{VERSION 2 3 "IBM INTEL NT" "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 "Hyperlink" -1 17 "" 0 1 0 128 128 1 0 0 1 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 "Helvetica" 0 24 0 0 0 0 2 1 2 0 0 0 0 0 0 }0 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 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 74 0 115 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 1 251 0 4 0 0 0 0 0 0 0 0 0 0 }1 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 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Bullet Item" 0 15 1 {CSTYLE "" -1 -1 "" 0 1 94 1 85 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 3 3 0 0 0 0 0 0 15 2 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 0 24 0 0 0 0 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE " " -1 -1 "Helvetica" 0 24 0 0 0 0 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 3 258 1 {CSTYLE "" -1 -1 "" 0 1 89 1 28 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 {SECT 0 {PARA 258 "" 0 "" {TEXT -1 8 "Class 23" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 61 " Agenda: 1. Even still yet continue talk ing about Tapatan\n\n " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 106 "Proble m 2: Given a nonwinning position, and a color find all the positio ns you can get to from there." }}{PARA 0 "" 0 "" {TEXT -1 1 " " }} {PARA 0 "" 0 "" {TEXT -1 75 "Lets allow only horizontal and vertical m oves. No diagonal moves allowed. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 55 "Get the procedures we need from the previ ous worksheet." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 2 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 125 " tiles := [1+x,x+x^2,y+x*y,x*y+x^2 *y,y^2+x*y^2,x*y^2+x^2*y^2,\n 1+y,y+y^2,x+x*y,x*y+x*y^2,x^2+ x^2*y,x^2*y+x^2*y^2];\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&tilesG7. ,&\"\"\"F'%\"xGF',&F(F'*$F(\"\"#F',&%\"yGF'*&F(F'F-F'F',&F.F'*&F(F+F-F 'F',&*$F-F+F'*&F(F'F-F+F',&F3F'*&F(F+F-F+F',&F'F'F-F',&F-F'F2F',&F(F'F .F',&F.F'F3F',&F*F'F0F',&F0F'F5F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "xmove:=1+x+x^2;ymove:=1+y+y^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&xmoveG,(\"\"\"F&%\"xGF&*$F'\"\"#F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&ymoveG,(\"\"\"F&%\"yGF&*$F'\"\"#F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "ROWCOLS:=expand(\{xmove, y*xmove,y^ 2*xmove,ymove,x*ymove,x^2*ymove\});" }}{PARA 12 "" 1 "" {XPPMATH 20 "6 #>%(ROWCOLSG<(,(%\"yG\"\"\"*&%\"xGF(F'F(F(*&F*\"\"#F'F(F(,(*$F'F,F(*&F *F(F'F,F(*&F*F,F'F,F(,(F*F(F)F(F/F(,(F(F(F'F(F.F(,(F(F(F*F(*$F*F,F(,(F 4F(F+F(F0F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 510 "getposs := \+ proc(f,c)\n local po,lf,t,ct,fct,symdiff,d,tmp,nen,rc;\n po := NU LL: lf := NULL:\n for t in tiles do\n ct := expand(c*t) :\n \+ fct := expand(f+c*t);\n if nops(fct) = 7 and nops(fc t mod 3) = 7 \n then tmp := convert( \n(\{op(f)\} union \+ \{op(ct)\}) minus (\{ op(f)\} intersect \{op(ct)\}),`+`);\n nen : =true;\n for rc in ROWCOLS do \n if nops(expand(tmp+rc))=9 then \+ nen:=false; \n break fi od;\n if nen = true then po:=po,tmp fi; \n fi;\n od;\n getrep([po]);\n end:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 " getposs is constructed to take a position and whose move it i s and" }}{PARA 0 "" 0 "" {TEXT -1 49 "return all positions you can mo ve to from there." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 575 "getpo ss := proc(f,c)\nlocal po,lf,t,ct,fct,symdiff,d,tmp,nen,rc;\n po := NULL;\n lf := NULL;\n for t in tiles do\n ct := expand(c *t);\n fct := expand(f+c*t);\n if nops(fct) = 7 and nops (fct mod 3) = 7 then ; \n tmp := convert(\n \+ (\{op(f)\} union \{op(ct)\}) minus (\{op(f)\} intersect \{op(ct)\}),` +`\n );\n if nops(tmp+1+x^2+x^2*y^2+y^2) < n ops(tmp) +2 then po := po,tmp fi\n fi\n od;\n \n \+ tmp := getrep([po]);\n tw := \{op(tmp)\} intersect \{wins\};\n \+ if tw = \{\} then tmp else tw fi;\nend:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 42 "gp :=getposs(2+2*x^2*y+2*y^2+x*y+y+x^2,1);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%#gpG7%,.\"\"#\"\"\"%\"xGF(%\"yGF(*$F *F'F'*&F)F'F*F(F'*&F)F(F*F(F(,.F'F(F*F(F+F'*$F)F'F(F,F'*&F)F(F*F'F(,.F 'F(F)F(F*F(F+F'F/F(F,F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 " showpos(2+2*x^2*y+2*y^2+x*y+y+x^2);" }}{PARA 13 "" 1 "" {INLPLOT "62-% 'CURVESG6%7'7$\"\"!F(7$$\"\"$F(F(7$F*F*7$F(F*F'-%'COLOURG6&%$RGBG$\")# )eqk!\")$\"))eqk\"F4F5-%*THICKNESSG6#\"\"%-F$6%7$7$F($\"\"\"F(7$F*F?F. F7-F$6%7$7$F($\"\"#F(7$F*FFF.F7-F$6%7$7$F?F(7$F?F*F.F7-F$6%7$7$FFF(7$F FF*F.F7-F$6%7'7$$\"1G9dG9dG9!#;FW7$$\"1r&G9dG9d)FYFW7$FenFen7$FWFenFV- F/6&F1F(F($\"*++++\"F4F7-F$6%7$7$FW$\"1Vr&G9dG9\"!#:7$Fen$\"1dG9dG9d=F co-F/6&F1F[oF(F(F7-F$6%7$7$FWFeo7$FenFaoFgoF7-F$6%7'7$FW$\"1Vr&G9dG9#F co7$FenFbp7$Fen$\"1dG9dG9dGFco7$FWFfpFapFinF7-F$6%7$7$FaoFeo7$FeoFaoFg oF7-F$6%7$7$FaoFao7$FeoFeoFgoF7-F$6%7$7$FbpFW7$FfpFenFgoF7-F$6%7$7$Fbp Fen7$FfpFWFgoF7-F$6%7'7$FbpFao7$FfpFao7$FfpFeo7$FbpFeoF`rFinF7-%(SCALI NGG6#%,CONSTRAINEDG-%*AXESSTYLEG6#%%NONEG" 2 397 397 397 2 0 1 0 2 9 0 1 1 1.000000 45.000000 45.000000 10030 10061 10056 10074 0 0 0 20040 0 12010 0 0 0 255 0 0 255 1 4 0 0 0 0 0 0 0 0 0 0 1 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "showpos(gp[3]);" }}{PARA 13 "" 1 " " {INLPLOT "62-%'CURVESG6%7'7$\"\"!F(7$$\"\"$F(F(7$F*F*7$F(F*F'-%'COLO URG6&%$RGBG$\")#)eqk!\")$\"))eqk\"F4F5-%*THICKNESSG6#\"\"%-F$6%7$7$F($ \"\"\"F(7$F*F?F.F7-F$6%7$7$F($\"\"#F(7$F*FFF.F7-F$6%7$7$F?F(7$F?F*F.F7 -F$6%7$7$FFF(7$FFF*F.F7-F$6%7'7$$\"1G9dG9dG9!#;FW7$$\"1r&G9dG9d)FYFW7$ FenFen7$FWFenFV-F/6&F1F(F($\"*++++\"F4F7-F$6%7$7$FW$\"1dG9dG9d=!#:7$Fe n$\"1Vr&G9dG9\"Fco-F/6&F1F[oF(F(F7-F$6%7$7$FWFeo7$FenFaoFgoF7-F$6%7'7$ FW$\"1Vr&G9dG9#Fco7$FenFbp7$Fen$\"1dG9dG9dGFco7$FWFfpFapFinF7-F$6%7$7$ FeoFW7$FaoFenFgoF7-F$6%7$7$FeoFen7$FaoFWFgoF7-F$6%7$7$FbpFen7$FfpFWFgo F7-F$6%7$7$FbpFW7$FfpFenFgoF7-F$6%7'7$FbpFeo7$FfpFeo7$FfpFao7$FbpFaoF` rFinF7-%(SCALINGG6#%,CONSTRAINEDG-%*AXESSTYLEG6#%%NONEG" 2 397 397 397 2 0 1 0 2 9 0 1 1 1.000000 45.000000 45.000000 10030 10061 10056 10074 0 0 0 20040 0 12010 0 0 0 255 0 0 255 1 4 0 0 0 0 0 0 0 0 0 0 1 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "bill:=getposs(1+2*y+2*y^2 +x*y+x*y^2+2*x^2,2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 " ge tposs(qnons[6],2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 93 " Assignment : \n\n1. modify getposs so that no row or column is left vacant by \+ a legal move.\n" }{MPLTEXT 1 0 46 " getclass := proc(game)\n loc al class,mv;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 " class := \{\}: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 " for mv in game do class : = class union orbit(mv) od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 " \+ class; end: " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 34 " Let's make a graph of positions." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 " with(netwo rks):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 " new(G):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 " addvertex(v1,G);addvertex(v 2,G): addvertex(v3,G);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 " \+ addedge([v3,v2],G);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 " add edge( [v1,v3],G);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 " draw(G );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 " T := shortpathtree(G ,v1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 " draw(T);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 794 " build := proc(f,used,clr,` tap`,`V`,`Ht`)\n local c,sats,lev,n,v,k,pos;\n new(tap):\n c := clr:\n V := table([]):\n Ht := table([]):\n addvertex(v1,tap):\n V[v1] := f: \n sats := getclass(used):\n lev := 0: n := 1:\n Ht[lev] := v1:\n \+ while not Ht[lev]=NULL do\n lev := lev+1:\n Ht[lev] := NULL:\n for \+ v in [Ht[lev-1]] do \n if member(V[v],\{wins\}) then next \+ fi ;\n k :=getposs(V[v],c); \n for pos in k \+ do \n if not member(pos,sats) then \n n := n+1:\n addvertex(v.n, tap):\n V[v.n] := pos :\n Ht[lev] := Ht[lev],v.n:\n sats := sats \+ union orbit(pos);\n addedge([v,v.n],tap); \n \+ fi;\n od;\n od: \n c := c mod 2 +1 ; \+ \n od ; print(`ok `); \nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 " f:=2+2*y+ 2*x^2*y + x*y^2+ x^2*y^2+ x^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,.\"\" #\"\"\"%\"yGF&*$%\"xGF&F'*&F*F&F(F&F'*&F*F&F(F'F&*&F*F'F(F&F'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 " used:=\{f\};" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%%usedG<#,.\"\"#\"\"\"%\"yGF'*$%\"xGF'F(*&F+F'F )F'F(*&F+F'F)F(F'*&F+F(F)F'F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 " clr:=2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$clrG\"\"#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 30 " build(f,used,clr,tap,V,Ht) ;\n" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#%$ok~G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "o p(Ht);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#-%&TABLEG6#7./\"\"$66%$v16G% $v17G%$v18G%$v19G%$v20G%$v21G%$v22G%$v23G%$v24G%$v25G%$v26G%$v27G%$v28 G%$v29G%$v30G%$v31G%$v32G%$v33G%$v34G%$v35G/\"\"%6>%$v36G%$v37G%$v38G% $v39G%$v40G%$v41G%$v42G%$v43G%$v44G%$v45G%$v46G%$v47G%$v48G%$v49G%$v50 G%$v51G%$v52G%$v53G%$v54G%$v55G%$v56G%$v57G%$v58G%$v59G%$v60G%$v61G%$v 62G%$v63G/\"\"&6C%$v64G%$v65G%$v66G%$v67G%$v68G%$v69G%$v70G%$v71G%$v72 G%$v73G%$v74G%$v75G%$v76G%$v77G%$v78G%$v79G%$v80G%$v81G%$v82G%$v83G%$v 84G%$v85G%$v86G%$v87G%$v88G%$v89G%$v90G%$v91G%$v92G%$v93G%$v94G%$v95G% $v96G/\"\"'6D%$v97G%$v98G%$v99G%%v100G%%v101G%%v102G%%v103G%%v104G%%v1 05G%%v106G%%v107G%%v108G%%v109G%%v110G%%v111G%%v112G%%v113G%%v114G%%v1 15G%%v116G%%v117G%%v118G%%v119G%%v120G%%v121G%%v122G%%v123G%%v124G%%v1 25G%%v126G%%v127G%%v128G%%v129G%%v130G/\"\"(6<%%v131G%%v132G%%v133G%%v 134G%%v135G%%v136G%%v137G%%v138G%%v139G%%v140G%%v141G%%v142G%%v143G%%v 144G%%v145G%%v146G%%v147G%%v148G%%v149G%%v150G%%v151G%%v152G%%v153G%%v 154G%%v155G%%v156G/\"\")64%%v157G%%v158G%%v159G%%v160G%%v161G%%v162G%% v163G%%v164G%%v165G%%v166G%%v167G%%v168G%%v169G%%v170G%%v171G%%v172G%% v173G%%v174G/\"\"*6.%%v175G%%v176G%%v177G%%v178G%%v179G%%v180G%%v181G% %v182G%%v183G%%v184G%%v185G%%v186G/\"#56%%%v187G%%v188G%%v189G/\"#66\" /\"\"!%#v1G/\"\"\"6&%#v2G%#v3G%#v4G%#v5G/\"\"#6,%#v6G%#v7G%#v8G%#v9G%$ v10G%$v11G%$v12G%$v13G%$v14G%$v15G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "draw(Linear(seq([Ht[i]],i=0..10)),tap);\n" }}{PARA 13 "" 1 "" {INLPLOT "6c^m-%'POINTSG6#7$\"\")\"#D-F$6#7$\"#5\"#A-%'CURV ESG6$7$7$F,\"#97$\"#6#\"#L\"\"#-%'COLOURG6&%$RGBG\"\"!$F,!\"\"F=-%%TEX TG6$7$$\"#zF?\"#C%%v151G-F$6#7$F'FF-FA6$7$FD\"#B%%v150G-F$6#7$F'\"#E-F 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