{VERSION 2 3 "SUN SPARC SOLARIS" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {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 -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 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 2264 "pib := proc( dC, dCpr)\n# INPUT: A list dC (minimal bounding sequence for an order 1 ptn ideal C)\n# whe re each entry of dC is either 0 or infinity,\n# and a list dCpr (mi nimal bounding sequence for an order 1 ptn ideal Cprime),\n# whe re dCp is the min bounding seq for a ptn ideal Cprime which is \n# \+ equivalent to C.\n# Note: Since minimal bounding sequences are a ctually infinite sequences \n# but dC and dCpr are forced to be fin ite sequences by the computer, \n# all terms are assumed to be 'inf inity' beyond nops(dC) and nops(dCpr).\n# OUTPUT: The partitions of in finity needed to bijectively map C to Cprime.\n# (Also printed out, b ut not returned as output is the associated multiset M(C).)\nlocal c1, c2,dCprime, g,i,j,k,L, MC, MCprime, s;\n### ERROR screening:\n# Make s ure inputs are lists:\nif not (type(dC,list) and type(dCpr,list)) then \n ERROR(`Both arguments must be lists.`)\nfi;\n# Make sure dC conta ins only zeros and infinities:\nfor j from 1 to nops(dC) do\n if not \+ (op(j,dC)=0 or op(j,dC)=infinity) then \n ERROR(`First argument mus t be a list of zeros and infinities.`)\n fi\nod;\n# Extract the j's i n dC for which dC[j] = 0:\nMC:=\{\};\nfor j from 1 to nops(dC) do\n i f op(j,dC)=0 then MC:= MC union \{j\} fi\nod;\nprint('M(C)'=MC);\n# Ma ke sure dC and dCprime represent equivalent partition ideals:\nMCprime :=\{\};\nfor j from 1 to nops(dCpr) do\n if op(j,dCpr) <> infinity th en MCprime:=MCprime union \{j*(op(j,dCpr)+1)\} fi\nod;\nif not MC=MCpr ime then \n ERROR(`The two specified sequences do not represent equia valent partition ideals.`)\nfi;\n# If dCprime list is shorter than dC, fill it out with infinities:\ndCprime:= dCpr;\nif nops(dCpr) < nops(d C) then\n for i from 1 to nops(dC)-nops(dCpr) do\n dCprime:= [op(d Cprime),infinity]\n od\nfi;\nprint('d'(C)=dC);\nprint('d'(Cprime)=dCp rime);\n# Main part:\nfor j from 1 while j<=nops(dC) do \n #print('j' =j);\n g[j,0]:=j;\n if op(j,dC)=infinity then \n for k from 1 whi le (g[j,k-1]<> infinity) do\n if j*k > nops(dC) then g[j,k]:=inf inity else \n g[j,k]:= op(j*product(g[j,L],L=1..k-1),dCprime) + \+ 1 fi\n od;\n s[j]:= k-1;\n else s[j] :=1;\n g[j,1]:=0\n \+ fi\nod;\nfor j from 1 to nops(dC) do\n for k from 1 to s[j] do\n \+ print('g'(j,k) = g[j,k])\n od\nod;\nRETURN(g)\nend: \n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "#### EXAMPLES" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "G:=pib( [infinity,infinity,0,infinity,0,0,0,0 ],[2,2,infinity,1,0,infinity,0]):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/ -%\"MG6#%\"CG<'\"\"$\"\"&\"\"'\"\"(\"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"dG6#%\"CG7*%)infinityGF)\"\"!F)F*F*F*F*" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#/-%\"dG6#%'CprimeG7*\"\"#F)%)infinityG\"\"\"\"\"!F*F, F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"\"F'\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"\"\"\"#%)infinityG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"#\"\"\"\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"#F'%)infinityG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"$\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"%\"\"\"\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-% \"gG6$\"\"%\"\"#%)infinityG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG 6$\"\"&\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"'\" \"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"(\"\"\"\"\"! " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\")\"\"\"\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "G[4,1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "G[2, 1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "G[2,2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%)infi nityG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "pib([infinity,0,infinity],[1]):" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#/-%\"MG6#%\"CG<#\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"dG6#%\"CG7%%)infinityG\"\"!F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"dG6#%'CprimeG7%\"\"\"%)infinityGF*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"\"F'\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"\"\"\"#%)infinityG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# /-%\"gG6$\"\"#\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$ \"\"$\"\"\"%)infinityG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 195 " pib([infinity,0,0,infinity,0,infinity,0,0,infinity,0,infinity,0,0,infi nity,0,infinity,0,0,infinity,0],\n[1,4,0,1,0,1,0,infinity,1,1,infinity ,infinity,0,infinity,0,infinity,0,0,infinity,infinity]):" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#/-%\"MG6#%\"CG<.\"\"#\"\"$\"\"&\"\"(\"\")\"#5\"# 7\"#8\"#:\"#<\"#=\"#?" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"dG6#%\"C G76%)infinityG\"\"!F*F)F*F)F*F*F)F*F)F*F*F)F*F)F*F*F)F*" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#/-%\"dG6#%'CprimeG76\"\"\"\"\"%\"\"!F)F+F)F+%)in finityGF)F)F,F,F+F,F+F,F+F+F,F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-% \"gG6$\"\"\"F'\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"\" \"\"#\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"\"\"\"$\"\" #" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"\"\"\"%%)infinityG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"#\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"$\"\"\"\"\"!" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#/-%\"gG6$\"\"%\"\"\"\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"%\"\"#%)infinityG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"&\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"'\"\"\"\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-% \"gG6$\"\"'\"\"#%)infinityG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG 6$\"\"(\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\")\" \"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"*\"\"\"\"\"# " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"*\"\"#\"\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"*\"\"$%)infinityG" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"#5\"\"\"\"\"!" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#/-%\"gG6$\"#6\"\"\"%)infinityG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"#7\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"#8\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"#9\"\"\"%)infinityG" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#/-%\"gG6$\"#:\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6 $\"#;\"\"\"%)infinityG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"# <\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"#=\"\"\"\" \"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"#>\"\"\"%)infinityG " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"#?\"\"\"\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "pib([infinity,0,infinity,0], [1,1]):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"MG6#%\"CG<$\"\"#\"\"% " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"dG6#%\"CG7&%)infinityG\"\"!F) F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"dG6#%'CprimeG7&\"\"\"F)%)in finityGF*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"\"F'\"\"#" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"\"\"\"#F(" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"\"\"\"$%)infinityG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"#\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"$\"\"\"%)infinityG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6$\"\"%\"\"\"\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "7 1 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }