{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 "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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "L4NormToPower4:=proc(L)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "local sum,x,M;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "M:=convert(L,list);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "sum:=0;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "for x in M do sum:= sum+x^4;od;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "return(eval(s um));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%/L4NormToPower4Gf*6#%\"LG6%%$sumG%\"xG%\"MG6\"F,C&>8& -%(convertG6$9$%%listG>8$\"\"!?&8%F/%%trueG>F6,&F6\"\"\"*$)F9\"\"%F=F= O-%%evalG6#F6F,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 56 "verify_surface_subcube:=proc(centre,halfside,face_i ndex)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "global T;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "local \+ s,n,y;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "n:=coldim(T);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "i f (24^2*halfside^4*n >=1) then return(1);fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "y:=evalm(T &* centre);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "s:=L4NormToPower4(y)/L4N ormToPower4(centre);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "if (evalb(s > 1)) then return(0);fi;" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "s:=evalb(24^2*n*halfside^4<=(1-s)^2);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "if s then return(2) else return(1);fi;" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 4 "end;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 12 "" 1 "" {XPPMATH 20 "6# >%7verify_surface_subcubeGf*6%%'centreG%)halfsideG%+face_indexG6%%\"sG %\"nG%\"yG6\"F.C)>8%-_%'linalgG%'coldimG6#%\"TG@$1\"\"\",$*(\"$w&F:)9% \"\"%F:F1F:F:OF:>8&-%&evalmG6#-%#&*G6$F79$>8$*&-%/L4NormToPower4G6#FCF :-FO6#FJ!\"\"@$-%&evalbG6#2F:FLO\"\"!>FL-FV6#1F;*$),&F:F:FLFS\"\"#F:@% FLOF\\oOF:F.F6F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 52 "do_surface_subcube:=proc(centre,halfside,face_index )" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "global T;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "local n,h,k,kk, new_centre,i,j;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "k:=verify_surface_subcube(centre,halfside,face_i ndex);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "if k=0 then return(false);fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "if k=2 then return(true);fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "n:=coldim(T);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "h:=halfside/2;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "for k from \+ 0 to 2^(n-1)-1 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 " kk:=k;" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 " new_centre:=[0$n];" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 24 " for j from 1 to n do" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 62 " if j=face_index then new_centre[j]:=centre[ j];next;fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 52 " new_centre[j ]:=centre[j]+h*(2*irem(kk,2)-1);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " kk:=iquo(kk,2);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 " " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 " od;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "if not do_surface_subcube(new_centre,h,face_inde x) then return(false);fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "return(true);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%3d o_surface_subcubeGf*6%%'centreG%)halfsideG%+face_indexG6)%\"nG%\"hG%\" kG%#kkG%+new_centreG%\"iG%\"jG6\"F2C)>8&-%7verify_surface_subcubeG6%9$ 9%9&@$/F5\"\"!O%&falseG@$/F5\"\"#O%%trueG>8$-_%'linalgG%'coldimG6#%\"T G>8%,$*&#\"\"\"FCFSF:FSFS?(F5F>FS,&)FC,&FGFSFS!\"\"FSFSFXFEC&>8'F5>8(7 #-%\"$G6$F>FG?(8*FSFSFGFEC%@$/F]oF;C$>&Fgn6#F]o&F9Fdo\\>Fco,&FeoFS*&FO FS,&*&FCFS-%%iremG6$FenFCFSFSFSFXFSFS>Fen-%%iquoGF^p@$4-F$6%FgnFOF;OF@ OFEF2FLF2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "verify_face:=proc(face_index)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "global T;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "local \+ halfside,n,centre;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "n:=cold im(T);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "halfside:=1;" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 14 "centre:=[0$n];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "centre[face_index]:=1;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "return(do_surface_subcub e(centre, halfside,face_index));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%,verify_faceGf*6#%+fa ce_indexG6%%)halfsideG%\"nG%'centreG6\"F,C'>8%-_%'linalgG%'coldimG6#% \"TG>8$\"\"\">8&7#-%\"$G6$\"\"!F/>&F:6#9$F8O-%3do_surface_subcubeG6%F: F7FCF,F4F," }}}{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 18 "verify_ all:=proc()" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "global T;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "local n,j;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "n:=coldim(T);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "for j from 1 to n do if not verif y_face(j) then return(false);fi;od;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "return(true);" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 4 "end;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%+verify_allGf*6\"6$%\"nG%\"jGF&F&C%> 8$-_%'linalgG%'coldimG6#%\"TG?(8%\"\"\"F5F,%%trueG@$4-%,verify_faceG6# F4O%&falseGOF6F&F1F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 80 "T:=matrix([[-292187/1000000,812218/1000000],[-95848 9/1000000,-113428/1000000]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"T GK%'matrixG6#7$7$#!'(=#H\"(+++\"#\"'4hS\"'++]7$#!'*[e*F,#!&d$G\"'++DQ( pprint06\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "verify_all();" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%tr ueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "T:=array(1..7,1..5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"TG-%&a rrayG6%;\"\"\"\"\"(;F)\"\"&7\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "C:=652773/100000;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG#\" 'tFl\"'++5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "c:=[1,2,-22/5 ];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG7%\"\"\"\"\"##!#A\"\"&" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "mu:=[263485/1000000,385467/ 1000000,360598/1000000,302274/1000000,165718/1000000];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#muG7'#\"&(p_\"'++?#\"'naQ\"(+++\"#\"'*H!=\"'++] #\"'P6:F.#\"&fG)F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 110 "nu:= [64388/1000000,146465/1000000,300904/1000000,364746/1000000,318525/100 0000,247617/1000000,123827/1000000];" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%#nuG7)#\"&(4;\"'++D#\"&$HH\"'++?#\"&8w$\"'+]7#\"'tB=\"'++]#\"&TF\" \"&++%#\"' " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 124 "for j from 1 to 7 do for k from 1 to 5 do if j-k>=0 and j-k<=2 then T[j,k]:=mu[k]*c[j -k+1]/nu[j]/C; else T[j,k]:=0;fi;od;od;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "print(T);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'matrix G6#7)7'#\"++]7(e'\",\")po20\"\"\"!F+F+F+7'#\",++SR0\"\",*[z;7>#\"+++yp D\"+jJ*QP'F+F+F+7'#!++]U<8\"+f#o?B##\"++]A7K\"+$G]U=)#\"++]Z2X\",\\3v_ X#F+F+7'F+#!+++ypD\"+8._2O#\",++!)fg$\"-H.<[!>\"#\"+++Iz;\",\"[uvA8F+7 'F+F+#!*+o&pd\"*j\"*3c(#\"*+!)oo#\"*x*3T#*#\"*+?(Gm\"+$z!)pJ)7'F+F+F+# !+++WV8\"+fRqK;#\",++gVJ$\"-T>pP;;7'F+F+F+F+#!+++sGm\"+hcE[tQ(pprint06 \"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "verify_all();" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "35 0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }