X(*RG,:eF=7$$\"3.n3p46^WlF=$\"33g0 zi&Qs3'F=7$$\"3oHyF.C6noF=$\"3h+)=j,t*RjF=7$$\"3(*zx.5Ir.sF=$\"3Qz3MFx j'f'F=7$$\"3'pz!QUu\"G^(F=$\"3$[8q$y.wDoF=7$$\"3A\"3@7LGi%yF=$\"3wm47u KelqF=7$$\"3)3\"HIT&[D>)F=$\"3M(RvZssjI(F=7$$\"3gv)\\AI@S\\)F=$\"3C>#p \"po&)3vF=7$$\"3vn()=V,i>))F=$\"3%4zeG%\\()>xF=7$$\"3'G:[dg&*f:*F=$\"3 1()\\)y]!GHzF=7$$\"3sSt6rL2&[*F=$\"3g&H%*=Uja7)F=7$$\"3mka(*HIZ.)*F=$ \"3%3R7+w2pI)F=7$$\"3Em\"[l:+d,\"!#<$\"3Q?Zs+w\\)\\)F=7$$\"3c!3XyEmu/ \"F_u$\"3Ih!)R3tfh')F=7$$\"3sJ_*>P$Q\"3\"F_u$\"3VZPF_)*3E))F=7$$\"3.M \"G%4t676F_u$\"3kW#3Hj\"Qm*)F=7$$\"3co*Q4iq'*z.@\"F_u$\"3Y(Q,up+vN*F=7 $$\"34Q$[)>&*oU7F_u$\"3OZ!)zP7am%*F=7$$\"3I^lOFY^w7F_u$\"3-w%)pSt5q&*F =7$$\"3`!)f6EA448F_u$\"3-KPDS[]f'*F=7$$\"3=;T7EvSU8F_u$\"3B\"='y#[C.u* F=7$$\"3a_wiepWv8F_u$\"3$oY$>Q\"*z4)*F=7$$\"3U$obdw1eS\"F_u$\"3#4Wi\"* p+U')*F=7$$\"3s$)o#3`-1W\"F_u$\"3aZ!3__n`\"**F=7$$\"3-#*)4zFC " 0 "" {MPLTEXT 1 0 29 "f:=eval(sin(x),x=Pi/4* (1+X));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG-%$sinG6#,$*(\"\"%!\" \"%#PiG\"\"\",&F-F-%\"XGF-F-F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "plot(f,X=-1..1);" }}{PARA 13 "" 1 "" {GLPLOT2D 494 494 494 {PLOTDATA 2 "6%-%'CURVESG6$7S7$$!\"\"\"\"!$F*F*7$$!3ommm;p0k&*!#=$\"3: LVVP+ABM!#>7$$!3wKL$3szX@i)R'F27$$!3mmmmT%p\"e()F/$\"3Q%* GfN$eyt*F27$$!3:mmm\"4m(G$)F/$\"3j3(*>`#=)38F/7$$!3\"QLL3i.9!zF/$\"3a8 I*[,\"yS;F/7$$!3\"ommT!R=0vF/$\"3U+o7h)4p%>F/7$$!3u****\\P8#\\4(F/$\"3 Y/OoW#)*=E#F/7$$!3+nm;/siqmF/$\"3%QBn!=d=&e#F/7$$!3[++](y$pZiF/$\"3oV; AE+e/HF/7$$!33LLL$yaE\"eF/$\"3V6y++%p(HKF/7$$!3hmmm\">s%HaF/$\"3Sc2Z&) e38NF/7$$!3Q+++]$*4)*\\F/$\"3%G)R!zT8#GQF/7$$!39+++]_&\\c%F/$\"3%Q7=b] 8-9%F/7$$!31+++]1aZTF/$\"34a2P:VNOWF/7$$!3umm;/#)[oPF/$\"31.;zvj:,ZF/7 $$!3hLLL$=exJ$F/$\"3&\\9E.3!f5]F/7$$!3*RLLLtIf$HF/$\"35!)\\-qS#yE&F/7$ $!3]++]PYx\"\\#F/$\"3sj)*pxF /7$$\"3I*******pvxl\"F/$\"3#o\\a!>0GHzF/7$$\"3#z****\\_qn2#F/$\"3ydN'H Vja7)F/7$$\"3U)***\\i&p@[#F/$\"3VD(R4x2pI)F/7$$\"3B)****\\2'HKHF/$\"3O m>W6w\\)\\)F/7$$\"3ElmmmZvOLF/$\"3wf)y)=tfh')F/7$$\"3i******\\2goPF/$ \"3&ex^C')*3E))F/7$$\"3UKL$eR<*fTF/$\"378nwU;Qm*)F/7$$\"3m******\\)Hxe %F/$\"3V=A=!zi+6*F/7$$\"3ckm;H!o-*\\F/$\"3(eH:lfneB*F/7$$\"3y)***\\7k. 6aF/$\"3/4v%fq+vN*F/7$$\"3#emmmT9C#eF/$\"3QQc\"eCTlY*F/7$$\"33****\\i! *3`iF/$\"3_)Q6\"[t5q&*F/7$$\"3%QLLL$*zym'F/$\"3]0[.Z[]f'*F/7$$\"3wKLL3 N1#4(F/$\"3[@7())[C.u*F/7$$\"3Nmm;HYt7vF/$\"35A)QN9*z4)*F/7$$\"3Y***** **p(G**yF/$\"3eZ^y.2?k)*F/7$$\"3]mmmT6KU$)F/$\"3OVD&*GvO:**F/7$$\"3fKL LLbdQ()F/$\"3s\"*z!pxj4&**F/7$$\"3[++]i`1h\"*F/$\"3u(=<=a+$y**F/7$$\"3 W++]P?Wl&*F/$\"3s\"H^eCwT***F/7$$\"\"\"F*Fez-%'COLOURG6&%$RGBG$\"#5F)F +F+-%+AXESLABELSG6$Q\"X6\"Q!Fa[l-%%VIEWG6$;F(Fez%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "a:=int(f*phi0,X=-1..1)/alpha0;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG,$*&\"\"#\"\"\"%#PiG!\"\"F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "b:=int(f*phi1,X=-1..1)/alpha 1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG,$*(\"\"'\"\"\",&\"\"%!\" \"%#PiGF(F(F,!\"#F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "c:=i nt(f*phi2,X=-1..1)/alpha2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG,$ *(\"#:\"\"\",(*&\"#7F(%#PiGF(F(\"#[!\"\"*$)F,\"\"#F(F(F(F,!\"$F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "P2:=a*phi0+b*phi1+c*phi2;" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#P2G,(*&\"\"#\"\"\"%#PiG!\"\"F(**\" \"'F(,&\"\"%F*F)F(F(F)!\"#%\"XGF(F***\"#:F(,(*&\"#7F(F)F(F(\"#[F**$)F) F'F(F(F(F)!\"$,&*$)F0F'F(F(#F(\"\"$F*F(F(" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 32 "p2:=expand(eval(P2,X=4/Pi*x-1));" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%#p2G,4*&\"#=\"\"\"%#PiG!\"\"F(*(\"%W8F(F)!\"$%\"xGF (F**&\"#'*F(F)!\"#F(*(\"$W\"F(F)F1F.F(F**(\"%!)GF(F)!\"%F.\"\"#F(*(\"& ?:\"F(F)!\"&F.F7F**(\"%gdF(F)F6F.F(F(*&\"$![F(F)F-F**(\"$S#F(F)F-F.F7F (" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#,($\"(%\\KC!\")!\"\"*&$\"*1Xd>\"F&\"\"\"%\"xGF+F +*&$\")+S#Q$F&F+)F,\"\"#F+F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "plot(\{sin(x),p2\},x=0..Pi/2);" }}{PARA 13 "" 1 "" {GLPLOT2D 494 494 494 {PLOTDATA 2 "6&-%'CURVESG6$7S7$$\"\"!F)$!32<)4jp%\\KC!#>7$ $\"3NGK5j*))QU$F,$\"3)o62Eq^>i\"F,7$$\"3DXXYUk*HS'F,$\"3cg`XFQ=&3&F,7$ $\"3=N68yVJ`(*F,$\"3k)QI'yZA3*)F,7$$\"3%3h%eRSe78!#=$\"3s@!y$G=*zE\"F? 7$$\"3k+,hQPB[;F?$\"3\\@NP)3Hdj\"F?7$$\"3'H#*ed(RUf>F?$\"3s8]if,')p>F? 7$$\"3kHX[TMk\"G#F?$\"3ow&*Hb,$*3BF?7$$\"3Saq%HF?$\"3#RAC7X5p)HF?7$$\"3)pq'4OKt)G$F?$\"3c#HrWd/MK$F ?7$$\"3#f/N#RTo*e$F?$\"3ycre>sC8OF?7$$\"3Ut79wN[GRF?$\"3l(pGj85A$RF?7$ $\"3/W^PQXF?7$$\" 3%[IQ)4z@%*[F?$\"3k!RvHm)y)z%F?7$$\"31\\,oR/A[_F?$\"3^Jth&4U15&F?7$$\" 3uvW/+?IP'F?7$$\"3(*zx.5Ir.sF?$\"328l:Y'4`h'F?7$$\"3'pz !QUu\"G^(F?$\"3.S)f?Bc5$oF?7$$\"3A\"3@7LGi%yF?$\"3UKy`RA_cqF?7$$\"3)3 \"HIT&[D>)F?$\"3Qw\"G#Hdv#G(F?7$$\"3gv)\\AI@S\\)F?$\"3UphU#4(3tuF?7$$ \"3vn()=V,i>))F?$\"3_[)*f/UurwF?7$$\"3'G:[dg&*f:*F?$\"3QuR3&yW%pyF?7$$ \"3sSt6rL2&[*F?$\"3!)4M%\\D\\a0)F?7$$\"3mka(*HIZ.)*F?$\"3.5M&H5X%G#)F? 7$$\"3Em\"[l:+d,\"!#<$\"3t\\c6[F\\7%)F?7$$\"3c!3XyEmu/\"Fau$\"3e]P5*4c 1d)F?7$$\"3sJ_*>P$Q\"3\"Fau$\"3$fa&=xR*>t)F?7$$\"3.M\"G%4t676Fau$\"3-f 8G4$p9())F?7$$\"3co*Q4i6k;!*F?7$$\"3[cr`&*GLx6Fau$\" 3+uVzq'*z.@\"Fau$\"3-#extdEXF*F?7$$\"34Q$[)>&*oU7Fa u$\"3yOv%)>cy#R*F?7$$\"3I^lOFY^w7Fau$\"3OrA-3a-4&*F?7$$\"3`!)f6EA448Fa u$\"3)**4?Q>hOh*F?7$$\"3=;T7EvSU8Fau$\"3sqY&>@TKr*F?7$$\"3a_wiepWv8Fau $\"3%ye5ZM\"e/)*F?7$$\"3U$obdw1eS\"Fau$\"3#*Gf.NI+#))*F?7$$\"3s$)o#3`- 1W\"Fau$\"3qx)G9moI'**F?7$$\"3-#*)4zFC5Fau-%'COLOURG6&%$RGBG$\"#5!\"\"F(F(-F$6 $7S7$F(F(7$F.$\"3QsLeI+ABMF,7$F3$\"3]DS+L@i)R'F,7$F8$\"3_b&ehJeyt*F,7$ F=$\"3<&Q%f]#=)38F?7$FC$\"3V-yj65yS;F?7$FH$\"3q)*)ys&)4p%>F?7$FM$\"3G3 RBS#)*=E#F?7$FR$\"3GM*4Ir&=&e#F?7$FW$\"3=7dd?+e/HF?7$Ffn$\"3c0jx$Rp(HK F?7$F[o$\"3ML>uye38NF?7$F`o$\"3V3zj5M@GQF?7$Feo$\"3T$oQx\\8-9%F?7$Fjo$ \"3UOK72VNOWF?7$F_p$\"3=(>VrOc6q%F?7$Fdp$\"3SMGBr+f5]F?7$Fip$\"37xKegS #yE&F?7$F^q$\"3AFv)ygs5c&F?7$Fcq$\"3M>X(*RG,:eF?7$Fhq$\"33g0zi&Qs3'F?7 $F]r$\"3h+)=j,t*RjF?7$Fbr$\"3Qz3MFxj'f'F?7$Fgr$\"3$[8q$y.wDoF?7$F\\s$ \"3wm47uKelqF?7$Fas$\"3M(RvZssjI(F?7$Ffs$\"3C>#p\"po&)3vF?7$F[t$\"3%4z