{VERSION 6 0 "IBM INTEL LINUX" "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 "Text Output" -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 "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }1 0 0 0 8 4 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 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 "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 3 "" 0 "" {TEXT -1 60 " \+ Magilatin cubic count" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 90 "COMPUTE: the number of magilatin squares with magic sum equal t o t, for small values of t." }}{PARA 0 "" 0 "" {TEXT -1 172 "METHOD: g enerate all weakly magilatin positive squares and eliminate those that have repeated values in a row or column. This is the stupid method; \+ there are no shortcuts." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 101 "Notat ion: the 3x3 square is x, with cells numbered from 1 to 9 across rows, starting at the top left." }}{PARA 0 "" 0 "" {TEXT -1 37 "The values \+ of t range from 1 to tmax." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "tmax: =100;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%tmaxG\"$+\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "The generating function, computed separat ely." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 178 "Lgf := 12*x^4*\n(79*x^15+1 90*x^14+260*x^13+250*x^12+211*x^11+179*x^10+181*x^9+198*x^8+210*x^7+18 1*x^6+125*x^5+61*x^4+22*x^3+8*x^2+4*x+1)/(x-1)^2/(x^4-1)/(x^5-1)/(x^3- 1)^2/(x+1)^2;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$LgfG,$*2\"#7\"\"\" %\"xG\"\"%,B*&\"#zF()F)\"#:F(F(*&\"$!>F()F)\"#9F(F(*&\"$g#F()F)\"#8F(F (*&\"$]#F()F)F'F(F(*&\"$6#F()F)\"#6F(F(*&\"$z\"F()F)\"#5F(F(*&\"$\"=F( )F)\"\"*F(F(*&\"$)>F()F)\"\")F(F(*&\"$5#F()F)\"\"(F(F(*&FDF()F)\"\"'F( F(*&\"$D\"F()F)\"\"&F(F(*&\"#hF()F)F*F(F(*&\"#AF()F)\"\"$F(F(*&FJF()F) \"\"#F(F(*&F*F(F)F(F(F(F(F(,&F)F(F(!\"\"!\"#,&*$FXF(F(F(F\\oF\\o,&*$FT F(F(F(F\\oF\\o,&*$FenF(F(F(F\\oF]o,&F)F(F(F(F]oF(" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 17 "Series expansion." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "series(Lgf,x=0,50); " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#+[q%\"xG \"#7\"\"%\"#[\"\"&\"$?\"\"\"'\"$%Q\"\"(\"%o5\"\")\"%sC\"\"*\"%'*[\"#5 \"%s!*\"#6\"&;b\"F%\"&3c#\"#8\"&'HS\"#9\"&3;'\"#:\"&o5*\"#;\"'S;8\"#< \"'O^=\"#=\"'gfD\"#>\"'goM\"#?\"'[KY\"#@\"')33'\"#A\"'S#*y\"#B\"(;.,\" \"#C\"(W0G\"\"#D\"(K[g\"\"#E\"(kS*>\"#F\"(7SX#\"#G\"(c')*H\"#H\"(7Rj$ \"#I\"(kgP%\"#J\"(sHB&\"#K\"(!3Bi\"#L\"('*[N(\"#M\"('*3l)\"#N\")O-75\" #O\")oxy6\"#P\")'4lO\"\"#Q\")C+y:\"#R\")w[9=\"#S\")!G#z?\"#T\")[[tB\"# U\")k'3q#\"#V\")!eH1$\"#W\")gljM\"#X\")/h/R\"#Y\")!3.R%\"#Z\")C\\A\\F' \")w,1b\"#\\-%\"OG6#\"\"\"\"#]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1733 "for t from 1 to tmax do\n count[t]:=0:\n for x[1] from 1 to \+ t-1 do\n for x[2] from 1 to t-1 do \n for x[3] from 1 to t-1 do\n \+ if( x[1]=x[2] or x[3]=x[1] or x[3]=x[2] ) then \n #print( \"21 \+ or 31 or 32\", x[1],x[2],x[3] );\n else \n magicsum:=x[1]+x[2]+ x[3]: \n #print(t,x[1],x[2],x[3],magicsum);\n for x[4] from 1 \+ to t-1 do\n if( x[4]=x[1] ) then \n #print( \"41\", x[1],x [2],x[3],x[4] );\n else\n x[7]:=magicsum-x[1]-x[4]:\n \+ if( x[7]<=0 or x[7]>=t or x[7]=x[1] or x[7]=x[4] ) then \n \+ #print( \"7 or 71 or 74\", x[1],x[2],x[3],x[4],x[7] );\n else \n #print( x[1],x[2],x[3],x[4],x[7] );\n for x[5] fr om 1 to t-1 do\n if( x[5]<=0 or x[5]>=t or x[5]=x[2] or x[5 ]=x[4] ) then \n #print(\"5 or 52 or 54\", x[1],x[2],x[3], x[4],x[5],x[7] );\n else \n ok:=1: \n \+ x[6]:=magicsum-x[5]-x[4]:\n x[8]:=magicsum-x[5]-x[2]:\n x[9]:=magicsum-x[3]-x[6]:\n #print( ok, x ); \n if( x[8]<=0 or x[8]>=t or x[8]=x[5] or x[8]=x[2] or x[8 ]=x[7] ) then \n ok:=0: \n fi:\n \+ if( x[6]<=0 or x[6]>=t or x[6]=x[5] or x[6]=x[4] or x[6]=x[3] ) then \n ok:=0:\n fi:\n if( x[9]=x[6] \+ or x[9]=x[3] or x[9]=x[8] or x[9]=x[7] ) then\n ok:=0:\n fi:\n if( x[9]<=0 or x[9]>=t ) then ok:=0 fi: \n count[t]:=count[t]+ok:\n #print(count[t],ok ,x);\n fi:\n od:\n fi:\n fi:\n od: \n fi:\n od:\n od:\n od:\n Lc[t]:=coeff(series(Lgf,x=0,tmax+1),x ^t):\n if( count[t]=Lc[t] ) then print(t,count[t],\"Consistent\");\n \+ else print(t,count[t],Lc[t],\"Inconsistency\"); \n fi: \nod:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"\"\"\"!Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"#\"\"!Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"$\"\"!Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"%\"#7Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\" &\"#[Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"'\"$?\"Q+C onsistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"(\"$%QQ+Consistent 6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\")\"%o5Q+Consistent6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"*\"%sCQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#5\"%'*[Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#6\"%s!*Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#7\"&;b\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\" #8\"&3c#Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#9\"&'HSQ +Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#:\"&3;'Q+Consiste nt6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#;\"&o5*Q+Consistent6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#<\"'S;8Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#=\"'O^=Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#>\"'gfDQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#?\"'goMQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"# @\"'[KYQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#A\"')33'Q +Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#B\"'S#*yQ+Consist ent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#C\"(;.,\"Q+Consistent6\" " }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#D\"(W0G\"Q+Consistent6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#E\"(K[g\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#F\"(kS*>Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#G\"(7SX#Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#H\"(c')*HQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#I\"(7Rj$Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#J\"(kgP%Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#K\"(sHB&Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#L\"(!3BiQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#M\"('*[N(Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#N\"('*3l)Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#O\")O-75Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#P\")oxy6Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#Q\")'4lO\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#R\")C+y:Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#S\")w[9=Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#T\")!G#z?Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#U\")[[tBQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#V\")k'3q#Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#W\")!eH1$Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#X\")gljMQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#Y\")/h/RQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#Z\")!3.R%Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#[\")C\\A\\Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#\\\")w,1bQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#]\")S%H9'Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#^\")s]QoQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#_\")S&[f(Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#`\")S!zT)Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#a\")g()4$*Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#b\"*s5x-\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#c\"*oAA8\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#d\"*3'>X7Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#e\"*?.pO\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#f\"*G(4)\\\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#g\"*_e!R;Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#h\"*_&e!z\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#i\"*C+I&>Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#j\"*'4:F@Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#k\"*gsLJ#Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#l\"*o(f7DQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#m\"*Ko^s#Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#n\"*))o?&HQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#o\"*/%p$>$Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#p\"*+!3^MQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#q\"*OHYs$Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#r\"*Cwa,%Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#s\"*gKSK%Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#t\"*W*[^YQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#u\"*W8$)*\\Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#v\"*[_dO&Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#w\"*?'GadQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#x\"*Wl_;'Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#y\"*#*z\"*f'Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#z\"*GXu0(Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#!)\"*+61a(Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#\")\"*?`,0)Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"##)\"*sIme)Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#$)\"*wP;:*Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#%)\"*%ouX(*Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#&)\"+C;1P5Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#')\"+%=)o-6Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#()\"+))oir6Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#))\"+3H%RC\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#*)\"+C7#)>8Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#!*\"+syK*R\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#\"*\"+w^l#[\"Q+Consistent6\"" }}{PARA 7 "" 1 "" {TEXT -1 151 "Warning, License manager heartbeat failed. We have lost \+ connection to the license manager for feature Maple9. We have attempte d to reconnect 1 time(s)\n" }}{PARA 7 "" 1 "" {TEXT -1 151 "Warning, L icense manager heartbeat failed. We have lost connection to the licens e manager for feature Maple9. We have attempted to reconnect 2 time(s) \n" }}{PARA 7 "" 1 "" {TEXT -1 151 "Warning, License manager heartbeat failed. We have lost connection to the license manager for feature Ma ple9. We have attempted to reconnect 3 time(s)\n" }}{PARA 7 "" 1 "" {TEXT -1 151 "Warning, License manager heartbeat failed. We have lost \+ connection to the license manager for feature Maple9. We have attempte d to reconnect 4 time(s)\n" }}}}{MARK "5 95" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }