{VERSION 5 0 "IBM INTEL LINUX" "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 }{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 "Text Ou tput" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 0 }0 0 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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "#This graph plots th e normal derivative of the heat kernel over two different boundary poi nts." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "#First we load the necessary data. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "read \"values_5. m\";" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "read \"values_2.m\" ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 111 "#Then we create the function we wish to graph , which combines the functions for both the 2-series and 5-series." }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 130 "summery:=log(abs((sum('(exp(-(El5[j])*x))*(-2*((dn 5[j])^2)/3)','j'=1..512)) + (sum('(exp(-(El[j])*x))*((dn[j])^2)','j'=1 ..512)))):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "#And then we create the graph. Yay !" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 189 "plot([log(1/x),summery,x=10^(-6)..1],title=\" Plot of function with norm at different points on j=512\", style=point , numpoints=1000,labels=[\"log(1/time)\",\"normal derivative of heat k ernel\"]);" }}{PARA 13 "" 1 "" {GLPLOT2D 382 382 382 {PLOTDATA 2 "6'-% 'CURVESG6$7c[o7$$\"3OFkzb5b\"Q\"!#;$!3DB&o/jvYh\"!#<7$$\"3H1xbaprH5F*$ !3.^q/\")F-7$$\"3]fh-yuD#\\(F-$!3S1R[ ecYj!)F-7$$\"3l8gCT()>NuF-$!3aHi2-g46zF-7$$\"3*=.OJr?7Q(F-$!3Csw@&p0,j (F-7$$\"39'>&R*p2+L(F-$!34R#*oeQuVsF-7$$\"3#*4YM,i$[B(F-$!3$p2TN6Q]L'F -7$$\"3/)\\wrSSz9(F-$!3b]UtNp&=W&F-7$$\"3+mI\\%QrR*pF-$!30(QR%eeGRRF-7 $$\"31&\\&QcidgoF-$!3`qf.8J6zFF-7$$\"3GO#>moFRm'F-$!3UF'z\">c))38F-7$$ \"3;6Jndwm*\\'F-$!3-7t:\\IT&y#!#=7$$\"3d1IFh2iejF-$\"3#y![JrMi*y%F\\r7 $$\"3$er@`8J]B'F-$\"3#f]3>)f$e0\"F-7$$\"3l`'3S[RF+'F-$\"3,+0\"e1?h%>F- 7$$\"3/Xese`O9eF-$\"3Nz&QmKfe]#F-7$$\"3j)*Hs$yvu^&F-$\"3woq.=)*G&F-$\"3;FJJ&H.XX$F-7$$\"3.!=y;>0p6&F-$\"3>l/#f\")=vg$F-7 $$\"32.*4'*H$ok\\F-$\"3%)p>@n(\\#)o$F-7$$\"3\\jSy)3y$G[F-$\"3AGgdO\")3 @PF-7$$\"3Hx^gua!)3ZF-$\"3_(pYR$pi?PF-7$$\"3%)fG>127*f%F-$\"3G@EVu)okp $F-7$$\"3$QI;.Gn:^%F-$\"3@gH&=kq1m$F-7$$\"3'**>0h&eQ@WF-$\"3FD`B)*=(zg $F-7$$\"3^*GNOqU$QVF-$\"3\"Q6hZm&eWNF-7$$\"3#*p&)>XRNkUF-$\"32/4EI.TvM F-7$$\"30\"[X'y7g,UF-$\"3PgHHu\\v1MF-7$$\"3[.&f'=7xJTF-$\"3ya#=,f)y=LF -7$$\"3y&\\r\"\\o?wSF-$\"33l$QuW#RRKF-7$$\"3..x)*oCB:SF-$\"3q(\\:t**y< 9$F-7$$\"37j)z-4(>kRF-$\"3>g4=h=!30$F-7$$\"3#49'z6f/6RF-$\"3S&yL04Mg%H F-7$$\"3(*p73g7$H'QF-$\"3^3p([1$GTGF-7$$\"3iSSk$f!3:QF-$\"3W5^;:)Qks#F -7$$\"33C5]&\\oIx$F-$\"3Pg@A F-7$$\"3\\)zlcp1Fh$F-$\"3eFSTkW6p?F-7$$\"33)G$oOzFvNF-$\"3gPnDK]G**=F- 7$$\"3?#oR(e(o*RNF-$\"3Bq\\(f>,_r\"F-7$$\"3_N$oK]_p]$F-$\"3K1`CQPc9:F- 7$$\"3P2Hc+r_rMF-$\"3wp\\$eb'3b7F-7$$\"3%f9#)44K2W$F-$\"3(RRw&zlL@(*F \\r7$$\"3D&)e9=h')3MF-$\"3\"HG0BJ\"36eF\\r7$$\"3+E*=2RU3Q$F-$\"3]'zZ)= G\\\"o'!#>7$$\"3o[%*G`x2^LF-$!3Y-%H<_ix2\"F-7$$\"3qdU9*\\MwM$F-$!30Qj0 =pG`8F-7$$\"3$GjE.1.UM$F-$!3(Qf!*eVU0t\"F-7$$\"3#H7!QY<\\ULF-$!3?^\\_6 Vq))>F-7$$\"3&HcEgN$ySLF-$!3VShKLimNBF-7$$\"3Z4PHzy2RLF-$!3IdV]di3oGF- 7$$\"3\"HDgiIvtL$F-$!3A!\\`ctD72%F-7$$\"3w)*)e=$)yRL$F-$!37k[R'*=X#y#F -7$$\"3m^wXaQfILF-$!3_[^(o$\\Zl>F-7$$\"3ZrZ['H?sK$F-$!3[chE'3!HD:F-7$$ \"3#)e4:\"3eQK$F-$!3q2!o@#3;B7F-7$$\"3$\\G_$F-$\"3#Q=z8='>s5F-7$$\"3[:7vj\\LoJF-$\"3e/@q CB#H?\"F-7$$\"3]2\"ow'G]YJF-$\"3=ZT[kHk,8F-7$$\"3s;\\eFL0AJF-$\"3KEAj] 'pfR\"F-7$$\"3Or*ehc!o+JF-$\"3s5ED9?4n9F-7$$\"3bB=IV\\QyIF-$\"3iy'Gl*f )>`\"F-7$$\"3*G\\e!=4]dIF-$\"3YYz$Q[_ae\"F-7$$\"3jl0-8<\"[.$F-$\"3)[(Q 3+cjO;F-7$$\"3HVXb\"oAH-'G)=F-7$$\"3&*QHwR2r7GF-$\"3sKu:!3% e!*=F-7$$\"3m#R&)\\')Gbz#F-$\"357)HH\\;r*=F-7$$\"3kF3B$oD-y#F-$\"3)>t. 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