eG%\\()>xF?7$F`t$\"31()\\)y]!GHzF?7$Fet$\"3g&H%*=Uja7)F?7$Fjt$\"3%3R7+ w2pI)F?7$F_u$\"3Q?Zs+w\\)\\)F?7$Feu$\"3Ih!)R3tfh')F?7$Fju$\"3VZPF_)*3E ))F?7$F_v$\"3kW#3Hj\"Qm*)F?7$Fdv$\"3OvDs!yi+6*F?7$Fiv$\"3Uh#yueneB*F?7 $F^w$\"3Y(Q,up+vN*F?7$Fcw$\"3OZ!)zP7am%*F?7$Fhw$\"3-w%)pSt5q&*F?7$F]x$ \"3-KPDS[]f'*F?7$Fbx$\"3B\"='y#[C.u*F?7$Fgx$\"3$oY$>Q\"*z4)*F?7$F\\y$ \"3#4Wi\"*p+U')*F?7$Fay$\"3aZ!3__n`\"**F?7$Ffy$\"3-jN*Rxj4&**F?7$F[z$ \"3%zPL)R0Iy**F?7$F`z$\"3Qg9![CwT***F?7$Fez$\"\"\"F)-Fjz6&F\\[lF(F][lF (-%+AXESLABELSG6$Q\"x6\"Q!Fjdl-%%VIEWG6$;F($\"+Fjzq:!\"*%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "plot(sin(x)-p2,x=0.. Pi/2);" }}{PARA 13 "" 1 "" {GLPLOT2D 494 494 494 {PLOTDATA 2 "6%-%'CUR VESG6$7en7$$\"\"!F)$\"32<)4jp%\\KC!#>7$$\"3=9;b\"[W>r\"F,$\"3Xed$eP>s5 #F,7$$\"3NGK5j*))QU$F,$\"3oMi(zKo7!=F,7$$\"3X')Qy-FW8\\F,$\"3e8TR3MR]: F,7$$\"3DXXYUk*HS'F,$\"3$)y'[bIQMJ\"F,7$$\"3!4%yH5a:y!)F,$\"3S*pJRawJ1 \"F,7$$\"3=N68yVJ`(*F,$\"3!fw\"Gv`L'H)!#?7$$\"3Di))pQx&R9\"!#=$\"3!y5f d6R&4hFK7$$\"3%3h%eRSe78FO$\"3/dfj@Ak#3%FK7$$\"3k+,hQPB[;FO$\"3I\"\\\" HkK#>0&!#@7$$\"3'H#*ed(RUf>FO$!3eh8hM-.&H#FK7$$\"3kHX[TMk\"G#FO$!3Nthc 1:>.ZFK7$$\"3Saq%HFO$!3Y'G^[1VI B)FK7$$\"3)pq'4OKt)G$FO$!3cJ0]p!=NO*FK7$$\"3#f/N#RTo*e$FO$!3!*RAX3Mh,5 F,7$$\"3of\")odQ3fPFO$!3j&[[5BH_-\"F,7$$\"3Ut79wN[GRFO$!3$*ex!pDn*R5F, 7$$\"3]XR6m)y&)4%FO$!3sMzxqsGY5F,7$$\"3/t)[(pvj%FK7$$\"3oHyF.C6noFO$!3TV#>#e&)p/LFK7$$\"3(*zx.5Ir.sF O$!3Kr$f:)=>n=FK7$$\"3'pz!QUu\"G^(FO$!3/*Q1'*o`eH&Ffn7$$\"3A\"3@7LGi%y FO$\"3?_a8$eM51*Ffn7$$\"3)3\"HIT&[D>)FO$\"3S[msa&*phBFK7$$\"3gv)\\AI@S \\)FO$\"3%=a*Huw(pd$FK7$$\"3vn()=V,i>))FO$\"3'Q\"*))e#Q28[FK7$$\"3'G:[ dg&*f:*FO$\"3GvA4!GsN)fFK7$$\"3sSt6rL2&[*FO$\"3ZUU4&p;9+(FK7$$\"3mka(* HIZ.)*FO$\"31TE*eqli%yFK7$$\"3Em\"[l:+d,\"!#<$\"3-'G34E&[+')FK7$$\"3c! 3XyEmu/\"Faw$\"31+kVH47%4*FK7$$\"3sJ_*>P$Q\"3\"Faw$\"3)f[;)3ve4%*FK7$$ \"3.M\"G%4t676Faw$\"3E,]piBB\"\\*FK7$$\"3co*Q4iq'*z.@\"Faw$\"3-X&zB+7u H)FK7$$\"34Q$[)>&*oU7Faw$\"3?3Y0&zhbP(FK7$$\"3I^lOFY^w7Faw$\"3l:qinK>3 hFK7$$\"3`!)f6EA448Faw$\"3#pJgLkkVe%FK7$$\"3=;T7EvSU8Faw$\"3\\0O:$3F$3 FFK7$$\"3a_wiepWv8Faw$\"3K^,\"G[$z<_Ffn7$$\"3U$obdw1eS\"Faw$!3egLM(eL- y\"FK7$$\"3s$)o#3`-1W\"Faw$!3?pl3AO6qZFK7$$\"3-#*)4zFCJ\"F,7$$\"3\\3Y:@imO:Faw$!3dVmVKrx,:F,7$$\"3C/BSs7t`:Faw$!31P%)f#* >%[r\"F,7$$\"3+++lBjzq:Faw$!3\\BF\\CLKP>F,-%'COLOURG6&%$RGBG$\"#5!\"\" F(F(-%+AXESLABELSG6$Q\"x6\"Q!F^^l-%%VIEWG6$;F($\"+Fjzq:!\"*%(DEFAULTG " 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }} }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "d:=int(f*phi3,X=-1..1)/alp ha3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dG,$*(\"#N\"\"\",*\"$g*F(* &\"#CF()%#PiG\"\"#F(!\"\"*&\"$S#F(F.F(F0*$)F.\"\"$F(F(F(F.!\"%F0" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "P3:=P2+d*phi3;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%#P3G,**&\"\"#\"\"\"%#PiG!\"\"F(**\"\"'F(,&\"\" %F*F)F(F(F)!\"#%\"XGF(F***\"#:F(,(*&\"#7F(F)F(F(\"#[F**$)F)F'F(F(F(F)! \"$,&*$)F0F'F(F(#F(\"\"$F*F(F(**\"#NF(,*\"$g*F(*&\"#CF(F8F(F**&\"$S#F( F)F(F**$)F)F>F(F(F(F)!\"%,&*$)F0F>F(F(*&#F>\"\"&F(F0F(F*F(F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "p3:=evalf(expand(eval(P3,X=4 /Pi*x-1)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#p3G,*$\"']eA!\")!\" \"*&$\"(*oQ6!\"(\"\"\")%\"xG\"\"$F.F)*&$\"'W%*pF-F.)F0\"\"#F.F)*&$\")' pr-\"F-F.F0F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "plot(sin (x)-p3,x=0..Pi/2);" }}{PARA 13 "" 1 "" {GLPLOT2D 494 494 494 {PLOTDATA 2 "6%-%'CURVESG6$7`p7$$\"\"!F)$\"35+++++]eA!#?7$$\"3)32exSA( f&)F,$\"3:>SM*RF5.#F,7$$\"3=9;b\"[W>r\"!#>$\"3i0w:Dcg8=F,7$$\"3W@uKAn \"zc#F5$\"3tE(y'eg.1;F,7$$\"3NGK5j*))QU$F5$\"3+vC/t,739F,7$$\"3X')Qy-F W8\\F5$\"3#*e#f_*f8'3\"F,7$$\"3DXXYUk*HS'F5$\"3-4zlD(4u\"z!#@7$$\"3!4% yH5a:y!)F5$\"3$f')pg!*pK#\\FL7$$\"3=N68yVJ`(*F5$\"3A3,[Z37]AFL7$$\"3Di ))pQx&R9\"!#=$!3xE$zs!RS98!#A7$$\"3%3h%eRSe78FZ$!3W2z\\R'ev@#FL7$$\"3u bt4*))3/[\"FZ$!3'**\\?Mq>^,%FL7$$\"3k+,hQPB[;FZ$!3=arHCwB\\bFL7$$\"3'H #*ed(RUf>FZ$!3'Q?cz(=fXxFL7$$\"3IE;,kGFZ$!3aSaq% HFZ$!3gSo#e;om+\"F,7$$\"3on$***=Q*y6$FZ$!3+>jrD75!*)*FL7$$\"3)pq'4OKt) G$FZ$!39(yDa+>)y&*FL7$$\"3twem(o3#RMFZ$!3K&z0!=TxD'FL7$$\"3oHyF.C6noFZ$\"3eKi=& 4&e`uFL7$$\"3(*zx.5Ir.sFZ$\"3h'*pE(R?[U)FL7$$\"3'pz!QUu\"G^(FZ$\"3$z\\ \"f>gSU!*FL7$$\"33R4!o)G_zwFZ$\"3]W/J'fJ*f#*FL7$$\"3A\"3@7LGi%yFZ$\"3O Tn]OH&QR*FL7$$\"30'*>EO%)Q>!)FZ$\"33qaU<\"QHW*FL7$$\"3)3\"HIT&[D>)FZ$ \"39I9ok6O*R*FL7$$\"3p#Rw<#\\GV$)FZ$\"3'HQ51DNdG*FL7$$\"3gv)\\AI@S\\)F Z$\"3SK8`0#e=5*FL7$$\"3vn()=V,i>))FZ$\"3-5`HKTAo%)FL7$$\"3'G:[dg&*f:*F Z$\"3[P$Q\"3\"Fiz$!3M^G:e'zU5\"FL7$$\"3.M\"G %4t676Fiz$!3?([>D!p]`IFL7$$\"3co*Q4id6)**pFL7$$\"3Hk&>q'*z.@\"Fiz$!3^*Q7KWU@r)FL7$$\"34Q$ [)>&*oU7Fiz$!3;ga-)*=!e+\"F,7$$\"3qWugt?gf7Fiz$!3Qsp%=$*3%f5F,7$$\"3I^ lOFY^w7Fiz$!3MD;;#fP\"*4\"F,7$$\"3m3R0F!fYG\"Fiz$!30=<2hUD7\"F,7$$\"3ioi!R\"Fiz$!3JEM7$*f'*Q&)FL7$ $\"3U$obdw1eS\"Fiz$!3\"R!=-u4uCtFL7$$\"3Y$G\"H[Y?B9Fiz$!38V(fW!)p!4cFL 7$$\"3s$)o#3`-1W\"Fiz$!3p*GXAOw1_$FL7$$\"3w(QoVSjhX\"Fiz$!3ed`k![&f88F L7$$\"3-#*)4zFC;*4d\"zFL7$$\"3^lB')ok%G^\"Fiz$\"3# f)pk'HdOy*FL7$$\"3D8JH'Q'y?:Fiz$\"3!*z'>Kc.i<\"F,7$$\"3)4'Qs.jsG:Fiz$ \"35\\W!)o%*R&Q\"F,7$$\"3\\3Y:@imO:Fiz$\"3q-jD#Rsig\"F,7$$\"3[c%ynu)>X :Fiz$\"3=Cv+ij,d=F,7$$\"3C/BSs7t`:Fiz$\"3rpzF0V-A@F,7$$\"3+_h-)zjAc\"F iz$\"3%*Qoi&Q2m?['p#F,-%'COLOURG6&%$RG BG$\"#5!\"\"F(F(-%+AXESLABELSG6$Q\"x6\"Q!Fffl-%%VIEWG6$;F($\"+Fjzq:!\" *%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 " Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "e:=int(f*phi4,X =-1..1)/alpha4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"eG,$**\"$:$\"\" \"\"\"%!\"\",,*&\"%?nF(%#PiGF(F**&\"#SF()F.\"\"$F(F(*$)F.F)F(F(\"&!)o# F(*&\"$?(F()F.\"\"#F(F*F(F.!\"&F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "P4:=P3+e*phi4;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%# P4G,,*&\"\"#\"\"\"%#PiG!\"\"F(**\"\"'F(,&\"\"%F*F)F(F(F)!\"#%\"XGF(F** *\"#:F(,(*&\"#7F(F)F(F(\"#[F**$)F)F'F(F(F(F)!\"$,&*$)F0F'F(F(#F(\"\"$F *F(F(**\"#NF(,*\"$g*F(*&\"#CF(F8F(F**&\"$S#F(F)F(F**$)F)F>F(F(F(F)!\"% ,&*$)F0F>F(F(*&#F>\"\"&F(F0F(F*F(F**,\"$:$F(F.F*,,*&\"%?nF(F)F(F**&\"# SF(FHF(F(*$)F)F.F(F(\"&!)o#F(*&\"$?(F(F8F(F*F(F)!\"&,(*$)F0F.F(F(*&#F, \"\"(F(F;F(F*#F>F@F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "p4:=evalf(expand(eval(P4,X=4/Pi*x-1)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#p4G,,*&$\"((fa**!\"(\"\"\"%\"xGF*F**&$\"&%Q?!\"&F*)F+\"\"$F*! \"\"*&$\"%&4#F/F*)F+\"\"#F*F*$\"&8K#!\")F**&$\"%lGF/F*)F+\"\"%F*F*" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "plot(p4-sin(x),x=0..Pi/2); " }}{PARA 13 "" 1 "" {GLPLOT2D 494 494 494 {PLOTDATA 2 "6%-%'CURVESG6$ 7_q7$$\"\"!F)$\"3))**********H@B!#@7$$\"3WN!zQ?h)zU!#?$\"3[LVer)*yI@F, 7$$\"3)32exSA(f&)F0$\"3E^2mW6yZ>F,7$$\"3s5P;h$eRG\"!#>$\"3?)G\\$4C5sr\"F;$\"3#ecF;$\"3Ub_G *G3de$FM7$$\"3DXXYUk*HS'F;$\"3z#f-=SY?!=FM7$$\"33$>\"QEfdSsF;$!3U]8<.n T97!#C7$$\"3!4%yH5a:y!)F;$!3Ql$Hw!zXL;FM7$$\"3t)[9U*[t:*)F;$!3wK'Q8ry? 2$FM7$$\"3=N68yVJ`(*F;$!3#H\\`bx\"*yL%FM7$$\"3Di))pQx&R9\"!#=$!3@lDu@2 v+kFM7$$\"3%3h%eRSe78Fdp$!31v!RUlsk(yFM7$$\"3ubt4*))3/[\"Fdp$!3#*ynj.w pJ))FM7$$\"3k+,hQPB[;Fdp$!3*\\*)y:VF%R$*FM7$$\"3O.PD=D8(o\"Fdp$!3cT`9i gs*R*FM7$$\"3O1t*yHJgs\"Fdp$!3C%4ngVk*R%*FM7$$\"3344ax+$\\w\"Fdp$!3iYq Fs,&3Y*FM7$$\"3!=^%=d)GQ!=Fdp$!3cy;9z!zIY*FM7$$\"3_9\"GojFF%=Fdp$!3_3. @U_LZ%*FM7$$\"3C<D0#>Fdp$!3QC $G2f2YO*FM7$$\"3'H#*ed(RUf>Fdp$!3s4*f:7M*)H*FM7$$\"3IESaq%HFdp$!3?6OT(o&RBSFM7$$\"3)pq'4OKt)G$Fdp$!3#4n YM)e(RU\"FM7$$\"3#f/N#RTo*e$Fdp$\"3A5,@Kwy%f)!#B7$$\"3Ut79wN[GRFdp$\"3 SE[)*ztviKFM7$$\"3/72&Fdp$\" 3x7)o#=?oR')FM7$$\"31\\,oR/A[_Fdp$\"3(*H+'Q5%G,!*FM7$$\"3%HJi$GP;)R&Fd p$\"3$GP!fo<6/#*FM7$$\"3uvW/_B'oJNcF dp$\"3zbAL'>$GN$*FM7$$\"3c4*fwqEDs&Fdp$\"3)Gc\"4W(*zE$*FM7$$\"3.Fw'HbO (4eFdp$\"39mlG>%[))G*FM7$$\"3]W`F)RYp*eFdp$\"3Ss/5a#3AA*FM7$$\"3G:#\\( ytL^gFdp$\"3a=Fl$zul.*FM7$$\"33'3B#f$Gd?'Fdp$\"31svj#=.\"p()FM7$$\"3.n 3p46^WlFdp$\"3'yO[`X>d#zFM7$$\"3oHyF.C6noFdp$\"3#\\M?0<(y]oFM7$$\"3(*z x.5Ir.sFdp$\"3C%y%FM7$$ \"3A\"3@7LGi%yFdp$\"3gv!3H([^PFFM7$$\"3)3\"HIT&[D>)Fdp$\"3a]*zN[2qF\"F M7$$\"3gv)\\AI@S\\)Fdp$\"3-T5;w\"y_H\"F\\v7$$\"3vn()=V,i>))Fdp$!3cHU&* ))>=l!*F\\v7$$\"3'G:[dg&*f:*Fdp$!3-:Ivp\"QIo\"FM7$$\"3zYFV)[M0K*Fdp$!3 6))p]%QmQ$>FM7$$\"3sSt6rL2&[*Fdp$!3_F$=IC-24#FM7$$\"3p-ka+KFW'*Fdp$!31 A`)*Ql]Z@FM7$$\"3mka(*HIZ.)*Fdp$!3AkNeR:V1@FM7$$\"3gj&GxHP-)**Fdp$!3+G AL5v#=%>FM7$$\"3Em\"[l:+d,\"!#<$!3e#z8tF#e[;FM7$$\"3IBm>7KeJ5F\\_l$!3% y\\DC<7OF\"FM7$$\"3c!3XyEmu/\"F\\_l$!3Z+[B%p@l#zF\\v7$$\"3sJ_*>P$Q\"3 \"F\\_l$\"3908_1^!p%eF\\v7$$\"3.M\"G%4t676F\\_l$\"3A$>=\"HA\\EAFM7$$\" 3co*Q4iq'*z.@\"F\\_l$\"3/*za7\\[-W*FM7$$\"34Q$[)>&*oU7F\\_l$\"3AYG' H!=R;7F,7$$\"3I^lOFY^w7F\\_l$\"3A\"o/w$=t'\\\"F,7$$\"3`!)f6EA448F\\_l$ \"3vw2r[!3Su\"F,7$$\"3=;T7EvSU8F\\_l$\"3Q(yJ[NZ?&>F,7$$\"3C%)ePUs#*e8F \\_l$\"3x&\\4,dI2.#F,7$$\"3a_wiepWv8F\\_l$\"3sGkN\\Tn)3#F,7$$\"3Eg'4/ \"p.$Q\"F\\_l$\"3'4pT`9]t5#F,7$$\"3'zm\">ioi!R\"F\\_l$\"3]?U(>0907#F,7 $$\"3#=n#3Q=U%R\"F\\_l$\"3(z$oWF6\"\\7#F,7$$\"3ovO(R\"o@)R\"F\\_l$\"3> W!Q.a(yF@F,7$$\"3czY')*y6?S\"F\\_l$\"3i4dDjW4H@F,7$$\"3U$obdw1eS\"F\\_ l$\"3ri8n^CyG@F,7$$\"3V$e*QOi:59F\\_l$\"3\\.D7<#pj7#F,7$$\"3W$[Bqq0XT \"F\\_l$\"3BJn$pB(o@@F,7$$\"3X$Qdw1_5#F,7$$\"3[$3f&*e.>V\"F\\_l$\"3ItMCgoqy?F,7$$ \"3s$)o#3`-1W\"F\\_l$\"3qB4DB&R:/#F,7$$\"3w(QoVSjhX\"F\\_l$\"3;,g$opJj %>F,7$$\"3-#*)4zFC`dST-*FM7$$\"3\\3Y:@imO:F\\_l$\"3_X:F\\_l$\"3Y$**R>%4(\\(\\FM7$$\"3C/BSs7t`:F\\_l$\"39z*[P) y.*e#FM7$$\"3+_h-)zjAc\"F\\_l$!3<@)y\\\"[)y$[!#D7$$\"3+++lBjzq:F\\_l$! 3gRd]X()G:GFM-%'COLOURG6&%$RGBG$\"#5!\"\"F(F(-%+AXESLABELSG6$Q\"x6\"Q! Fd[m-%%VIEWG6$;F($\"+Fjzq:!\"*%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 72 "int(f^2,X=-1..1)-a^2*alpha0-b^2*alpha1-c^2*alpha2-d ^2*alpha3-e^2*alpha4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,.\"\"\"F$*& \"\")F$%#PiG!\"#!\"\"*(\"#CF$,&\"\"%F)F'F$\"\"#F'!\"%F)*(\"#SF$,(*&\"# 7F$F'F$F$\"#[F)*$)F'F.F$F$F.F'!\"'F)*(\"#cF$,*\"$g*F$*&F+F$F7F$F)*&\"$ S#F$F'F$F)*$)F'\"\"$F$F$F.F'!\")F)*(\"#sF$,,*&\"%?nF$F'F$F)*&F1F$FAF$F $*$)F'F-F$F$\"&!)o#F$*&\"$?(F$F7F$F)F.F'!#5F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"( /C!**!#:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "sqrt(%/2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+7yZOq!#9" }}}}{MARK "38" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }