{VERSION 3 0 "IBM INTEL NT" "3.0" } {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 "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 }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 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 } 0 0 0 -1 8 2 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 3" 4 5 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 0 1 0 0 0 0 0 0 0 0 }0 0 0 -1 0 0 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 -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 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 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 }{PSTYLE "Maple P lot" 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 }} {SECT 0 {SECT 1 {PARA 3 "" 0 "" {TEXT -1 23 "2. Alapveto adattipusok" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "halmaz:=\{sorozat1\};" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%'halmazG<'\"\"!\"\"\"\"\"#\"\"%\"\"' " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "lista;op(lista);convert (lista,set);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7*\"\"#\"\"\"\"\"%F&\" \"'F$F&\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6*\"\"#\"\"\"\"\"%F%\"\" 'F#F%\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<'\"\"!\"\"\"\"\"#\"\"% \"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "halmaz;op(halmaz); convert(halmaz,list);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<'\"\"!\"\"\" \"\"#\"\"%\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'\"\"!\"\"\"\"\"#\" \"%\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7'\"\"!\"\"\"\"\"#\"\"%\" \"'" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 16 "3. Kombinatorika" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(combinat);" }}{PARA 7 " " 1 "" {TEXT -1 31 "Warning, new definition for Chi" }}{PARA 12 "" 1 " " {XPPMATH 20 "6#7B%$ChiG%%bellG%)binomialG%)cartprodG%*characterG%'ch ooseG%,compositionG%)conjpartG%+decodepartG%+encodepartG%*fibonacciG%* firstpartG%)graycodeG%)inttovecG%)lastpartG%,multinomialG%)nextpartG%) numbcombG%)numbcompG%)numbpartG%)numbpermG%*partitionG%(permuteG%)powe rsetG%)prevpartG%)randcombG%)randpartG%)randpermG%*stirling1G%*stirlin g2G%(subsetsG%)vectointG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "with(combstruct);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7+%+allstructsG% &countG%%drawG%)finishedG%'gfeqnsG%)gfseriesG%(gfsolveG%,iterstructsG% +nextstructG" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 16 "3.1. Permutaciok " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "numbperm(6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$?(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "numbperm(\{A,B,C,D,E,F,G,H,J,K\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"(+)GO" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "p ermute([k,r,k,o,d,i,l]):numbperm([k,r,o,k,o,d,i,l]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"&!35" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "8!/(2!*2!);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"&!35" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "randperm(\{m,a,p,l,e\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7'%\"pG%\"mG%\"lG%\"eG%\"aG" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 16 "3.2. Kombinaciok" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "numbcomb(\{Maria,Eva,Istvan,Peter,Janos,Zoltan\} ,2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#:" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 14 "3.3. Variaciok" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "permute([alpha,beta,gamma,delta],3);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7:7%%&alphaG%%betaG%&gammaG7%F%F&%&deltaG7%F%F'F&7%F%F' F)7%F%F)F&7%F%F)F'7%F&F%F'7%F&F%F)7%F&F'F%7%F&F'F)7%F&F)F%7%F&F)F'7%F' F%F&7%F'F%F)7%F'F&F%7%F'F&F)7%F'F)F%7%F'F)F&7%F)F%F&7%F)F%F'7%F)F&F%7% F)F&F'7%F)F'F%7%F)F'F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "v arszam:=proc(m,n)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "local s,i:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "if n>m then s:=0 else s:=1:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "for i from 0 to n-1 do s:=s*(m-i): \+ od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "fi:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "s" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "varszam(5,3);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#\"#g" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "ismvarszam:=(m,n)->m^n;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+ismv arszamGR6$%\"mG%\"nG6\"6$%)operatorG%&arrowGF))9$9%F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "ismvarszam(3,5);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#\"$V#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "v ariaciok:=proc(A,n)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "local C,D,i: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "C:=[op(choose(A,n))]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "D:=\{\}:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "for i from 1 to nops(C) do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "D:=D union \{op(permute([op(C[i])]))\}: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "D" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "variaciok(\{a,b,c,d\},3);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#< :7%%\"bG%\"cG%\"dG7%%\"aGF&F'7%F)F%F'7%F)F%F&7%F&F%F)7%F&F)F%7%F%F&F)7 %F%F)F&7%F)F&F%7%F'F%F)7%F'F)F%7%F%F'F)7%F%F)F'7%F)F'F%7%F'F&F)7%F'F)F &7%F&F'F)7%F&F)F'7%F)F'F&7%F'F&F%7%F'F%F&7%F&F'F%7%F&F%F'7%F%F'F&" }}} }{SECT 1 {PARA 4 "" 0 "" {TEXT -1 37 "3.4. Binomialis es polinomialis \+ tetel" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "binomial(6,2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"#:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "convert(binomial(m,n),factorial);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#*&-%*factorialG6#%\"mG\"\"\"*&-F%6#%\"nG\"\"\"-F%6#,& F'\"\"\"F,!\"\"\"\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "multinomial(8,2,2,1,1,1,1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"& !35" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "convert(multinomial( n,a,b,c,d),factorial);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%*factori alG6#%\"nG\"\"\"**-F%6#%\"aG\"\"\"-F%6#%\"bG\"\"\"-F%6#%\"cG\"\"\"-F%6 #%\"dG\"\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "choose (\{Maria,Eva,Istvan,Peter,Janos,Zoltan\},2);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<1<$%&MariaG%'IstvanG<$F%%$EvaG<$F%%&PeterG<$F%%&JanosG <$F%%'ZoltanG<$F&F(<$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 38 "randcomb(\{alma,kort e,szilva,banan\},2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$%&korteG%'sz ilvaG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "randcomb(5,3);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<%\"\"#\"\"$\"\"%" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 18 "choose([a,b,a],2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$7$%\"aGF%7$F%%\"bG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "numbcomb([a,b,a],2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 35 "3.5. A combstruct c somag hasznalata" }}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 51 "3.5.1. Kombin atorikai strukturak nyelvtani leirasai" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "binfa:=\{B=Union(Z, Prod(B,B))\};" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%&binfaG<#/%\"BG-%&UnionG6$%\"ZG-%%ProdG6$F'F'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "draw([B,binfa,labelled],size =5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%%ProdG6$-F$6$&%\"ZG6#\"\"$-F $6$&F)6#\"\"#-F$6$&F)6#\"\"&&F)6#\"\"\"&F)6#\"\"%" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 33 "count([B,binfa,labelled],size=5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"%!o\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "count([B,binfa,unlabelled],size=5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "n yaklanc:=\{N=Cycle(Union(piros,kek,zold)),piros=Atom,kek=Atom,zold=Ato m\}:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "draw([N,nyaklanc,un labelled],size=10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%&CycleG6,%&pi rosGF&%$kekGF&F'%%zoldGF'F(F&F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "binfa2:=\{T=Union(Epsilon,B),B=Union(Z,Prod(Z,Z))\}:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "draw([T,binfa2,unlabelled],s ize=0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%(EpsilonG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "count([M,\{M=Set(Z,card>8)\},labell ed],size=7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "draw([A,\{A=Cycle(Z,card=4)\},label led],size=4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%&CycleG6&&%\"ZG6#\" \"\"&F'6#\"\"%&F'6#\"\"#&F'6#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "count([A,\{A=Cycle(Z,card=4)\},labelled],size=3);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "draw([S,\{S=Sequence(Set(Z,card>0),card<=10)\},labell ed],size=6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%)SequenceG6'-%$SetG6 #&%\"ZG6#\"\"'-F'6#&F*6#\"\"%-F'6$&F*6#\"\"\"&F*6#\"\"#-F'6#&F*6#\"\"& -F'6#&F*6#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "count([S ,\{S=Sequence(Z,card<=10)\},labelled],size=13);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "fa2 3:=\{T=Union(Z,Subst(Union(Prod(Z,Z),Prod(Z,Z,Z)),T))\}:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "draw([T,fa23],size=11);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%%ProdG6$-F$6$-F$6$%\"ZGF*-F$6%F*F*F*-F$6%F (F(F(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 33 "3.5.2. Elore-definialt strukturak" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "draw(Combination(\{a,b,c,d,e,f,g\}),size=5);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<'%\"bG%\"gG%\"cG%\"dG%\"eG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "count(Partition(95),size=40) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"'o2X" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "draw(Combination(\{a,b,c,d,e,f,g\}));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<&%\"bG%\"fG%\"gG%\"dG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "draw(Permutation(42));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7L\"#J\"#<\"#;\"#P\"#G\"#L\"#7\"#E\"#S\"#9\"#I\"\")\"#A \"\"&\"\"*\"#@\"#>\"\"$\"#8\"#=\"#M\"#D\"\"#\"#K\"#H\"#R\"#O\"#F\"#?\" \"%\"\"'\"#6\"#:\"#N\"#5\"#Q\"\"(\"#B\"\"\"\"#T\"#C\"#U" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "draw(Permutation(16),size='allsizes ');" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7-\"\")\"\"(\"\"\"\"#7\"\"$\"#5 \"\"*\"#9\"\"&\"#:\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 " draw(Composition(32));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#76\"\"\"F$F$ F$\"\"#F$F%F$F$F$F$\"\"$\"\"%F&F$F$F%F%F%F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "allstructs(Combination(4));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<2<\"<#\"\"\"<$F&\"\"$<$F&\"\"%<$\"\"#F*<%F&F,F*<#F,<$F &F,<#F(<$F,F(<%F&F,F(<&F&F,F(F*<%F,F(F*<$F(F*<%F&F(F*<#F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "allstructs(Permutation([a,a,b,c]),s ize=3);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7.7%%\"aGF%%\"bG7%F%F%%\"cG 7%F%F&F%7%F%F&F(7%F%F(F%7%F%F(F&7%F&F%F%7%F&F%F(7%F&F(F%7%F(F%F%7%F(F% F&7%F(F&F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "allstructs(Pa rtition(4));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7'7&\"\"\"F%F%F%7%F%F% \"\"#7$F'F'7$F%\"\"$7#\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "allstructs(Composition(6));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7B7 (\"\"\"F%F%F%F%F%7&F%F%F%\"\"$7&F%\"\"#F%F)7&F%F%F)F)7'F)F%F%F%F%7'F%F )F%F%F%7'F%F%F)F%F%7'F%F%F%F)F%7'F%F%F%F%F)7&F%F)F)F%7&F%F%F'F%7&F)F%F %F)7%F)F%F'7%F%F)F'7%F%F%\"\"%7&F)F)F%F%7&F%F'F%F%7&F'F%F%F%7&F)F%F)F% 7%F'F)F%7%F)F'F%7%F%F6F%7%F6F%F%7#\"\"'7$\"\"&F%7$F6F)7$F'F'7$F)F67$F% FB7%F)F)F)7%F%F'F)7%F'F%F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "it:=iterstructs(Combination([a,o,b]),size=2):while not finished(it ) do nextstruct(it) od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$%\"aG%\"b G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$%\"aG%\"oG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$%\"bG%\"oG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "it:=iterstructs(Permutation(3),size='allsizes'):while not finished (it) do nextstruct(it) od; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#\"\"$" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#7$\"\"\"\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #7$\"\"#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"\"\"\"$" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"$\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"$ \"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"\"\"\"#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"#\"\"\"\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"$\"\"\"\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7 %\"\"\"\"\"$\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"#\"\"$\"\" \"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"$\"\"#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "s:=\{L=PowerSet(Sequence(Z,card>=1) )\},unlabelled;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG6$<#/%\"LG-%) PowerSetG6#-%)SequenceG6$%\"ZG1\"\"\"%%cardG%+unlabelledG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "draw([L,s],size=5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%)PowerSetG6$-%)SequenceG6$%\"ZGF)-F'6%F)F)F)" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "seq(count([L,s],size=i),i=1 ..10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6,\"\"\"F#\"\"#F$\"\"$\"\"%\" \"&\"\"'\"\")\"#5" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 26 "3.5.3. Gen eratorfuggvenyek" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "A(z)=Sum (a[n]*z^n,n=0..infinity):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "lanc:=\{N=Cycle(gyongy),gyongy=Union(piros,kek,zold),piros=Atom,ke k=Atom,zold=Atom\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%lancG<'/%\"N G-%&CycleG6#%'gyongyG/F+-%&UnionG6%%&pirosG%$kekG%%zoldG/F0%%AtomG/F1F 4/F2F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "gfeqns(lanc,unlab elled,z);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7'/-%\"NG6#%\"zG-%$SumG6$ *&*&-&%*numtheoryG6#%$phiG6#&%\"jG6#\"\"\"F7-%#lnG6#*&\"\"\"F<,&F7F7-% 'gyongyG6#)F(F4!\"\"!\"\"F7F " 0 "" {MPLTEXT 1 0 28 "gfsolve(lanc, unlabelled,z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<'/-%'gyongyG6#%\"zG,$F(\"\"$/-%\"NGF'-%$SumG6$*&*&-&%* numtheoryG6#%$phiG6#&%\"jG6#\"\"\"F<-%#lnG6#,$*&\"\"\"FB,&!\"\"F<)F(F9 F*!\"\"FDF " 0 "" {MPLTEXT 1 0 28 "gfseries(lanc,unlabe lled,z);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#-%&TABLEG6#7'/-%$kekG6#%\" zG+%F+\"\"\"\"\"\"/-%%zoldGF*F,/-%&pirosGF*F,/-%\"NGF*+/F+\"\"$\"\"\" \"\"'\"\"#\"#6\"\"$\"#C\"\"%\"#^\"\"&-%\"OG6#F-\"\"'/-%'gyongyGF*+%F+F 9\"\"\"" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 17 "3.5.4. Alkalmazas" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "haromszog:=[T,\{T=Union(Z,P rod(Epsilon,Z,T),Prod(T,Z,Epsilon),Prod(T,Z,T))\},unlabelled]:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "count(haromszog,size=100);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"Z?$4fuQ:_P3UK15u+2qro'\\J,4Z*>l*) " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "seq(count(haromszog,siz e=i),i=0..20);" }}{PARA 12 "" 1 "" {XPPMATH 20 "67\"\"!\"\"\"\"\"#\"\" &\"#9\"#U\"$K\"\"$H%\"%I9\"%i[\"&'z;\"&'ye\"'7!3#\"'+Hu\"(SWn#\"(X[p* \")qwNN\"*!zW'H\"\"*+(QwZ\"+!>jsw\"\"+?/7kl" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "draw(haromszog,size=10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%%ProdG6%-F$6%-F$6%-F$6%-F$6%-F$6%%(EpsilonG%\"ZGF1F1F .F1F0F1F0F1F1F1F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "size:= proc(t) convert(map(size,t),`+`) end: size(Epsilon):=0: size(Z):=1:" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "elek:=proc(fa,org,el)" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "local se1,se2;" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 49 "if fa=Epsilon then org,org,el union \{[org,org+1]\} " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 78 " elif fa=Z then org,org+1,el u nion \{[org,org+1],[org+1,org+2],[org+2,org]\}" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 34 " else se1:=elek(op(1,fa),org,el);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 " se2:=elek(op(3,fa),se1[2]+1,se1[3]);" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 " se1[1],se2[2],se2[3] union \+ \{[se1[1],se2[2]+1]\}" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "fi" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "rajz:=proc(n)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 116 " plot([op(map2(map,[cos,sin],expand(map(`*`,elek(draw(haromszog,size=n- 2),0,\{\})[3],2*Pi/n))))],color=blue,axes=NONE) " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "rajz (20);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6K-%'CURV ESG6#7$7$\"\"!$!\"\"F(7$$\"1v%\\P%*p,4$!#;$!1Q:&H;l0^*F.-F$6#7$F+7$$\" 1JZ#H__y(eF.$!1v%\\P%*p,4)F.-F$6#7$F47$$\"1v%\\P%*p,4)F.$!1JZ#H__y(eF. -F$6#7$F " 0 "" {MPLTEXT 1 0 37 "harom4:=allstructs(haromszog,size=4);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'harom4G70-%%ProdG6%%(EpsilonG%\"ZG-F'6%F*F*F*-F'6%F* F*-F'6%F*F*F)-F'6%-F'6%-F'6%F)F*F*F*F)F*F)-F'6%F/F*F*-F'6%F)F*-F'6%F)F *F/-F'6%F+F*F)-F'6%-F'6%F)F*F5F*F)-F'6%-F'6%F/F*F)F*F)-F'6%F*F*F5-F'6% F)F*FE-F'6%F5F*F*-F'6%F)F*F3-F'6%F;F*F)-F'6%F)F*FA" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "gfeqns(op(2,haromszog),unlabelled,z);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7$/-%\"TG6#%\"zG,(-%\"ZGF'\"\"\"*&F*F, F%F,\"\"#*&)F%F.\"\"\"F*F1F,/F*F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "gf:=gfsolve(op(2,haromszog),unlabelled,z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#gfG<$/-%\"TG6#%\"zG,$*&,(\"\"\"F.F*!\"#*$ -%%sqrtG6#,&F.F.F*!\"%\"\"\"!\"\"F6F*!\"\"#F.\"\"#/-%\"ZGF)F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "op([1,2],%);series(%,z=0,12) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&,(\"\"\"F&%\"zG!\"#*$-%%sqrtG 6#,&F&F&F'!\"%\"\"\"!\"\"F/F'!\"\"#F&\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#+9%\"zG\"\"\"\"\"\"\"\"#\"\"#\"\"&\"\"$\"#9\"\"%\"#U\" \"&\"$K\"\"\"'\"$H%\"\"(\"%I9\"\")\"%i[\"\"*\"&'z;\"#5-%\"OG6#F%\"#6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "seq(count(haromszog,size= n),n=0..10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6-\"\"!\"\"\"\"\"#\"\"& \"#9\"#U\"$K\"\"$H%\"%I9\"%i[\"&'z;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "gfseries(op(2..3,haromszog),z,[[z]],6);" }}{PARA 12 " " 1 "" {XPPMATH 20 "6#-%&TABLEG6#7$/-%\"ZG6#%\"zG+%F+\"\"\"\"\"\"/-%\" TGF*+/F+F-\"\"\"\"\"#\"\"#\"\"&\"\"$\"#9\"\"%\"#U\"\"&-%\"OG6#F-\"\"' " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 " " 0 "" {TEXT -1 35 "3.5.5. Termeszetes szamok particioi" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "partition(10);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7L7,\"\"\"F%F%F%F%F%F%F%F%F%7+F%F%F%F%F%F%F%F%\"\"#7*F% F%F%F%F%F%F'F'7)F%F%F%F%F'F'F'7(F%F%F'F'F'F'7'F'F'F'F'F'7*F%F%F%F%F%F% F%\"\"$7)F%F%F%F%F%F'F-7(F%F%F%F'F'F-7'F%F'F'F'F-7(F%F%F%F%F-F-7'F%F%F 'F-F-7&F'F'F-F-7&F%F-F-F-7)F%F%F%F%F%F%\"\"%7(F%F%F%F%F'F67'F%F%F'F'F6 7&F'F'F'F67'F%F%F%F-F67&F%F'F-F67%F-F-F67&F%F%F6F67%F'F6F67(F%F%F%F%F% \"\"&7'F%F%F%F'F@7&F%F'F'F@7&F%F%F-F@7%F'F-F@7%F%F6F@7$F@F@7'F%F%F%F% \"\"'7&F%F%F'FH7%F'F'FH7%F%F-FH7$F6FH7&F%F%F%\"\"(7%F%F'FN7$F-FN7%F%F% \"\")7$F'FR7$F%\"\"*7#\"#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "numbpart(10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#U" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "randpart(10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&\"\"\"F$\"\"$\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "allstructs(Partition(6),size=3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%7%\"\"\"F%\"\"%7%F%\"\"#\"\"$7%F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "for part in partition(6) do " }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 " if nops(part)=3 then print(part); " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"#F$F$" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"\"\"\"#\"\"$" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#7%\"\"\"F$\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "allstructs(Composition(6),size=3);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#7,7%\"\"#\"\"\"\"\"$7%F&F%F'7%F&F&\"\"%7%F'F%F&7%F%F' F&7%F&F*F&7%F*F&F&7%F%F%F%7%F&F'F%7%F'F&F%" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 27 "count(Partition(6),size=3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "cou nt(Composition(6),size=3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#5" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "numbcomp(6,3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "draw(Partition(6),size=3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\" \"\"F$\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "randpart(6); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"#\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 22 "4 . Halmazok generalasa" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 22 "4.1. Des cartes szorzat" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "descartes1 :=proc(X,Y)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "local Z,x,y;" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "Z:=\{\};" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "for x in X do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "f or y in Y do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "Z:=Z union \{[x,y] \};" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "Z" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "descartes1(\{2,5,8,3\},\{1,3,5,9,4\});" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<67$\"\")\"\"$7$\"\"#\"\"\"7$F(F&7$\"\"&F)7$F&F)7$F&F&7 $F(\"\"%7$F,F,7$F(F,7$F(\"\"*7$F&F,7$F&F47$F,F&7$F,F07$F,F47$F%F)7$F&F 07$F%F47$F%F07$F%F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "desc artes2:=proc()" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "local Z,k,x,y;" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "option remember;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " if nargs=0 then Z:=\{\}" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 " elif nargs=1 then Z:=args[1];" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 15 " else Z:=\{\};" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 54 " for x in descartes2(seq(args[k],k=1..nargs-1)) do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " for y in args[nargs] do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 " Z:=Z union \{[op(x),y]\};" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 " od;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 " od;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " fi;" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "RETURN(Z);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "B1: =\{1,2,3\}; B2:=\{b,a\}; B3:=\{a,c,b\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#B1G<%\"\"\"\"\"#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#B 2G<$%\"aG%\"bG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#B3G<%%\"aG%\"bG% \"cG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "descartes2(B1,B2,B3 );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<47%\"\"\"%\"aG%\"bG7%F%F&%\"cG7 %F%F'F&7%F%F'F'7%F%F'F)7%\"\"#F&F&7%F.F&F'7%F.F&F)7%F.F'F&7%F.F'F'7%F. F'F)7%\"\"$F&F&7%F5F&F'7%F5F&F)7%F5F'F&7%F5F'F'7%F5F'F)7%F%F&F&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "T:=cartprod([[1,2,3],[a,b]]) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "while not T[finished] \+ do T[nextvalue]() od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"\"%\"aG " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"\"%\"bG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"#%\"aG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"# %\"bG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"$%\"aG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"$%\"bG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 17 "4.2. Reszha lmazok" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "allstructs(Subset( \{a,b,c\}),size=2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%<$%\"bG%\"cG< $%\"aGF&<$F(F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "allstruct s(Subset(\{a,b,c,c\}),size=allsizes);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<*<\"<$%\"bG%\"cG<$%\"aGF'<#F'<#F)<#F&<$F)F&<%F)F&F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "count(Subset(\{a,b,c,c\}),size=alls izes);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\")" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 18 "powerset(\{a,b,c\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<*<\"<$%\"bG%\"cG<$%\"aGF'<#F'<#F)<#F&<$F)F&<%F)F&F'" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "powerset([a,b,c]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7*7\"7#%\"aG7#%\"bG7$F&F(7#%\"cG7$F&F+ 7$F(F+7%F&F(F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "powerset( \{a,b,c,c\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<*<\"<$%\"bG%\"cG<$% \"aGF'<#F'<#F)<#F&<$F)F&<%F)F&F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "powerset([a,b,c,c]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7.7\"7#%\"cG7$F&F&7#%\"bG7$F)F&7%F)F&F&7#%\"aG7$F-F&7%F-F&F&7$F-F)7 %F-F)F&7&F-F)F&F&" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 43 "4.2.1. Resz halmazokat meghatarozo eljarasok" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "allista:=proc(list,ini)[seq(list[i],i=ini..nops(list))]: end: " }}{PARA 7 "" 1 "" {TEXT -1 42 "Warning, `i` in call to `seq` is not \+ local" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "allista([a,b,c,d], 1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&%\"aG%\"bG%\"cG%\"dG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "allista([a,b,c,d],2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7%%\"bG%\"cG%\"dG" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 21 "allista([a,b,c,d],4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#%\"dG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "R endel:=proc(elt,list)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "local temp , i:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "temp:=[]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "for i from 1 to nops(list) do" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 38 " temp:=[op(temp),[elt, op(list[i])]]:" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 3 "od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "temp :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "Rendel(m,[[1,a],[2],[3,b,c],[4,d,x,y,x],[]]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7'7%%\"mG\"\"\"%\"aG7$F%\"\"#7&F%\"\"$ %\"bG%\"cG7(F%\"\"%%\"dG%\"xG%\"yGF17#F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "Rendel(a,[[b,c],[b,d],[c,d]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%7%%\"aG%\"bG%\"cG7%F%F&%\"dG7%F%F'F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "Ielemu_reszhalm:=proc(L,i)" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "local n,j,eredm,temp:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "n:=nops(L):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "if i=1 then eredm:=[]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 " f or j from 1 to n do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " eredm:=[ op(eredm),[L[j]]]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " od:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 " else eredm:=[]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 " for j from 1 to n-i+1 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 " temp:=Ielemu_reszhalm(allista(L,j+1),i-1):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " temp:=Rendel(L[j],temp):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 " eredm:=[op(eredm),op(temp)]:" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "fi:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "eredm" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Ielemu_reszhalm([a,b,c,d,e,f,g],1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7)7#%\"aG7#%\"bG7#%\"cG7#%\"dG7#%\"eG7#%\"fG7#%\"gG " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "Reszhalmazok:=proc(L)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "local n,i,temp,eredm:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "n:=nops(L):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "eredm:=[]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "for i from 1 \+ to n do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 " eredm:=[op(eredm),op(Ie lemu_reszhalm(L,i))]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "eredm" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Reszhalmazok ([x,y,z]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7)7#%\"xG7#%\"yG7#%\"zG7 $F%F'7$F%F)7$F'F)7%F%F'F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 23 "4.3. Halmazok particioi" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "particiok:=proc(n)" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "local P,A,B,C;" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 16 "option remember;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "if n=1 then P:=[\{1\}];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 " e lif n=2 then P:=[\{\{1\},\{2\}\},\{\{1,2\}\}];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 " elif n>2 then P:=[];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 " for A in particiok(n-1) do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 " P:=[op(P), A union \{\{n\}\}];" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 " for B in A do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 52 " C:=(A minus \{B\}) union \+ \{B union \{n\}\};" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " \+ P:=[op(P),C];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 " od; " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 " od;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 " elif n=0 then P:=[];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 " else P:=FAIL;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "RETURN(P)" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "for A in particiok(3) do print(A);od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%<#\"\"\"<#\"\"#<#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$<$\"\"\"\"\"$<#\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$<#\" \"\"<$\"\"#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$<$\"\"\"\"\"#<# \"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<#<%\"\"\"\"\"#\"\"$" }}} {SECT 1 {PARA 5 "" 0 "" {TEXT -1 36 "4.3.1. Stirling- es Bell-fele sza mok" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "stirling2(6,4);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"#l" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "bell(4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "'bell(8)'=bell(8); 'bell(10) '=bell(10); 'bell(20)'=bell(20); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/ -%%bellG6#\"\")\"%ST" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%bellG6#\"# 5\"'vf6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%bellG6#\"#?\"/s`BeTs^" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}}{SECT 1 {PARA 3 " " 0 "" {TEXT -1 16 "5. Grafok es fak" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(networks);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7go%)acycpolyG%(ad dedgeG%*addvertexG%*adjacencyG%)allpairsG%)ancestorG%)arrivalsG%-bicom ponentsG%)charpolyG%*chrompolyG%+complementG%)completeG%+componentsG%( connectG%-connectivityG%)contractG%*countcutsG%+counttreesG%%cubeG%&cy cleG%*cyclebaseG%)daughterG%*degreeseqG%'deleteG%+departuresG%)diamete rG%&dinicG%+djspantreeG%-dodecahedronG%%drawG%*duplicateG%&edgesG%%end sG%(eweightG%%flowG%)flowpolyG%(fundcycG%)getlabelG%&girthG%&graphG%*g raphicalG%&gsimpG%'gunionG%%headG%,icosahedronG%*incidenceG%)incidentG %)indegreeG%'induceG%)isplanarG%*maxdegreeG%'mincutG%*mindegreeG%*neig hborsG%$newG%+octahedronG%*outdegreeG%%pathG%)petersenG%'randomG%%rank G%)rankpolyG%.shortpathtreeG%%showG%'shrinkG%%spanG%)spanpolyG%)spantr eeG%%tailG%,tetrahedronG%*tuttepolyG%(vdegreeG%)verticesG%%voidG%(vwei ghtG" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 23 "5.1. Grafok letrehozasa " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "G1:=new():" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "csucsok:=\{A,B,C,D,E\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(csucsokG<'%\"AG%\"EG%\"BG%\"CG%\"DG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "addvertex(csucsok,G1);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6'%\"AG%\"EG%\"BG%\"CG%\"DG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "addedge(\{\{A,B\},\{A,C\},\{B,C\}, \{C,D\},\{B,E\},\{D,E\},\{B,D\}\},G1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6)%#e1G%#e2G%#e3G%#e4G%#e5G%#e6G%#e7G" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 19 "ends(G1);edges(G1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<)<$%\"AG%\"BG<$F%%\"CG<$F&F(<$F(%\"DG<$%\"EGF&<$F-F+<$F&F+" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<)%#e1G%#e2G%#e3G%#e5G%#e6G%#e7G%#e4G " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "draw(G1);" }}{PARA 13 " " 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "64-%'CURVESG6$7$7$$\"\"\"\" \"!F*7$$\"+Q*p,4$!#5$\"+l^c5&*F.-%'COLOURG6&%$RGBGF*$\"#5!\"\"F*-%'POI NTSG6#7$$\"+l*p,4$F.$!+c^c5&*F.-%%TEXTG6$F;Q\"E6\"-FA6$7$$!+]*p,4)F.$ \"+9D&y(eF.Q\"CFD-F96#7$$!+M*p,4)F.$!+PD&y(eF.-FA6$FOQ\"DFD-F96#FG-FA6 $F'Q\"AFD-F96#F+-FA6$F+Q\"BFD-F96#F'-F$6$7$F;FOF1-F$6$7$F;F+F1-F$6$7$F +FGF1-F$6$7$F'FGF1-F$6$7$FGFOF1-F$6$7$F+FOF1-%*AXESSTYLEG6#%%NONEG" 1 2 0 1 0 2 9 1 1 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "draw(Linear([A,B],[C,D,E]),G1);" }}{PARA 13 " " 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "64-%%TEXTG6$7$$\"\"*!\"\"#\" \"$\"\"#Q\"B6\"-F$6$7$F'#\"\"\"F,Q\"AF.-%'POINTSG6#7$F3F*-F66#7$F3F2-F $6$7$$\"$3#!\"#F3Q\"DF.-F$6$7$F?F,Q\"EF.-F66#7$F,F,-F66#7$F,F3-F$6$7$F ?\"\"!Q\"CF.-F66#7$F,FP-%'CURVESG6$7$FIF8-%'COLOURG6&%$RGBGFP$\"#5F)FP -FV6$7$F8FTFY-FV6$7$F;FTFY-FV6$7$F;F8FY-FV6$7$FTFLFY-FV6$7$F8FLFY-FV6$ 7$FIFLFY-%*AXESSTYLEG6#%%NONEG" 1 2 0 1 0 2 9 1 1 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "G2 :=graph(\{1,2,3,4,5,6,7,8\},\{\{1,2\},\{2,3\},\{3,4\},\{4,1\},\{5,6\}, \{6,7\},\{7,8\},\{8,5\},\{1,5\},\{2,6\}\}):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "draw(G2);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6=-%'CURVESG6$7$7$$!\"\"\"\"!$!+:w1-T!#>7$$\"+?y1rq!# 5$!+.y1rqF1-%'COLOURG6&%$RGBGF*$\"#5F)F*-F$6$7$7$$!+0y1rqF1$!+>y1rqF17 $$\"+A95`hF-F(F4-F$6$7$F'F=F4-F$6$7$7$$\"\"\"F*F*7$$!+=y1rqF1$\"+1y1rq F1F4-F$6$7$7$$\"+6y1rqF1$\"+8y1rqF17$$!+2Q.^?F-FLF4-F$6$7$FKFVF4-F$6$7 $FVF=F4-%%TEXTG6$FBQ\"76\"-%'POINTSG6#F.-F$6$7$FKF'F4-F_o6$F.Q\"8Fbo-F do6#FB-F_o6$FenQ\"3Fbo-Fdo6#FN-F_o6$FNQ\"4Fbo-Fdo6#F'-F_o6$F'Q\"5Fbo-F do6#F=-F_o6$F=Q\"6Fbo-F_o6$FVQ\"2Fbo-Fdo6#Fen-F_o6$FKQ\"1Fbo-Fdo6#FV-F $6$7$FBF.F4-F$6$7$FenFNF4-Fdo6#FK-%*AXESSTYLEG6#%%NONEG" 1 2 0 1 0 2 9 1 1 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "draw(petersen());" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6F-%%TEXTG6$7$$!+M*p,4)!#5$!+PD&y(eF)Q\"76\"-F$6$ 7$$!+]*p,4)F)$\"+9D&y(eF)Q#10F--F$6$7$$\"+Q*p,4$F)$\"+l^c5&*F)Q\"8F--F $6$7$$\"\"\"\"\"!FCQ\"6F--%'CURVESG6$7$7$$\"+nmmm;!\"*FC7$$\"+vKG]^F)$ !+$>%4&e\"FL-%'COLOURG6&%$RGBGFC$\"#5!\"\"FC-FF6$7$7$$!+e;O[8FL$\"+d3U 'z*F)7$$!+c;O[8FL$!+&*3U'z*F)FR-FF6$7$7$$\"+IKG]^F)$\"+%>%4&e\"FLFfnFR -FF6$7$FM7$$\"+l*p,4$F)$!+c^c5&*F)FR-FF6$7$FcoF8FR-FF6$7$FfnF0FR-FF6$7 $F[oF&FR-FF6$7$FIFcoFR-FF6$7$FIF@FR-F$6$F[oQ\"4F--%'POINTSG6#FM-F$6$FM Q\"5F--Fcq6#Ffn-F$6$FfnQ\"3F--Fcq6#F[o-F$6$FIQ\"1F--Fcq6#Fco-F$6$FcoQ \"2F--Fcq6#FI-F$6$F[pQ\"9F--FF6$7$F8F[pFR-FF6$7$F[oFMFR-FF6$7$F[pF0FR- FF6$7$F&F8FR-FF6$7$F@F&FR-Fcq6#F[p-Fcq6#F&-Fcq6#F0-Fcq6#F8-Fcq6#F@-FF6 $7$F@F0FR-%*AXESSTYLEG6#%%NONEG" 1 2 0 1 0 2 9 1 1 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 26 "5.2. Matrix-reprezentaciok" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "szomszed:=adjacency(G1);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%)szomszedG-%'matrixG6#7'7'\"\"!\"\" \"F+F*F*7'F+F*F+F+F+7'F+F+F*F+F*7'F*F+F+F*F+7'F*F+F*F+F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "incidence(G1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7'7)\"\"\"F(\"\"!F)F)F)F)7)F(F)F(F)F(F)F(7) F)F(F(F(F)F)F)7)F)F)F)F(F)F(F(7)F)F)F)F)F(F(F)" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 36 " Warning, new definition for charpoly" }}{PARA 7 "" 1 "" {TEXT -1 32 "W arning, new definition for norm" }}{PARA 7 "" 1 "" {TEXT -1 32 "Warnin g, new definition for rank" }}{PARA 7 "" 1 "" {TEXT -1 33 "Warning, ne w definition for trace" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "s zogpontok:=proc(A::matrix)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "local L,i:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "L:=\{\}:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "for i from 1 to rowdim(A) do L:=L union \{i\}:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "L" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "szogpontok(matrix(5,5,[0,1,1,0,0,1,0,1,1,1,1, 1,0,1,0,0,1,1,0,1,0,1,0,1,0]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<' \"\"\"\"\"#\"\"$\"\"%\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "elek:=proc(A::matrix)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "local \+ L,i,j:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "L:=\{\}:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "for i from 1 to rowdim(A) do" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 30 " for j from 1 to coldim(A) do" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 40 " if A[i,j]=1 then L:=L union \{\{i,j\}\}:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 " fi:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "L" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "elek(matrix(5,5, [0,1,1,0,0,1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,1,0]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<)<$\"\"#\"\"&<$\"\"\"\"\"$<$F%\"\"%<$F+F&<$F(F%<$ F%F)<$F)F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "graf:=proc(A: :matrix)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "local G:" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 9 "G:=new():" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "addvertex(szogpontok(A),G):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "add edge(elek(A),G):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "G" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "draw(graf(matrix(5,5,[0,1,1,0,0,1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,1, 0,1,0])));" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "64-% %TEXTG6$7$$\"\"\"\"\"!F)Q\"16\"-%'CURVESG6$7$7$$\"+Q*p,4$!#5$\"+l^c5&* F37$$\"+l*p,4$F3$!+c^c5&*F3-%'COLOURG6&%$RGBGF)$\"#5!\"\"F)-F-6$7$F&F0 F;-%'POINTSG6#F6-FF6#7$$!+M*p,4)F3$!+PD&y(eF3-FF6#7$$!+]*p,4)F3$\"+9D& y(eF3-FF6#F0-FF6#F&-F-6$7$F0FQF;-F-6$7$F&FQF;-F-6$7$FQFJF;-F-6$7$F0FJF ;-F-6$7$FJF6F;-F$6$F6Q\"5F+-F$6$FQQ\"3F+-F$6$FJQ\"4F+-F$6$F0Q\"2F+-%*A XESSTYLEG6#%%NONEG" 1 2 0 1 0 2 9 1 1 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "evalm(szomszed^20);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7'7'\"*'>%Gx#\"*8*)>U%\"* (oQ " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 26 "5.3. Grafok osszefuggose ge" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "G2:=new():" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "addvertex(\{v1,v2,v3,v4,v5,v6,v7,v8 ,v9\},G2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "addedge(\{\{v 1,v2\},\{v1,v3\},\{v5,v6\},\{v6,v7\},\{v7,v8\},\{v8,v9\}\},G2):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "components(G2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%<%%#v1G%#v3G%#v2G<#%#v4G<'%#v8G%#v9G%#v5G%#v7 G%#v6G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "draw(G2);" }} {PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6;-%'POINTSG6#7$$ \"\"\"\"\"!F)-%'CURVESG6$7$7$$!+2i#pR*!#5$\"+N9??MF17$$!+3i#pR*F1$!+L9 ??MF1-%'COLOURG6&%$RGBGF)$\"#5!\"\"F)-%%TEXTG6$7$$\"+HWWgwF1$!++h(yU'F 1Q#v96\"-F+6$7$F&7$$\"+JWWgwF1$\"+(4wyU'F1F9-FA6$7$$!+)*******\\F1$!+R SDg')F1Q#v7FI-F$6#7$$\"+\"y\"[O " 0 "" {MPLTEXT 1 0 14 "ad jacency(G2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7+7+\"\"! \"\"\"F)F(F(F(F(F(F(7+F)F(F(F(F(F(F(F(F(F*7+F(F(F(F(F(F(F(F(F(7+F(F(F( F(F(F)F(F(F(7+F(F(F(F(F)F(F)F(F(7+F(F(F(F(F(F)F(F)F(7+F(F(F(F(F(F(F)F( F)7+F(F(F(F(F(F(F(F)F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 17 "5.4. Euler-grafok" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "degreeseq(G2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7+\"\"!\"\"\"F%F%F%\"\"#F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "Euler:=proc(G::graph)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "local c,i,r:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "c: =degreeseq(G):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "i:=1:" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 20 "while i " 0 "" {MPLTEXT 1 0 39 " if (c[i] mod 2)<>0 then i:=nops(c)+2:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 " else i:=i+1:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " fi:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "if i=nops(c)+2 then r:=\"Nem Euler- graf\":" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " else r:=\"Euler-graf\" :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "fi:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "r" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "Euler(cycle(5));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q+Euler-graf6\"" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 21 "Euler(complete((4)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q/Nem~Euler-graf6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "Euler(G1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q/Nem~Euler-graf6\" " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "L:=[op(vertices(G2))]; \+ vdegree(L[1],G2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG7+%#v1G%#v3 G%#v2G%#v4G%#v8G%#v9G%#v5G%#v7G%#v6G" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "for i from 1 to \+ nops(L) do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "c[i]:=vdegree(L[i],G2 ):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "seq(c[j],j=1..nops(L));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6+\"\"#\"\"\"F$\"\"!F#F$F$F#F#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 21 "5.5. Sul yozott grafok" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "new(G3):" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "addvertex(\{a,b,c,d,y,z\},G 3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6(%\"bG%\"aG%\"yG%\"zG%\"cG%\"dG " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "addedge([\{a,b\},\{a,d \},\{b,c\},\{b,y\},\{c,z\},\{d,y\},\{y,z\}],weights=[4,2,3,3,2,3,1],G3 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6)%#e1G%#e2G%#e3G%#e4G%#e5G%#e6G%# e7G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "draw(G3);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "66-%'POINTSG6#7$$\"+-+++ ]!#5$\"+PSDg')F)-%%TEXTG6$F&Q\"b6\"-F-6$7$$!+(*******\\F)$\"+SSDg')F)Q \"cF0-F$6#7$$!\"\"\"\"!$\"+&QKz*e!#>-F$6#7$$\"\"\"F>F>-%'CURVESG6$7$7$ $!+2+++]F)$!+MSDg')F)7$$\"+\"*******\\F)$!+VSDg')F)-%'COLOURG6&%$RGBGF >$\"#5F=F>-FH6$7$FKF;FU-FH6$7$FPF3FU-FH6$7$F&F3FU-FH6$7$FDF;FU-FH6$7$F &FDFU-F-6$F;Q\"dF0-F$6#FK-F-6$FKQ\"yF0-F$6#FP-F-6$FPQ\"zF0-F-6$FDQ\"aF 0-FH6$7$F&FKFU-F$6#F3-%*AXESSTYLEG6#%%NONEG" 1 2 0 1 0 2 9 1 1 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "eweight(e5,G3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 " " {TEXT -1 42 "5.6. Feszitofak, minimalis hosszusagu utak" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "draw(spantree(petersen()));" }} {PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6@-%%TEXTG6$7$$\" \"\"\"\"!F)Q\"16\"-%'POINTSG6#7$$\"+V*p,4)!#5$\"+CD&y(eF2-F$6$F/Q\"2F+ -%'CURVESG6$7$7$$!\"\"F)$!+:w1-T!#>7$$\"+Z*p,4)F2$!+>D&y(eF2-%'COLOURG 6&%$RGBGF)$\"#5F>F)-F96$7$7$$!+U*p,4$F2$\"+j^c5&*F27$$!+S*p,4)F2$!+HD& y(eF2FG-F96$7$7$$\"+Q*p,4$F2$\"+l^c5&*F2FBFG-F96$7$F&F/FG-F$6$FBQ#10F+ -F-6#FB-F-6#F<-F$6$F " 0 "" {MPLTEXT 1 0 23 "counttrees(petersen());" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"% +?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "draw(shortpathtree(pe tersen(),5));" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6 @-%%TEXTG6$7$$\"\"\"\"\"!F)Q\"16\"-%'POINTSG6#7$$\"+V*p,4)!#5$\"+CD&y( eF2-F$6$F/Q\"2F+-%'CURVESG6$7$7$$!+U*p,4$F2$\"+j^c5&*F27$$!+S*p,4)F2$! +HD&y(eF2-%'COLOURG6&%$RGBGF)$\"#5!\"\"F)-F96$7$F&F/FF-F$6$7$$\"+Z*p,4 )F2$!+>D&y(eF2Q#10F+-F-6#FR-F-6#7$$FLF)$!+:w1-T!#>-F$6$FfnQ\"6F+-F-6#F A-F$6$FAQ\"7F+-F-6#7$$!+M*p,4$F2$!+m^c5&*F2-F$6$FeoQ\"8F+-F-6#7$$\"+Y* p,4$F2$!+i^c5&*F2-F$6$F_pQ\"9F+-F$6$7$$!+X*p,4)F2$\"+AD&y(eF2Q\"5F+-F9 6$7$F&FfnFF-F96$7$FipF_pFF-F96$7$F " 0 " " {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 32 "6. Linea ris rekurzios egyenletek" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " fibonacci:=f(n)=f(n-1)+f(n-2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*f ibonacciG/-%\"fG6#%\"nG,&-F'6#,&F)\"\"\"!\"\"F.F.-F'6#,&F)F.!\"#F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "kezdeti1:=f(0)=0,f(1)=1; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)kezdeti1G6$/-%\"fG6#\"\"!F*/-F( 6#\"\"\"F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "megoldas1:=rs olve(\{fibonacci,kezdeti1\},f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%* megoldas1G,&*&*&,&*$-%%sqrtG6#\"\"&\"\"\"#!\"\"F-\"\"\"F1F1),$*&F.F.,& F0F1F)F1!\"\"\"\"#%\"nGF1F.F5F6F1*&*&,&F0F1F)F/F1),$*&F.F.,&F1F1F)F1F6 !\"#F8F1F.F?F6F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "generat or1:=rsolve(\{fibonacci,kezdeti1\},f,'genfunc'(z));" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%+generator1G,$*&%\"zG\"\"\",(!\"\"\"\"\"F'F+*$)F'\" \"#F(F+!\"\"F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "fuggveny1 :=rsolve(\{fibonacci,kezdeti1\},f,'makeproc'):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 78 "fuggveny1(3);fuggveny1(4);fuggveny1(5);fuggven y1(6);fuggveny1(7);fuggveny1(8);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\" \"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\")" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"#8" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#\"#@" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "sorozat1:=seq([n, fuggveny1(n)],n=0..15);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%)sorozat1 G627$\"\"!F'7$\"\"\"F)7$\"\"#F)7$\"\"$F+7$\"\"%F-7$\"\"&F17$\"\"'\"\") 7$\"\"(\"#87$F4\"#@7$\"\"*\"#M7$\"#5\"#b7$\"#6\"#*)7$\"#7\"$W\"7$F7\"$ L#7$\"#9\"$x$7$\"#:\"$5'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "plot([sorozat1],style=point,symbol=diamond,title=\"Fibonacci sorozat \",color=blue);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6)-%'CURVESG6#727$\"\"!F(7$$\"\"\"F(F*7$$\"\"#F(F*7$$\"\"$F(F-7$$\"\" %F(F07$$\"\"&F(F67$$\"\"'F($\"\")F(7$$\"\"(F($\"#8F(7$F;$\"#@F(7$$\"\" *F($\"#MF(7$$\"#5F($\"#bF(7$$\"#6F($\"#*)F(7$$\"#7F($\"$W\"F(7$F@$\"$L #F(7$$\"#9F($\"$x$F(7$$\"#:F($\"$5'F(-%&STYLEG6#%&POINTG-%'COLOURG6&%$ RGBGF(F($\"*++++\"!\")-%'SYMBOLG6#%(DIAMONDG-%&TITLEG6#Q2Fibonacci~sor ozat6\"-%+AXESLABELSG6$%!GFgp-%%VIEWG6$%(DEFAULTGF[q" 1 5 2 1 0 2 6 1 4 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "karpol:=proc(egyenlet,a,n,rang,valtozo)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "local k,sor;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "sor:=seq(a(n-k)=valtozo^(rang-k),k=0..rang);" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 19 "subs(sor,egyenlet);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "karpol(fibon acci,f,n,2,z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*$)%\"zG\"\"#\"\"\" ,&F&\"\"\"F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}} {MARK "1" 0 }{VIEWOPTS 1 1 0 1 1 1803 }