Bevezet\303\251s a matematik\303\241ba J\303\241rai Antal Ezek a programok csak szeml\303\251ltet\303\251sre szolg\303\241lnak

restart;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

Logikai jelek: QyRRSyZub3Q7JmFuZDsmb3I7JkltcGxpZXM7JmlmZjsmb3BsdXM7fGdyJlZlcnQ7NiIiIiI=

UUsmbm90OyZhbmQ7Jm9yOyZJbXBsaWVzOyZpZmY7Jm9wbHVzO3xnciZWZXJ0OzYi

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn Kvantorok: QyRRMCZleGlzdDsmZm9yYWxsOzYiIiIi

UTAmZXhpc3Q7JmZvcmFsbDs2Ig==

Formul\303\241k gener\303\241l\303\241sa: QzA+SSZwcG5vdEc2IlEmJm5vdDtGJSEiIj5JJnBwYW5kR0YlUSYmYW5kO0YlRic+SSVwcG9yR0YlUSUmb3I7RiVGJz5JKHBwaW1wbHlHRiVRKiZJbXBsaWVzO0YlRic+SSZwcGlmZkdGJVEmJmlmZjtGJUYnPkkocHBleGlzdEdGJVEoJmV4aXN0O0YlRic+SSlwcGZvcmFsbEdGJVEpJmZvcmFsbDtGJUYn stringseq:=proc() local i,s; if nargs=0 then return "" fi; s:=convert(args[1],string); for i from 2 to nargs do s:=cat(s,",",args[i]) od; s; end;

Zio2IjYkSSJpR0YjSSJzR0YjRiNGI0MmQCQvJSZuYXJnc0ciIiFPUSFGIz5GJi1JKGNvbnZlcnRHJSpwcm90ZWN0ZWRHNiQmJSVhcmdzRzYjIiIiSSdzdHJpbmdHRjE/KEYlIiIjRjZGKkkldHJ1ZUdGMT5GJi1JJGNhdEdGMTYlRiZRIixGIyZGNDYjRiVGJkYjRiNGIw==

with(combinat): genform:=proc(L::list(list(string)),n::nonnegint) local V,VV,i,j,c,a,C,S,SL,SR,sr,sl; if nops(L)<=1 then return {} fi; S:={}; V:=L[1]; if n=0 then VV:=[]; for i from 2 to nops(L) do C:=choose(VV,i-2); for c in C do for a in L[i] do S:=S union {cat(a,"(",stringseq(op(c)),")")}; od; od; VV:=[op(VV),op(V)]; od; else SL:=genform(L,n-1); C:=choose(V,1); for sl in SL do S:=S union {cat(ppnot,sl)}; for c in C do S:=S union {cat("(",ppexist,op(c)," ",sl,")"), cat("(",ppforall,op(c)," ",sl,")")} od; od; for j to n do SL:=genform(L,j-1); SR:=genform(L,n-j); for sl in SL do for sr in SR do S:=S union {cat("(",sl,ppand,sr,")"),cat("(",sl,ppor,sr,")"), cat("(",sl,ppimply,sr,")"),cat("(",sl,ppiff,sr,")")} od; od; od; fi; S; end;

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

genform([["x","y"],["A","B"],["C","D"],["E","F"]],0);

PC5RJEEoKTYiUSRCKClGJFElQyh4KUYkUSVEKHgpRiRRJUMoeSlGJFElRCh5KUYkUSdFKHgseClGJFEnRih4LHgpRiRRJ0UoeCx5KUYkUSdGKHgseSlGJFEnRSh5LHkpRiRRJ0YoeSx5KUYk

genform([["x","y"],[],["P","E"],["I"]],1);

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

genform([["x","y"],[],["P"],["I"]],2): Az al\303\241bbi parser program egy sztring elemz\303\251s\303\251t v\303\251gzi, hogy az \303\251rv\303\251nyes formula-e? Ha igen, akkor a true \303\251rt\303\251ket \303\251s p\303\241rok egy list\303\241j\303\241t, \303\251s a marad\303\251k sztringet adja vissza. A p\303\241rok m\303\241sodik koordin\303\241t\303\241ja a megtal\303\241lt szintaktikai alapegys\303\251g. Az els\305\221 koordin\303\241ta az alapegys\303\251g tipusa, az al\303\241bbiak szerint: k kvantor l logikai jel p z\303\241r\303\263jel c vessz\305\221 f szabad v\303\241ltoz\303\263 b k\303\266t\303\266tt v\303\241ltoz\303\263 0,1,... predik\303\241tum, adott sz\303\241m\303\272 v\303\241ltoz\303\263val ? predik\303\241tum, m\303\251g ismeretlen sz\303\241m\303\272 v\303\241ltoz\303\263val Hiba eset\303\251n false \303\251rt\303\251ket kapunk, a lista \303\251s a marad\303\251k sztring pedig utal a hiba hely\303\251re. A v\303\241ltoz\303\263k \303\251s a predik\303\241tumok neve bet\305\261vel kell kezd\305\221dj\303\266n \303\251s bet\305\261ket \303\251s sz\303\241mjegyeket tartalmazhat. Elv\303\241laszt\303\263 jelk\303\251nt tetsz\305\221leges "whitespace" karakterekb\305\221l \303\241ll\303\263 sorozat haszn\303\241lhat\303\263. Az egyszer\305\261bb elj\303\241r\303\241sokkal kezdj\303\274k: A parseparentheses elj\303\241r\303\241s egy kezd\305\221 z\303\241r\303\263jellel kezd\305\221d\305\221 sztringben megkeresi az ehhez tartoz\303\263 z\303\241r\303\263 z\303\241r\303\263jelet, \303\251s ennek index\303\251t adja vissza. Ha sikertelen, akkor nulla az eredm\303\251ny. A parsename elj\303\241r\303\241s egy sztringet sz\303\251tv\303\241g egy n\303\251vre \303\251s egy marad\303\251kra. A parsevarsec elj\303\241r\303\241s vessz\305\221kel elv\303\241lasztott v\303\241ltoz\303\263k sorozat\303\241t ismeri fel. A parsepredicate elj\303\241r\303\241s egy predik\303\241tumot ismer fel. A f\305\221program a parsesentence elj\303\241r\303\241s. parseparentheses:=proc(s::string) local n,j; if s="" then return 0 fi; n:=0; for j to length(s) do if s[j]="(" then n:=n+1 fi; if s[j]=")" then n:=n-1; fi; if n=0 then return j fi; od; 0; end;

Zio2IydJInNHNiJJJ3N0cmluZ0clKnByb3RlY3RlZEc2JEkibkdGJkkiakdGJkYmRiZDJkAkL0YlUSFGJk8iIiE+RipGMT8oRisiIiJGNC1JJ2xlbmd0aEdGKDYjRiVJJXRydWVHRihDJUAkLyZGJTYjRitRIihGJj5GKiwmRipGNEY0RjRAJC9GPFEiKUYmPkYqLCZGKkY0RjQhIiJAJC9GKkYxT0YrRjFGJkYmRiY=

with(StringTools): parsename:=proc(s::string) local ls,rs; rs:=TrimLeft(s); if length(rs)=0 then return "","" fi; if IsAlpha(rs[1]) then ls:=rs[1]; rs:=Drop(rs,1) else return "",rs fi; while length(rs)>0 do if IsAlphaNumeric(rs[1]) then ls:=cat(ls,rs[1]); rs:=Drop(rs,1); else return ls,rs fi; od; ls,rs end;

Zio2IydJInNHNiJJJ3N0cmluZ0clKnByb3RlY3RlZEc2JEkjbHNHRiZJI3JzR0YmRiZGJkMnPkYrLV9JLFN0cmluZ1Rvb2xzRzYkRihJKF9zeXNsaWJHRiZJKVRyaW1MZWZ0R0YmNiNGJUAkLy1JJ2xlbmd0aEdGKDYjRisiIiFPNiRRIUYmRj1AJS1fRjBJKElzQWxwaGFHRiY2IyZGKzYjIiIiQyQ+RipGQz5GKy1fRjBJJURyb3BHRiY2JEYrRkVPNiRGPUYrPyhGJkZFRkVGJjJGOkY3QCUtX0YwSS9Jc0FscGhhTnVtZXJpY0dGJkZCQyQ+RiotSSRjYXRHRig2JEYqRkNGSE9GKUYpRiZGJkYm

parsevarseq:=proc(s::string) local L,rs,x; rs:=TrimLeft(s); L:=[]; if rs="" then return true,L,"" fi; while true do x:=parsename(rs); if x[1]="" then return false,L,x[2] fi; L:=[op(L),["f",x[1]]]; rs:=TrimLeft(x[2]); if rs="" then return true,L,"" fi; if rs[1]<>"," then return false,L,rs fi; L:=[op(L),["c",","]]; rs:=TrimLeft(Drop(rs,1)); if rs="" then return false,L,"" fi; od; end;

Zio2IydJInNHNiJJJ3N0cmluZ0clKnByb3RlY3RlZEc2JUkiTEdGJkkjcnNHRiZJInhHRiZGJkYmQyY+RistX0ksU3RyaW5nVG9vbHNHNiRGKEkoX3N5c2xpYkdGJkkpVHJpbUxlZnRHRiY2I0YlPkYqNyJAJC9GK1EhRiZPNiVJJXRydWVHRihGKkY6PyhGJiIiIkY/RiZGPUMrPkYsLUkqcGFyc2VuYW1lR0YmNiNGK0AkLyZGLDYjRj9GOk82JUkmZmFsc2VHRihGKiZGLDYjIiIjPkYqNyQtSSNvcEdGKDYjRio3JFEiZkYmRkc+RistRjA2I0ZMRjhAJDAmRitGSFEiLEYmTzYlRktGKkYrPkYqNyRGUTckUSJjRiZGZm4+RistRjA2Iy1fRjFJJURyb3BHRiY2JEYrRj9AJEY5TzYlRktGKkY6RiZGJkYm

parsepredicate:=proc(s::string) local L,x,ls,rs,j; x:=parsename(s);ls:=x[1]; if ls="" then return false,[],x[2] fi; rs:=x[2]; if rs="" then return false,["?",ls],"" fi; if rs[1]<>"(" then return false,["?",ls],rs fi; j:=parseparentheses(rs); if j=0 then return false,["?",ls],rs fi; x:=parsevarseq(rs[2..j-1]); if x[1] then if x[2]=[] then true,[[0,ls],["p","("],["p",")"]],Drop(rs,j) else true,[[(nops(x[2])+1)/2,ls],["p","("],op(x[2]),["p",")"]], Drop(rs,j) fi; else x[1],x[2],cat(x[3],Drop(rs,j-1)) fi; end;

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

parsesentence:=proc(s::string) local ls,rs,L,x,j,n; global ppnot,ppand,ppor,ppimply,ppiff,ppexist,ppforall; rs:=TrimLeft(s); if rs="" then return false,[],"" fi; if IsPrefix(ppnot,rs) then rs:=Drop(rs,length(ppnot)); x:=parsesentence(rs); x[1],[["l",ppnot],op(x[2])],x[3] elif rs[1]<>"(" then parsepredicate(rs) else L:=[["p","("]]; j:=parseparentheses(rs); if j=0 then return false,L,rs[2..-1] fi; ls:=TrimLeft(rs[2..j-1]); rs:=Drop(rs,j-1); if IsPrefix(ppexist,ls) or IsPrefix(ppforall,ls) then if IsPrefix(ppexist,ls) then L:=[op(L),["k",ppexist]]; ls:=Drop(ls,length(ppexist)); else L:=[op(L),["k",ppforall]]; ls:=Drop(ls,length(ppforall)); fi; x:=parsename(ls); if x[1]="" then return false,L,cat(x[2],rs) fi; n:=x[1];L:=[op(L),["b",n]]; x:=parsesentence(x[2]); if not x[1] or x[3]<>"" then return false,[op(L),op(x[2])],cat(x[3],rs) fi; for j in x[2] do if j[1]="f" and j[2]=n then L:=[op(L),["b",n]] else L:=[op(L),j] fi; od; L:=[op(L),["p",")"]]; rs:=TrimLeft(Drop(rs,1)); true,L,rs else x:=parsesentence(ls); if not x[1] then return false,x[2],cat(x[3],rs) fi; L:=[op(L),op(x[2])]; ls:=TrimLeft(x[3]); if IsPrefix(ppand,ls) or IsPrefix(ppor,ls) or IsPrefix(ppimply,ls) or IsPrefix(ppiff,ls) then if IsPrefix(ppand,ls) then L:=[op(L),["l",ppand]];ls:=Drop(ls,length(ppand)) elif IsPrefix(ppor,ls) then L:=[op(L),["l",ppor]];ls:=Drop(ls,length(ppor)) elif IsPrefix(ppor,ls) then L:=[op(L),["l",ppor]];ls:=Drop(ls,length(ppor)) else L:=[op(L),["l",ppor]];ls:=Drop(ls,length(ppor)) fi; x:=parsesentence(ls);L:=[op(L),op(x[2])]; if not x[1] or x[3]<>"" then return false,L,cat(x[3],rs) fi; L:=[op(L),["p",")"]]; rs:=TrimLeft(Drop(rs,1)); true,L,rs else false,L,cat(ls,rs) fi; fi; fi; end;

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

QywtSS5wYXJzZXNlbnRlbmNlRzYiNiNRJ0koeCx5KUYlIiIiLUYkNiNRMSZmb3JhbGw7eH5JKHgseClGJUYoLUYkNiNRMygmZm9yYWxsO3h+SSh4LHgpKUYlRigtRiQ2I1FUKCZmb3JhbGw7eCgmZm9yYWxsO3koJmV4aXN0O3ooSSh4LHopJmFuZDtJKHkseikpKSkpRiVGKC1GJDYjUUIoKEUoeCkmYW5kO0UoeSkpJmFuZDsmbm90O0koeCx5KSlGJUYo

NiVJJXRydWVHJSpwcm90ZWN0ZWRHNyg3JCIiI1EiSTYiNyRRInBGKVEiKEYpNyRRImZGKVEieEYpNyRRImNGKVEiLEYpNyRGLlEieUYpNyRGK1EiKUYpUSFGKQ==

NiVJJmZhbHNlRyUqcHJvdGVjdGVkRzciUTEmZm9yYWxsO3h+SSh4LHgpNiI=

NiVJJXRydWVHJSpwcm90ZWN0ZWRHNyw3JFEicDYiUSIoRig3JFEia0YoUSkmZm9yYWxsO0YoNyRRImJGKFEieEYoNyQiIiNRIklGKEYmRi03JFEiY0YoUSIsRihGLTckRidRIilGKEY2USFGKA==

NiVJJXRydWVHJSpwcm90ZWN0ZWRHNz03JFEicDYiUSIoRig3JFEia0YoUSkmZm9yYWxsO0YoNyRRImJGKFEieEYoRiZGKjckRi5RInlGKEYmNyRGK1EoJmV4aXN0O0YoNyRGLlEiekYoRiY3JCIiI1EiSUYoRiZGLTckUSJjRihRIixGKEY0NyRGJ1EiKUYoNyRRImxGKFEmJmFuZDtGKEY2RiZGMEY5RjRGPEY8RjxGPEY8USFGKA==

NiVJJXRydWVHJSpwcm90ZWN0ZWRHNzc3JFEicDYiUSIoRihGJjckIiIiUSJFRihGJjckUSJmRihRInhGKDckRidRIilGKDckUSJsRihRJiZhbmQ7RihGKkYmNyRGLlEieUYoRjBGMEYyNyRGM1EmJm5vdDtGKDckIiIjUSJJRihGJkYtNyRRImNGKFEiLEYoRjVGMEYwUSFGKA==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

restart; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

A:={a,b,c}; member(b,A); member(d,A); b in A; evalb(%); d in A; evalb(%);

PCVJImJHNiJJImNHRiRJImFHRiQ=

SSV0cnVlRyUqcHJvdGVjdGVkRw==

SSZmYWxzZUclKnByb3RlY3RlZEc=

LUkjaW5HJSpwcm90ZWN0ZWRHNiRJImJHNiI8JUYmSSJjR0YnSSJhR0Yn

SSV0cnVlRyUqcHJvdGVjdGVkRw==

LUkjaW5HJSpwcm90ZWN0ZWRHNiRJImRHNiI8JUkiYkdGJ0kiY0dGJ0kiYUdGJw==

SSZmYWxzZUclKnByb3RlY3RlZEc=

whattype(A); whattype(a); whattype(2); whattype(krikszkraksz); whattype("krikszkraksz");

SSRzZXRHJSpwcm90ZWN0ZWRH

SSdzeW1ib2xHJSpwcm90ZWN0ZWRH

SShpbnRlZ2VyRyUqcHJvdGVjdGVkRw==

SSdzeW1ib2xHJSpwcm90ZWN0ZWRH

SSdzdHJpbmdHJSpwcm90ZWN0ZWRH

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn {a,a,b,b,a}; {b,a};

PCRJImJHNiJJImFHRiQ=

PCRJImJHNiJJImFHRiQ=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

{a,b} subset {a,b,d};

SSV0cnVlRyUqcHJvdGVjdGVkRw==

{a,c} subset {a,b,d};

SSZmYWxzZUclKnByb3RlY3RlZEc=

{a,b} subset {a,b};

SSV0cnVlRyUqcHJvdGVjdGVkRw==

X subset X; X subset Y;

SSV0cnVlRyUqcHJvdGVjdGVkRw==

LUknc3Vic2V0RyUqcHJvdGVjdGVkRzYkSSJYRzYiSSJZR0Yn

A:={1,2,3,4,5,6,7}; select(x->isprime(x),A);

PCkiIiIiIiMiIiQiIiUiIiYiIiciIig=

PCYiIiMiIiQiIiYiIig=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

{}; {a,b}; {a,a}; {a,b,c};

PCI=

PCRJImJHNiJJImFHRiQ=

PCNJImFHNiI=

PCVJImJHNiJJImNHRiRJImFHRiQ=

a:=b; {a,b};

SSJiRzYi

PCNJImJHNiI=

a:='a'; {a,b};

SSJhRzYi

PCRJImJHNiJJImFHRiQ=

{} subset X;

SSV0cnVlRyUqcHJvdGVjdGVkRw==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

QyYtSSZ1bmlvbkclKnByb3RlY3RlZEc2JDwkSSJiRzYiSSJhR0YpPCRGKEkiY0dGKSIiIkYjRi0=

PCVJImJHNiJJImNHRiRJImFHRiQ=

PCVJImJHNiJJImNHRiRJImFHRiQ=

Qyo+SScmQXNjcjtHNiI8JzwiPCRJImJHRiVJImFHRiU8I0YqPCUiIiIiIiNGKTwkRilJImNHRiVGLS1JI29wRyUqcHJvdGVjdGVkRzYjRiRGLS1JJnVuaW9uR0YzNiNGMUYtLUY2NidGK0YvRixGJ0YoRi0=

PCc8IjwkSSJiRzYiSSJhR0YmPCNGJzwlIiIiIiIjRiU8JEYlSSJjR0Ym

Nic8IjwkSSJiRzYiSSJhR0YmPCNGJzwlIiIiIiIjRiU8JEYlSSJjR0Ym

PCciIiIiIiNJImJHNiJJImNHRiZJImFHRiY=

PCciIiIiIiNJImJHNiJJImNHRiZJImFHRiY=

{a,b} union {b,c}; `union`({a},{b,c},{1,2,b},{},{a,b});

PCVJImJHNiJJImNHRiRJImFHRiQ=

PCciIiIiIiNJImJHNiJJImNHRiZJImFHRiY=

A:={a,b}; B:={b,c}; `union`(A,B);

PCRJImJHNiJJImFHRiQ=

PCRJImJHNiJJImNHRiQ=

PCVJImJHNiJJImNHRiRJImFHRiQ=

`union`();

PCI=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

X union {};

SSJYRzYi

X union Y; Y union X;

LUkmdW5pb25HJSpwcm90ZWN0ZWRHNiRJIlhHNiJJIllHRic=

LUkmdW5pb25HJSpwcm90ZWN0ZWRHNiRJIlhHNiJJIllHRic=

(X union Y) union Z; X union (Y union Z);

LUkmdW5pb25HJSpwcm90ZWN0ZWRHNiVJIlhHNiJJIllHRidJIlpHRic=

LUkmdW5pb25HJSpwcm90ZWN0ZWRHNiVJIlhHNiJJIllHRidJIlpHRic=

X union X;

SSJYRzYi

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

{a,b,1} intersect {a,c,2,1};

PCQiIiJJImFHNiI=

`intersect`({a,b,c,d},{a,b,c,1},{a,b,1,2});

PCRJImJHNiJJImFHRiQ=

A:={a,b}; B:={b,c}; C:={c,a}; A intersect B; B intersect C; C intersect A; `intersect`(A,B); `intersect`(A,B,C);

PCRJImJHNiJJImFHRiQ=

PCRJImJHNiJJImNHRiQ=

PCRJImNHNiJJImFHRiQ=

PCNJImJHNiI=

PCNJImNHNiI=

PCNJImFHNiI=

PCNJImJHNiI=

PCI=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

Az els\305\221 n\303\251gy tulajdons\303\241got a Maple is ismeri: X intersect {};

PCI=

X intersect Y; Y intersect X;

LUkqaW50ZXJzZWN0RyUqcHJvdGVjdGVkRzYkSSJYRzYiSSJZR0Yn

LUkqaW50ZXJzZWN0RyUqcHJvdGVjdGVkRzYkSSJYRzYiSSJZR0Yn

X intersect (Y intersect Z); (X intersect Y) intersect Z;

LUkqaW50ZXJzZWN0RyUqcHJvdGVjdGVkRzYlSSJYRzYiSSJZR0YnSSJaR0Yn

LUkqaW50ZXJzZWN0RyUqcHJvdGVjdGVkRzYlSSJYRzYiSSJZR0YnSSJaR0Yn

X intersect X;

SSJYRzYi

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

X intersect (Y union Z); expand(%);

LUkqaW50ZXJzZWN0RyUqcHJvdGVjdGVkRzYkLUkmdW5pb25HRiQ2JEkiWUc2IkkiWkdGKkkiWEdGKg==

LUkmdW5pb25HJSpwcm90ZWN0ZWRHNiQtSSppbnRlcnNlY3RHRiQ2JEkiWEc2IkkiWUdGKi1GJzYkRilJIlpHRio=

X union (Y intersect Z); A:={a,b,c}; B:={b,c,d}; C:={c,d,e}; A union (B intersect C); (A union B) intersect (A union C);

LUkmdW5pb25HJSpwcm90ZWN0ZWRHNiRJIlhHNiItSSppbnRlcnNlY3RHRiQ2JEkiWUdGJ0kiWkdGJw==

PCVJImJHNiJJImNHRiRJImFHRiQ=

PCVJImJHNiJJImNHRiRJImRHRiQ=

PCVJImNHNiJJImRHRiRJImVHRiQ=

PCZJImJHNiJJImNHRiRJImFHRiRJImRHRiQ=

PCZJImJHNiJJImNHRiRJImFHRiRJImRHRiQ=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

A:={a,b}; B:={b,c}; C:={a,b,c,d}; A minus B; symmdiff(A,B); symmdiff(A,B,C);

PCRJImJHNiJJImFHRiQ=

PCRJImJHNiJJImNHRiQ=

PCZJImJHNiJJImNHRiRJImFHRiRJImRHRiQ=

PCNJImFHNiI=

PCRJImNHNiJJImFHRiQ=

PCRJImJHNiJJImRHRiQ=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

A; C minus (C minus A);

PCRJImJHNiJJImFHRiQ=

PCRJImJHNiJJImFHRiQ=

C; C minus {};

PCZJImJHNiJJImNHRiRJImFHRiRJImRHRiQ=

PCZJImJHNiJJImNHRiRJImFHRiRJImRHRiQ=

{}, C minus C;

NiQ8IkYj

{}; A intersect (C minus A);

PCI=

PCI=

C; A union (C minus A);

PCZJImJHNiJJImNHRiRJImFHRiRJImRHRiQ=

PCZJImJHNiJJImNHRiRJImFHRiRJImRHRiQ=

B:={a,b,d}; A; C minus B; C minus A;

PCVJImJHNiJJImFHRiRJImRHRiQ=

PCRJImJHNiJJImFHRiQ=

PCNJImNHNiI=

PCRJImNHNiJJImRHRiQ=

A; B:={b,c}; C minus (A union B); (C minus A) intersect (C minus B);

PCRJImJHNiJJImFHRiQ=

PCRJImJHNiJJImNHRiQ=

PCNJImRHNiI=

PCNJImRHNiI=

C minus (A intersect B); (C minus A) union (C minus B);

PCVJImNHNiJJImFHRiRJImRHRiQ=

PCVJImNHNiJJImFHRiRJImRHRiQ=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

with(combinat,powerset): powerset({a,b,c}); powerset({a,b}); powerset({a}); powerset({});

PCo8IjwlSSJiRzYiSSJjR0YmSSJhR0YmPCRGJUYoPCRGJ0YoPCNGJTwjRic8I0YoPCRGJUYn

PCY8IjwkSSJiRzYiSSJhR0YmPCNGJTwjRic=

PCQ8IjwjSSJhRzYi

PCM8Ig==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

A rendezett p\303\241r a Maple-ben [x,y]. evalb({{x},{x,y}}={{y},{x,y}});evalb([x,y]=[y,x]);

SSZmYWxzZUclKnByb3RlY3RlZEc=

SSZmYWxzZUclKnByb3RlY3RlZEc=

p:=[x,y]; p[1]; p[2];

NyRJInhHNiJJInlHRiQ=

SSJ4RzYi

SSJ5RzYi

`type/ordpair`:=proc(x) type(x,list) and nops(x)=2 end; type([a,b],ordpair); type([1,2,3],ordpair);

Zio2I0kieEc2IkYlRiVGJTMtSSV0eXBlRyUqcHJvdGVjdGVkRzYkRiRJJWxpc3RHRikvLUklbm9wc0dGKUYjIiIjRiVGJUYl

SSV0cnVlRyUqcHJvdGVjdGVkRw==

SSZmYWxzZUclKnByb3RlY3RlZEc=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

bincartprod:=proc(X::set,Y::set) local x,y,Z; Z:={}; for x in X do for y in Y do Z:=Z union {[x,y]}; od; od; Z; end;

Zio2JCdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJZR0YmRic2JUkieEdGJkkieUdGJkkiWkdGJkYmRiZDJT5GLjwiPyZGLEYlSSV0cnVlR0YoPyZGLUYqRjM+Ri4tSSZ1bmlvbkdGKDYkRi48IzckRixGLUYuRiZGJkYm

bincartprod({1,2,3},{a,b});

PCg3JCIiIkkiYkc2IjckRiRJImFHRiY3JCIiI0YlNyRGKkYoNyQiIiRGJTckRi1GKA==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

binrel:=proc(R::set(ordpair),X::set,Y::set) local r; if nargs<1 or nargs>3 then error ": needs 1..3 arguments" fi; for r in R do if nargs=2 and not (member(r[1],X) and member(r[2],X)) then return false; elif nargs=3 and not (member(r[1],X) and member(r[2],Y)) then return false fi; od; true; end;

Zio2JSdJIlJHNiItSSRzZXRHJSpwcm90ZWN0ZWRHNiNJKG9yZHBhaXJHRiYnSSJYR0YmRignSSJZR0YmRig2I0kickdGJkYmRiZDJUAkNTIlJm5hcmdzRyIiIjIiIiRGNllRNzp+bmVlZHN+MS4uM35hcmd1bWVudHNGJj8mRjFGJUkldHJ1ZUdGKUAmMy9GNiIiIzQzLUknbWVtYmVyR0YpNiQmRjE2I0Y3Ri0tRkU2JCZGMTYjRkFGLU9JJmZhbHNlR0YpMy9GNkY5NDNGRC1GRTYkRktGL0ZNRj1GJkYmRiY=

binrel({}); R:=bincartprod({1,2,3},{a,b});binrel(R);binrel(R,{0,1,2,3},{a,b,c}); binrel(R,{a,b},{1,2,3});binrel(R,{1,2,3,a,b});

SSV0cnVlRyUqcHJvdGVjdGVkRw==

PCg3JCIiIkkiYkc2IjckRiRJImFHRiY3JCIiI0YlNyRGKkYoNyQiIiRGJTckRi1GKA==

SSV0cnVlRyUqcHJvdGVjdGVkRw==

SSV0cnVlRyUqcHJvdGVjdGVkRw==

SSZmYWxzZUclKnByb3RlY3RlZEc=

SSV0cnVlRyUqcHJvdGVjdGVkRw==

id:=proc(X) local x; map(x->[x,x],X); end; id({1,3,a});

Zio2I0kiWEc2IjYjSSJ4R0YlRiVGJS1JJG1hcEclKnByb3RlY3RlZEc2JGYqRiZGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJTckRidGJ0YlRiVGJUYkRiVGJUYl

PCU3JCIiIkYkNyQiIiRGJjckSSJhRzYiRig=

F:={{1},{2},{1,2}}; FF:=bincartprod(F,F); select(x->x[1] subset x[2],FF);select(x->x[1] subset x[2] and not x[1]=x[2],FF);

PCU8IyIiIjwjIiIjPCRGJEYm

PCs3JDwjIiIjPCMiIiI3JEYkRiQ3JEYkPCRGJ0YlNyRGKkYmNyRGKkYkNyRGKkYqNyRGJkYmNyRGJkYkNyRGJkYq

PCc3JDwjIiIjRiQ3JEYkPCQiIiJGJTckRidGJzckPCNGKEYrNyRGK0Yn

PCQ3JDwjIiIjPCQiIiJGJTckPCNGJ0Ym

irem(13,5); X:={1,2,3,4,5,6};XX:=bincartprod(X,X): R:=select(x->irem(x[2],x[1])=0,XX);

IiIk

PCgiIiIiIiMiIiQiIiUiIiYiIic=

PDA3JCIiIiIiIzckRiRGJDckIiIkRig3JCIiJkYqNyQiIidGLDckRiRGKDckRiQiIiU3JEYkRio3JEYkRiw3JEYlRiU3JEYlRi83JEYlRiw3JEYoRiw3JEYvRi8=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

R:={[1,a],[1,b],[2,b],[3,d],[2,d],[4,e]}; dmn:=proc(R::set(ordpair)) map(x->x[1],R); end; dmn(R); rng:=proc(R::set(ordpair)) map(x->x[2],R); end; rng(R);

PCg3JCIiIkkiYkc2IjckRiRJImFHRiY3JCIiI0YlNyQiIiRJImRHRiY3JEYqRi03JCIiJUkiZUdGJg==

Zio2IydJIlJHNiItSSRzZXRHJSpwcm90ZWN0ZWRHNiNJKG9yZHBhaXJHRiZGJkYmRiYtSSRtYXBHRik2JGYqNiNJInhHRiZGJjYkSSlvcGVyYXRvckdGJkkmYXJyb3dHRiZGJiZGMTYjIiIiRiZGJkYmRiVGJkYmRiY=

PCYiIiIiIiMiIiQiIiU=

Zio2IydJIlJHNiItSSRzZXRHJSpwcm90ZWN0ZWRHNiNJKG9yZHBhaXJHRiZGJkYmRiYtSSRtYXBHRik2JGYqNiNJInhHRiZGJjYkSSlvcGVyYXRvckdGJkkmYXJyb3dHRiZGJiZGMTYjIiIjRiZGJkYmRiVGJkYmRiY=

PCZJImJHNiJJImFHRiRJImRHRiRJImVHRiQ=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

R; select(x->(x[1]>1 and x[2]<>b),R); restrict:=proc(R::set(ordpair),X) select(x->(x[1] in X),R); end; X:={2,3}; restrict(R,X);

PCg3JCIiIkkiYkc2IjckRiRJImFHRiY3JCIiI0YlNyQiIiRJImRHRiY3JEYqRi03JCIiJUkiZUdGJg==

PCU3JCIiJEkiZEc2IjckIiIjRiU3JCIiJUkiZUdGJg==

Zio2JCdJIlJHNiItSSRzZXRHJSpwcm90ZWN0ZWRHNiNJKG9yZHBhaXJHRiZJIlhHRiZGJkYmRiYtSSdzZWxlY3RHRik2JGYqNiNJInhHRiZGJjYkSSlvcGVyYXRvckdGJkkmYXJyb3dHRiZGJi1JI2luR0YpNiQmRjI2IyIiIkYsRiZGJjYkRiw5JUYlRiZGJkYm

PCQiIiMiIiQ=

PCU3JCIiI0kiYkc2IjckIiIkSSJkR0YmNyRGJEYp

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

relinv:=proc(R::set(ordpair)) map(x->[x[2],x[1]],R); end; R; dmn(R); rng(R); S:=relinv(R); dmn(S); rng(S); relinv(S);

Zio2IydJIlJHNiItSSRzZXRHJSpwcm90ZWN0ZWRHNiNJKG9yZHBhaXJHRiZGJkYmRiYtSSRtYXBHRik2JGYqNiNJInhHRiZGJjYkSSlvcGVyYXRvckdGJkkmYXJyb3dHRiZGJjckJkYxNiMiIiMmRjE2IyIiIkYmRiZGJkYlRiZGJkYm

PCg3JCIiIkkiYkc2IjckRiRJImFHRiY3JCIiI0YlNyQiIiRJImRHRiY3JEYqRi03JCIiJUkiZUdGJg==

PCYiIiIiIiMiIiQiIiU=

PCZJImJHNiJJImFHRiRJImRHRiRJImVHRiQ=

PCg3JEkiYkc2IiIiIzckSSJkR0YlIiIkNyRGKEYmNyRJImVHRiUiIiU3JEYkIiIiNyRJImFHRiVGLw==

PCZJImJHNiJJImFHRiRJImRHRiRJImVHRiQ=

PCYiIiIiIiMiIiQiIiU=

PCg3JCIiIkkiYkc2IjckRiRJImFHRiY3JCIiI0YlNyQiIiRJImRHRiY3JEYqRi03JCIiJUkiZUdGJg==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

mapset:=proc(R::set(ordpair),A::set) rng(restrict(R,A)) end; invmapset:=proc(R::set(ordpair),A::set) rng(restrict(relinv(R),A)) end; R; S:=relinv(R); A:={1,4}; B:={b,e}; mapset(R,A); mapset(R,B); invmapset(R,B); mapset(S,B);

Zio2JCdJIlJHNiItSSRzZXRHJSpwcm90ZWN0ZWRHNiNJKG9yZHBhaXJHRiYnSSJBR0YmRihGJkYmRiYtSSRybmdHRiY2Iy1JKXJlc3RyaWN0R0YmNiRGJUYtRiZGJkYm

Zio2JCdJIlJHNiItSSRzZXRHJSpwcm90ZWN0ZWRHNiNJKG9yZHBhaXJHRiYnSSJBR0YmRihGJkYmRiYtSSRybmdHRiY2Iy1JKXJlc3RyaWN0R0YmNiQtSSdyZWxpbnZHRiY2I0YlRi1GJkYmRiY=

PCg3JCIiIkkiYkc2IjckRiRJImFHRiY3JCIiI0YlNyQiIiRJImRHRiY3JEYqRi03JCIiJUkiZUdGJg==

PCg3JEkiYkc2IiIiIzckSSJkR0YlIiIkNyRGKEYmNyRJImVHRiUiIiU3JEYkIiIiNyRJImFHRiVGLw==

PCQiIiIiIiU=

PCRJImJHNiJJImVHRiQ=

PCVJImJHNiJJImFHRiRJImVHRiQ=

PCI=

PCUiIiIiIiMiIiU=

PCUiIiIiIiMiIiU=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

relcomp:=proc(R::set(ordpair),S::set(ordpair)) local r,s,T; T:={}; for r in R do for s in S do if s[2]=r[1] then T:=T union {[s[1],r[2]]}; fi; od; od; T; end; R; S:={[aa,1],[bb,3],[cc,5]}; relcomp(R,S);

Zio2JCdJIlJHNiItSSRzZXRHJSpwcm90ZWN0ZWRHNiNJKG9yZHBhaXJHRiYnSSJTR0YmRic2JUkickdGJkkic0dGJkkiVEdGJkYmRiZDJT5GMTwiPyZGL0YlSSV0cnVlR0YpPyZGMEYtRjZAJC8mRjA2IyIiIyZGLzYjIiIiPkYxLUkmdW5pb25HRik2JEYxPCM3JCZGMEY+JkYvRjtGMUYmRiZGJg==

PCg3JCIiIkkiYkc2IjckRiRJImFHRiY3JCIiI0YlNyQiIiRJImRHRiY3JEYqRi03JCIiJUkiZUdGJg==

PCU3JEkjYWFHNiIiIiI3JEkjYmJHRiUiIiQ3JEkjY2NHRiUiIiY=

PCU3JEkjYWFHNiJJImJHRiU3JEYkSSJhR0YlNyRJI2JiR0YlSSJkR0Yl

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

R; S:={[aa,1],[aa,2],[bb,3],[cc,4],[dd,5]}; relcomp(R,S); rng(R); rng(%%);

PCg3JCIiIkkiYkc2IjckRiRJImFHRiY3JCIiI0YlNyQiIiRJImRHRiY3JEYqRi03JCIiJUkiZUdGJg==

PCc3JEkjYWFHNiIiIiI3JEkjYmJHRiUiIiQ3JEYkIiIjNyRJI2NjR0YlIiIlNyRJI2RkR0YlIiIm

PCc3JEkjYWFHNiJJImJHRiU3JEYkSSJhR0YlNyRJI2JiR0YlSSJkR0YlNyRGJEYrNyRJI2NjR0YlSSJlR0Yl

PCZJImJHNiJJImFHRiRJImRHRiRJImVHRiQ=

PCZJImJHNiJJImFHRiRJImRHRiRJImVHRiQ=

T:={[xx,aa],[xx,cc]}; relcomp(R,relcomp(S,T)); relcomp(relcomp(R,S),T);

PCQ3JEkjeHhHNiJJI2FhR0YlNyRGJEkjY2NHRiU=

PCY3JEkjeHhHNiJJImJHRiU3JEYkSSJhR0YlNyRGJEkiZEdGJTckRiRJImVHRiU=

PCY3JEkjeHhHNiJJImJHRiU3JEYkSSJhR0YlNyRGJEkiZEdGJTckRiRJImVHRiU=

relinv(relcomp(R,S)); relcomp(relinv(S),relinv(R));

PCc3JEkiYkc2IkkjYWFHRiU3JEkiYUdGJUYmNyRJImRHRiVJI2JiR0YlNyRGKkYmNyRJImVHRiVJI2NjR0Yl

PCc3JEkiYkc2IkkjYWFHRiU3JEkiYUdGJUYmNyRJImRHRiVJI2JiR0YlNyRGKkYmNyRJImVHRiVJI2NjR0Yl

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

R; IX:=id({1,2,3,4,5}); relcomp(R,IX); IY:=id({a,b,c,d,e}); relcomp(IY,R);

PCg3JCIiIkkiYkc2IjckRiRJImFHRiY3JCIiI0YlNyQiIiRJImRHRiY3JEYqRi03JCIiJUkiZUdGJg==

PCc3JCIiIkYkNyQiIiRGJjckIiImRig3JCIiI0YqNyQiIiVGLA==

PCg3JCIiIkkiYkc2IjckRiRJImFHRiY3JCIiI0YlNyQiIiRJImRHRiY3JEYqRi03JCIiJUkiZUdGJg==

PCc3JEkiYUc2IkYkNyRJImJHRiVGJzckSSJjR0YlRik3JEkiZEdGJUYrNyRJImVHRiVGLQ==

PCg3JCIiIkkiYkc2IjckRiRJImFHRiY3JCIiI0YlNyQiIiRJImRHRiY3JEYqRi03JCIiJUkiZUdGJg==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

istransitive:=proc(R::set(ordpair)) local r,s; for r in R do for s in R do if r[2]=s[1] and not [r[1],s[2]] in R then return false fi; od; od; true; end; X:={1,2,3,4,5,6}; XX:=bincartprod(X,X): R:=select(x->irem(x[2],x[1])=0,XX); istransitive(R);

Zio2IydJIlJHNiItSSRzZXRHJSpwcm90ZWN0ZWRHNiNJKG9yZHBhaXJHRiY2JEkickdGJkkic0dGJkYmRiZDJD8mRi1GJUkldHJ1ZUdGKT8mRi5GJUYxQCQzLyZGLTYjIiIjJkYuNiMiIiI0LUkjaW5HRik2JDckJkYtRjomRi5GN0YlT0kmZmFsc2VHRilGMUYmRiZGJg==

PCgiIiIiIiMiIiQiIiUiIiYiIic=

PDA3JCIiIiIiIzckRiRGJDckIiIkRig3JCIiJkYqNyQiIidGLDckRiRGKDckRiQiIiU3JEYkRio3JEYkRiw3JEYlRiU3JEYlRi83JEYlRiw3JEYoRiw3JEYvRi8=

SSV0cnVlRyUqcHJvdGVjdGVkRw==

issymmetric:=proc(R::set(ordpair)) local r,s; for r in R do if not [r[2],r[1]] in R then return false fi; od; true; end; issymmetric(R);

Zio2IydJIlJHNiItSSRzZXRHJSpwcm90ZWN0ZWRHNiNJKG9yZHBhaXJHRiY2JEkickdGJkkic0dGJkYmRiZDJD8mRi1GJUkldHJ1ZUdGKUAkNC1JI2luR0YpNiQ3JCZGLTYjIiIjJkYtNiMiIiJGJU9JJmZhbHNlR0YpRjFGJkYmRiY=

SSZmYWxzZUclKnByb3RlY3RlZEc=

isantisymmetric:=proc(R::set(ordpair)) local r; for r in R do if [r[2],r[1]] in R then if r[1]<>r[2] then return false fi; fi; od; true; end; isantisymmetric(R);

Zio2IydJIlJHNiItSSRzZXRHJSpwcm90ZWN0ZWRHNiNJKG9yZHBhaXJHRiY2I0kickdGJkYmRiZDJD8mRi1GJUkldHJ1ZUdGKUAkLUkjaW5HRik2JDckJkYtNiMiIiMmRi02IyIiIkYlQCQwRjlGNk9JJmZhbHNlR0YpRjBGJkYmRiY=

SSV0cnVlRyUqcHJvdGVjdGVkRw==

isstriclyantisymmetric:=proc(R::set(ordpair)) local r; for r in R do if [r[2],r[1]] in R then return false fi; od; true; end; isstriclyantisymmetric(R);

Zio2IydJIlJHNiItSSRzZXRHJSpwcm90ZWN0ZWRHNiNJKG9yZHBhaXJHRiY2I0kickdGJkYmRiZDJD8mRi1GJUkldHJ1ZUdGKUAkLUkjaW5HRik2JDckJkYtNiMiIiMmRi02IyIiIkYlT0kmZmFsc2VHRilGMEYmRiZGJg==

SSZmYWxzZUclKnByb3RlY3RlZEc=

isreflexive:=proc(X::set,R::set(ordpair)) local x; if not binrel(R,X) then return false fi; for x in X do if not [x,x] in R then return false fi; od; true; end; isreflexive(X,R);

Zio2JCdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiY2I0kieEdGJkYmRiZDJUAkNC1JJ2JpbnJlbEdGJjYkRipGJU9JJmZhbHNlR0YoPyZGL0YlSSV0cnVlR0YoQCQ0LUkjaW5HRig2JDckRi9GL0YqRjZGOUYmRiZGJg==

SSV0cnVlRyUqcHJvdGVjdGVkRw==

isirreflexive:=proc(X::set,R::set(ordpair)) local x; if not binrel(R,X) then return false fi; for x in X do if [x,x] in R then return false fi; od; true; end; isirreflexive(X,R);

Zio2JCdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiY2I0kieEdGJkYmRiZDJUAkNC1JJ2JpbnJlbEdGJjYkRipGJU9JJmZhbHNlR0YoPyZGL0YlSSV0cnVlR0YoQCQtSSNpbkdGKDYkNyRGL0YvRipGNkY5RiZGJkYm

SSZmYWxzZUclKnByb3RlY3RlZEc=

istrichotom:=proc(X::set,R::set(ordpair)) local x,y; if not binrel(R,X) then return false fi; for x in X do for y in X do if x<>y then if ([x,y] in R and [y,x] in R) or ((not [x,y] in R) and (not [y,x] in R)) then return false fi; fi; od; od; true; end; istrichotom(X,R);

Zio2JCdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiY2JEkieEdGJkkieUdGJkYmRiZDJUAkNC1JJ2JpbnJlbEdGJjYkRipGJU9JJmZhbHNlR0YoPyZGL0YlSSV0cnVlR0YoPyZGMEYlRjpAJDBGL0YwQCQ1My1JI2luR0YoNiQ3JEYvRjBGKi1GQjYkNyRGMEYvRio0NUZBRkVGN0Y6RiZGJkYm

SSZmYWxzZUclKnByb3RlY3RlZEc=

isdichotom:=proc(X::set,R::set(ordpair)) local x,y; if not binrel(R,X) then return false fi; for x in X do for y in X do if not([x,y] in R or [y,x] in R) then return false fi; od; od; true; end; isdichotom(X,R);

Zio2JCdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiY2JEkieEdGJkkieUdGJkYmRiZDJUAkNC1JJ2JpbnJlbEdGJjYkRipGJU9JJmZhbHNlR0YoPyZGL0YlSSV0cnVlR0YoPyZGMEYlRjpAJDQ1LUkjaW5HRig2JDckRi9GMEYqLUZANiQ3JEYwRi9GKkY3RjpGJkYmRiY=

SSZmYWxzZUclKnByb3RlY3RlZEc=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

isequivalence:=proc(X::set,R::set(ordpair)) istransitive(R) and issymmetric(R) and isreflexive(X,R); end; isequivalence(X,R);

Zio2JCdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiZGJkYmRiYzMy1JLWlzdHJhbnNpdGl2ZUdGJjYjRiotSSxpc3N5bW1ldHJpY0dGJkYyLUksaXNyZWZsZXhpdmVHRiY2JEYlRipGJkYmRiY=

SSZmYWxzZUclKnByb3RlY3RlZEc=

E:=select(x->irem(x[1],3)=irem(x[2],3),XX); isequivalence(X,E);

PC43JCIiIkYkNyQiIiRGJjckIiImRig3JCIiJ0YmNyRGKkYqNyRGJCIiJTckIiIjRi83JEYvRig3JEYmRio3JEYtRiQ3JEYtRi03JEYoRi8=

SSV0cnVlRyUqcHJvdGVjdGVkRw==

ispartition:=proc(X::set,cO::set(set)) local Y,Z; for Y in cO do if Y={} then return false fi; for Z in cO do if Y<>Z and Y intersect Z<>{} then return false; fi; od; od; if `union`(op(cO))<>X then false else true fi; end;

Zio2JCdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSNjT0dGJi1GJzYjRic2JEkiWUdGJkkiWkdGJkYmRiZDJD8mRi5GKkkldHJ1ZUdGKEMkQCQvRi48Ik9JJmZhbHNlR0YoPyZGL0YqRjJAJDMwRi5GLzAtSSppbnRlcnNlY3RHRihGLUY2RjdAJTAtSSZ1bmlvbkdGKDYjLUkjb3BHRig2I0YqRiVGOEYyRiZGJkYm

X; cO:={{1,4},{2,5},{3,6}}; ispartition(X,cO); cO:={{1},{2,3,4}}; ispartition(X,cO); cO:={{1,2,3},{4,5,6,7}}; ispartition(X,cO); cO:={{1,2,3,4},{4,5,6}}; ispartition(X,cO);

PCgiIiIiIiMiIiQiIiUiIiYiIic=

PCU8JCIiIiIiJTwkIiIjIiImPCQiIiQiIic=

SSV0cnVlRyUqcHJvdGVjdGVkRw==

PCQ8IyIiIjwlIiIjIiIkIiIl

SSZmYWxzZUclKnByb3RlY3RlZEc=

PCQ8JiIiJSIiJiIiJyIiKDwlIiIiIiIjIiIk

SSZmYWxzZUclKnByb3RlY3RlZEc=

PCQ8JSIiJSIiJiIiJzwmIiIiIiIjIiIkRiQ=

SSZmYWxzZUclKnByb3RlY3RlZEc=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

equi2part:=proc(X::set,E::set(ordpair)) local cO,x,y,tx; cO:={}; for x in X do tx:={}; for y in X do if [x,y] in E then tx:=tx union {y} fi; od; cO:=cO union {tx} od; cO; end; X; E; cO:=equi2part(X,E);

Zio2JCdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJFR0YmLUYnNiNJKG9yZHBhaXJHRiY2JkkjY09HRiZJInhHRiZJInlHRiZJI3R4R0YmRiZGJkMlPkYvPCI/JkYwRiVJJXRydWVHRihDJT5GMkY1PyZGMUYlRjdAJC1JI2luR0YoNiQ3JEYwRjFGKj5GMi1JJnVuaW9uR0YoNiRGMjwjRjE+Ri8tRkI2JEYvPCNGMkYvRiZGJkYm

PCgiIiIiIiMiIiQiIiUiIiYiIic=

PC43JCIiIkYkNyQiIiRGJjckIiImRig3JCIiJ0YmNyRGKkYqNyRGJCIiJTckIiIjRi83JEYvRig3JEYmRio3JEYtRiQ3JEYtRi03JEYoRi8=

PCU8JCIiIiIiJTwkIiIjIiImPCQiIiQiIic=

part2equi:=proc(X::set,cO::set(set)) local E,Y,x,y; E:={}; for Y in cO do for x in Y do for y in Y do E:=E union {[x,y]} od; od; od; E; end; part2equi(X,cO);

Zio2JCdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSNjT0dGJi1GJzYjRic2JkkiRUdGJkkiWUdGJkkieEdGJkkieUdGJkYmRiZDJT5GLjwiPyZGL0YqSSV0cnVlR0YoPyZGMEYvRjY/JkYxRi9GNj5GLi1JJnVuaW9uR0YoNiRGLjwjNyRGMEYxRi5GJkYmRiY=

PC43JCIiIkYkNyQiIiRGJjckIiImRig3JCIiJ0YmNyRGKkYqNyRGJCIiJTckIiIjRi83JEYvRig3JEYmRio3JEYtRiQ3JEYtRi03JEYoRi8=

cO; equi2part(X,part2equi(X,cO)); E; part2equi(X,equi2part(X,E));

PCU8JCIiIiIiJTwkIiIjIiImPCQiIiQiIic=

PCU8JCIiIiIiJTwkIiIjIiImPCQiIiQiIic=

PC43JCIiIkYkNyQiIiRGJjckIiImRig3JCIiJ0YmNyRGKkYqNyRGJCIiJTckIiIjRi83JEYvRig3JEYmRio3JEYtRiQ3JEYtRi03JEYoRi8=

PC43JCIiIkYkNyQiIiRGJjckIiImRig3JCIiJ0YmNyRGKkYqNyRGJCIiJTckIiIjRi83JEYvRig3JEYmRio3JEYtRiQ3JEYtRi03JEYoRi8=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

ispartialordering:=proc(X::set,R::set(ordpair)) istransitive(R) and isantisymmetric(R) and isreflexive(X,R); end; X; R; ispartialordering(X,R);

Zio2JCdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiZGJkYmRiYzMy1JLWlzdHJhbnNpdGl2ZUdGJjYjRiotSTBpc2FudGlzeW1tZXRyaWNHRiZGMi1JLGlzcmVmbGV4aXZlR0YmNiRGJUYqRiZGJkYm

PCgiIiIiIiMiIiQiIiUiIiYiIic=

PDA3JCIiIiIiIzckRiRGJDckIiIkRig3JCIiJkYqNyQiIidGLDckRiRGKDckRiQiIiU3JEYkRio3JEYkRiw3JEYlRiU3JEYlRi83JEYlRiw3JEYoRiw3JEYvRi8=

SSV0cnVlRyUqcHJvdGVjdGVkRw==

iscomparable:=proc(x,y,R::set(ordpair)) evalb([x,y] in R or [y,x] in R); end; iscomparable(2,6,R); iscomparable(2,3,R);

Zio2JUkieEc2IkkieUdGJSdJIlJHRiUtSSRzZXRHJSpwcm90ZWN0ZWRHNiNJKG9yZHBhaXJHRiVGJUYlRiUtSSZldmFsYkdGKzYjNS1JI2luR0YrNiQ3JEYkRiZGKC1GMzYkNyRGJkYkRihGJUYlRiU=

SSV0cnVlRyUqcHJvdGVjdGVkRw==

SSZmYWxzZUclKnByb3RlY3RlZEc=

isordering:=proc(X::set,R::set(ordpair)) local x; ispartialordering(X,R) and isdichotom(X,R) end; isordering(X,R); S:=select(x->x[1]<=x[2],XX); isordering(X,S);

Zio2JCdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiY2I0kieEdGJkYmRiYzLUkyaXNwYXJ0aWFsb3JkZXJpbmdHRiY2JEYlRiotSStpc2RpY2hvdG9tR0YmRjNGJkYmRiY=

SSZmYWxzZUclKnByb3RlY3RlZEc=

PDc3JCIiIiIiIzckRiRGJDckIiIkRig3JCIiJkYqNyRGKiIiJzckRixGLDckRiRGKDckRiQiIiU3JEYkRio3JEYkRiw3JEYlRiU3JEYlRig3JEYlRjA3JEYlRio3JEYlRiw3JEYoRjA3JEYoRio3JEYoRiw3JEYwRjA3JEYwRio3JEYwRiw=

SSV0cnVlRyUqcHJvdGVjdGVkRw==

ischain:=proc(X::set,R::set(ordpair)) local S; S:=R intersect bincartprod(X,X); isordering(X,S); end; ischain({1,2,4},R); ischain({1,2,3},R);

Zio2JCdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiY2I0kiU0dGJkYmRiZDJD5GLy1JKmludGVyc2VjdEdGKDYkRiotSSxiaW5jYXJ0cHJvZEdGJjYkRiVGJS1JK2lzb3JkZXJpbmdHRiY2JEYlRi9GJkYmRiY=

SSV0cnVlRyUqcHJvdGVjdGVkRw==

SSZmYWxzZUclKnByb3RlY3RlZEc=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

strictrel:=proc(X::set,R::set(ordpair)) R minus id(X); end; X; R; S:=strictrel(X,R);

Zio2JCdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiZGJkYmRiYtSSZtaW51c0dGKDYkRiotSSNpZEdGJjYjRiVGJkYmRiY=

PCgiIiIiIiMiIiQiIiUiIiYiIic=

PDA3JCIiIiIiIzckRiRGJDckIiIkRig3JCIiJkYqNyQiIidGLDckRiRGKDckRiQiIiU3JEYkRio3JEYkRiw3JEYlRiU3JEYlRi83JEYlRiw3JEYoRiw3JEYvRi8=

PCo3JCIiIiIiIzckRiQiIiQ3JEYkIiIlNyRGJCIiJjckRiQiIic3JEYlRik3JEYlRi03JEYnRi0=

weakrel:=proc(X::set,R::set(ordpair)) R union id(X); end; weakrel(X,R);

Zio2JCdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiZGJkYmRiYtSSZ1bmlvbkdGKDYkRiotSSNpZEdGJjYjRiVGJkYmRiY=

PDA3JCIiIiIiIzckRiRGJDckIiIkRig3JCIiJkYqNyQiIidGLDckRiRGKDckRiQiIiU3JEYkRio3JEYkRiw3JEYlRiU3JEYlRi83JEYlRiw3JEYoRiw3JEYvRi8=

istransitive(S); isirreflexive(X,S); isstriclyantisymmetric(S); istrichotom(X,S);

SSV0cnVlRyUqcHJvdGVjdGVkRw==

SSV0cnVlRyUqcHJvdGVjdGVkRw==

SSV0cnVlRyUqcHJvdGVjdGVkRw==

SSZmYWxzZUclKnByb3RlY3RlZEc=

R:=select(x->x[1]<=x[2],XX); S:=strictrel(X,R); istrichotom(X,S);

PDc3JCIiIiIiIzckRiRGJDckIiIkRig3JCIiJkYqNyRGKiIiJzckRixGLDckRiRGKDckRiQiIiU3JEYkRio3JEYkRiw3JEYlRiU3JEYlRig3JEYlRjA3JEYlRio3JEYlRiw3JEYoRjA3JEYoRio3JEYoRiw3JEYwRjA3JEYwRio3JEYwRiw=

PDE3JCIiIiIiIzckIiImIiInNyRGJCIiJDckRiQiIiU3JEYkRic3JEYkRig3JEYlRio3JEYlRiw3JEYlRic3JEYlRig3JEYqRiw3JEYqRic3JEYqRig3JEYsRic3JEYsRig=

SSV0cnVlRyUqcHJvdGVjdGVkRw==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

int_o_o:=proc(X::set,R::set(ordpair),x,y) local S,z; S:={}; for z in X do if [x,z] in R and x<>z and [z,y] in R and z<>y then S:=S union {z}; fi; od; S; end; int_o_c:=proc(X::set,R::set(ordpair),x,y) local S,z; S:={}; for z in X do if [x,z] in R and x<>z and [z,y] in R then S:=S union {z}; fi; od; S; end; int_i_o:=proc(X::set,R::set(ordpair),x) local S,y; S:={}; for y in X do if [y,x] in R and x<>y then S:=S union {y}; fi; od; S; end;

Zio2JidJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiZJInhHRiZJInlHRiY2JEkiU0dGJkkiekdGJkYmRiZDJT5GMTwiPyZGMkYlSSV0cnVlR0YoQCQzMzMtSSNpbkdGKDYkNyRGLkYyRiowRi5GMi1GPTYkNyRGMkYvRiowRjJGLz5GMS1JJnVuaW9uR0YoNiRGMTwjRjJGMUYmRiZGJg==

Zio2JidJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiZJInhHRiZJInlHRiY2JEkiU0dGJkkiekdGJkYmRiZDJT5GMTwiPyZGMkYlSSV0cnVlR0YoQCQzMy1JI2luR0YoNiQ3JEYuRjJGKjBGLkYyLUY8NiQ3JEYyRi9GKj5GMS1JJnVuaW9uR0YoNiRGMTwjRjJGMUYmRiZGJg==

Zio2JSdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiZJInhHRiY2JEkiU0dGJkkieUdGJkYmRiZDJT5GMDwiPyZGMUYlSSV0cnVlR0YoQCQzLUkjaW5HRig2JDckRjFGLkYqMEYuRjE+RjAtSSZ1bmlvbkdGKDYkRjA8I0YxRjBGJkYmRiY=

X:={1,2,3,4,5,6}; XX:=bincartprod(X,X): R:=select(x->irem(x[2],x[1])=0,XX); int_o_o(X,R,1,6); int_o_c(X,R,1,6); int_i_o(X,R,6);

PCgiIiIiIiMiIiQiIiUiIiYiIic=

PDA3JCIiIiIiIzckRiRGJDckIiIkRig3JCIiJkYqNyQiIidGLDckRiRGKDckRiQiIiU3JEYkRio3JEYkRiw3JEYlRiU3JEYlRi83JEYlRiw3JEYoRiw3JEYvRi8=

PCQiIiMiIiQ=

PCUiIiMiIiQiIic=

PCUiIiIiIiMiIiQ=

$ 2..6;$ 1..9;

NiciIiMiIiQiIiUiIiYiIic=

NisiIiIiIiMiIiQiIiUiIiYiIiciIigiIikiIio=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

least:=proc(X::set,R::set(ordpair)) local x,y,f; for x in X do f:=true; for y in X do if not [x,y] in R then f:=false; break; fi; od; if f then return x fi; od; NULL; end; greatest:=proc(X::set,R::set(ordpair)) local x,y,f; for x in X do f:=true; for y in X do if not [y,x] in R then f:=false; break; fi; od; if f then return x fi; od; NULL; end;

Zio2JCdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiY2JUkieEdGJkkieUdGJkkiZkdGJkYmRiZDJD8mRi9GJUkldHJ1ZUdGKEMlPkYxRjQ/JkYwRiVGNEAkNC1JI2luR0YoNiQ3JEYvRjBGKkMkPkYxSSZmYWxzZUdGKFtAJEYxT0YvSSVOVUxMR0YoRiZGJkYm

Zio2JCdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiY2JUkieEdGJkkieUdGJkkiZkdGJkYmRiZDJD8mRi9GJUkldHJ1ZUdGKEMlPkYxRjQ/JkYwRiVGNEAkNC1JI2luR0YoNiQ3JEYwRi9GKkMkPkYxSSZmYWxzZUdGKFtAJEYxT0YvSSVOVUxMR0YoRiZGJkYm

X; R; least(X,R); greatest(X,R);

PCgiIiIiIiMiIiQiIiUiIiYiIic=

PDA3JCIiIiIiIzckRiRGJDckIiIkRig3JCIiJkYqNyQiIidGLDckRiRGKDckRiQiIiU3JEYkRio3JEYkRiw3JEYlRiU3JEYlRi83JEYlRiw3JEYoRiw3JEYvRi8=

IiIi

mins:=proc(X::set,R::set(ordpair)) local x,y,f,S; S:={}; for x in X do f:=true; for y in X do if [y,x] in R and x<>y then f:=false; break; fi; od; if f then S:=S union {x}; fi; od; S; end; maxs:=proc(X::set,R::set(ordpair)) local x,y,f,S; S:={}; for x in X do f:=true; for y in X do if [x,y] in R and x<>y then f:=false; break; fi; od; if f then S:=S union {x}; fi; od; S; end;

Zio2JCdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiY2JkkieEdGJkkieUdGJkkiZkdGJkkiU0dGJkYmRiZDJT5GMjwiPyZGL0YlSSV0cnVlR0YoQyU+RjFGNz8mRjBGJUY3QCQzLUkjaW5HRig2JDckRjBGL0YqMEYvRjBDJD5GMUkmZmFsc2VHRihbQCRGMT5GMi1JJnVuaW9uR0YoNiRGMjwjRi9GMkYmRiZGJg==

Zio2JCdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiY2JkkieEdGJkkieUdGJkkiZkdGJkkiU0dGJkYmRiZDJT5GMjwiPyZGL0YlSSV0cnVlR0YoQyU+RjFGNz8mRjBGJUY3QCQzLUkjaW5HRig2JDckRi9GMEYqMEYvRjBDJD5GMUkmZmFsc2VHRihbQCRGMT5GMi1JJnVuaW9uR0YoNiRGMjwjRi9GMkYmRiZGJg==

X; R; mins(X,R); maxs(X,R);

PCgiIiIiIiMiIiQiIiUiIiYiIic=

PDA3JCIiIiIiIzckRiRGJDckIiIkRig3JCIiJkYqNyQiIidGLDckRiRGKDckRiQiIiU3JEYkRio3JEYkRiw3JEYlRiU3JEYlRi83JEYlRiw3JEYoRiw3JEYvRi8=

PCMiIiI=

PCUiIiUiIiYiIic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

islowerbound:=proc(X::set,R::set(ordpair),Y::set,x) local y; for y in Y do if not [x,y] in R then return false fi; od; true; end; isupperbound:=proc(X::set,R::set(ordpair),Y::set,x) local y; for y in Y do if not [y,x] in R then return false fi; od; true; end;

Zio2JidJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiYnSSJZR0YmRidJInhHRiY2I0kieUdGJkYmRiZDJD8mRjJGL0kldHJ1ZUdGKEAkNC1JI2luR0YoNiQ3JEYwRjJGKk9JJmZhbHNlR0YoRjVGJkYmRiY=

Zio2JidJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiYnSSJZR0YmRidJInhHRiY2I0kieUdGJkYmRiZDJD8mRjJGL0kldHJ1ZUdGKEAkNC1JI2luR0YoNiQ3JEYyRjBGKk9JJmZhbHNlR0YoRjVGJkYmRiY=

X; R; islowerbound(X,R,{2,3,5},1); isupperbound(X,R,{2,3,5},6);

PCgiIiIiIiMiIiQiIiUiIiYiIic=

PDA3JCIiIiIiIzckRiRGJDckIiIkRig3JCIiJkYqNyQiIidGLDckRiRGKDckRiQiIiU3JEYkRio3JEYkRiw3JEYlRiU3JEYlRi83JEYlRiw3JEYoRiw3JEYvRi8=

SSV0cnVlRyUqcHJvdGVjdGVkRw==

SSZmYWxzZUclKnByb3RlY3RlZEc=

lowerbounds:=proc(X::set,R::set(ordpair),Y::set) local S,x; S:={}; for x in X do if islowerbound(X,R,Y,x) then S:=S union {x} fi; od; S; end;

Zio2JSdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiYnSSJZR0YmRic2JEkiU0dGJkkieEdGJkYmRiZDJT5GMTwiPyZGMkYlSSV0cnVlR0YoQCQtSS1pc2xvd2VyYm91bmRHRiY2JkYlRipGL0YyPkYxLUkmdW5pb25HRig2JEYxPCNGMkYxRiZGJkYm

upperbounds:=proc(X::set,R::set(ordpair),Y::set) local S,x; S:={}; for x in X do if isupperbound(X,R,Y,x) then S:=S union {x} fi; od; S; end;

Zio2JSdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiYnSSJZR0YmRic2JEkiU0dGJkkieEdGJkYmRiZDJT5GMTwiPyZGMkYlSSV0cnVlR0YoQCQtSS1pc3VwcGVyYm91bmRHRiY2JkYlRipGL0YyPkYxLUkmdW5pb25HRig2JEYxPCNGMkYxRiZGJkYm

X:={1,2,3,4,5,6}; XX:=bincartprod(X,X): R:=select(x->irem(x[2],x[1])=0,XX); lowerbounds(X,R,{2,4}); upperbounds(X,R,{2,4});

PCgiIiIiIiMiIiQiIiUiIiYiIic=

PDA3JCIiIiIiIzckRiRGJDckIiIkRig3JCIiJkYqNyQiIidGLDckRiRGKDckRiQiIiU3JEYkRio3JEYkRiw3JEYlRiU3JEYlRi83JEYlRiw3JEYoRiw3JEYvRi8=

PCQiIiIiIiM=

PCMiIiU=

inf:=proc(X::set,R::set(ordpair),Y::set) greatest(lowerbounds(X,R,Y),R); end; sup:=proc(X::set,R::set(ordpair),Y::set) least(upperbounds(X,R,Y),R); end; inf(X,R,{2,4}); sup(X,R,{2,4});

Zio2JSdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiYnSSJZR0YmRidGJkYmRiYtSSlncmVhdGVzdEdGJjYkLUksbG93ZXJib3VuZHNHRiY2JUYlRipGL0YqRiZGJkYm

Zio2JSdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiYnSSJZR0YmRidGJkYmRiYtSSZsZWFzdEdGJjYkLUksdXBwZXJib3VuZHNHRiY2JUYlRipGL0YqRiZGJkYm

IiIj

IiIl

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

iswellordering:=proc(X::set,R::set(ordpair)) local f,Y,P; f:=isordering(X,R); if not f then return f fi; P:=powerset(X); for Y in P do if Y<>{} then f:=least(Y,R); if f=NULL then return f; fi; fi; od; true; end;

Zio2JCdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiY2JUkiZkdGJkkiWUdGJkkiUEdGJkYmRiZDJz5GLy1JK2lzb3JkZXJpbmdHRiY2JEYlRipAJDRGL09GLz5GMS1fSSljb21iaW5hdEc2JEYoSShfc3lzbGliR0YmSSlwb3dlcnNldEdGJjYjRiU/JkYwRjFJJXRydWVHRihAJDBGMDwiQyQ+Ri8tSSZsZWFzdEdGJjYkRjBGKkAkL0YvSSVOVUxMR0YoRjlGQ0YmRiZGJg==

X; R; iswellordering(X,R); R:=select(x->x[1]<=x[2],XX);iswellordering(X,R);

PCgiIiIiIiMiIiQiIiUiIiYiIic=

PDA3JCIiIiIiIzckRiRGJDckIiIkRig3JCIiJkYqNyQiIidGLDckRiRGKDckRiQiIiU3JEYkRio3JEYkRiw3JEYlRiU3JEYlRi83JEYlRiw3JEYoRiw3JEYvRi8=

SSZmYWxzZUclKnByb3RlY3RlZEc=

PDc3JCIiIiIiIzckRiRGJDckIiIkRig3JCIiJkYqNyRGKiIiJzckRixGLDckRiRGKDckRiQiIiU3JEYkRio3JEYkRiw3JEYlRiU3JEYlRig3JEYlRjA3JEYlRio3JEYlRiw3JEYoRjA3JEYoRio3JEYoRiw3JEYwRjA3JEYwRio3JEYwRiw=

SSV0cnVlRyUqcHJvdGVjdGVkRw==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

orderingprod:=proc(X::set,R::set(ordpair),Y::set,S::set(ordpair)) local x,y,xp,yp,RS; RS:={}; for x in X do for y in Y do for xp in X do for yp in Y do if [x,xp] in R and [y,yp] in S then RS:=RS union {[[x,y],[xp,yp]]}; fi; od; od; od; od; RS; end;

Zio2JidJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiYnSSJZR0YmRicnSSJTR0YmRis2J0kieEdGJkkieUdGJkkjeHBHRiZJI3lwR0YmSSNSU0dGJkYmRiZDJT5GNzwiPyZGM0YlSSV0cnVlR0YoPyZGNEYvRjw/JkY1RiVGPD8mRjZGL0Y8QCQzLUkjaW5HRig2JDckRjNGNUYqLUZDNiQ3JEY0RjZGMT5GNy1JJnVuaW9uR0YoNiRGNzwjNyQ3JEYzRjQ3JEY1RjZGN0YmRiZGJg==

X:={1,2}; R:={[1,1],[1,2],[2,2]}; isordering(X,R); Y:={a,b}; S:={[a,a],[a,b],[b,b]}; isordering(Y,S); XY:=bincartprod(X,Y); RS:=orderingprod(X,R,Y,S); isordering(XY,RS);

PCQiIiIiIiM=

PCU3JCIiIiIiIzckRiRGJDckRiVGJQ==

SSV0cnVlRyUqcHJvdGVjdGVkRw==

PCRJImJHNiJJImFHRiQ=

PCU3JEkiYUc2IkYkNyRJImJHRiVGJzckRiRGJw==

SSV0cnVlRyUqcHJvdGVjdGVkRw==

PCY3JCIiIkkiYkc2IjckRiRJImFHRiY3JCIiI0YlNyRGKkYo

PCs3JDckIiIiSSJiRzYiRiQ3JEYkNyQiIiNGJjckNyRGJUkiYUdGJ0YkNyRGLEYsNyRGLEYpNyRGLDckRipGLTckRilGKTckRjFGKTckRjFGMQ==

SSZmYWxzZUclKnByb3RlY3RlZEc=

strictorderingprod:=proc(X::set,R::set(ordpair),Y::set,S::set(ordpair)) local x,y,xp,yp,RS; RS:={}; for x in X do for y in Y do for xp in X do for yp in Y do if [x,xp] in R and x<>xp and [y,yp] in S and y<>yp then RS:=RS union {[[x,y],[xp,yp]]}; fi; od; od; od; od; RS; end;

Zio2JidJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiYnSSJZR0YmRicnSSJTR0YmRis2J0kieEdGJkkieUdGJkkjeHBHRiZJI3lwR0YmSSNSU0dGJkYmRiZDJT5GNzwiPyZGM0YlSSV0cnVlR0YoPyZGNEYvRjw/JkY1RiVGPD8mRjZGL0Y8QCQzMzMtSSNpbkdGKDYkNyRGM0Y1RiowRjNGNS1GRTYkNyRGNEY2RjEwRjRGNj5GNy1JJnVuaW9uR0YoNiRGNzwjNyQ3JEYzRjQ3JEY1RjZGN0YmRiZGJg==

lexorderingprod:=proc(X::set,R::set(ordpair),Y::set,S::set(ordpair)) local x,y,xp,yp,RS; RS:={}; for x in X do for y in Y do for xp in X do for yp in Y do if ([x,xp] in R and x<>xp) or (x=xp and [y,yp] in S) then RS:=RS union {[[x,y],[xp,yp]]}; fi; od; od; od; od; RS; end;

Zio2JidJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiYnSSJZR0YmRicnSSJTR0YmRis2J0kieEdGJkkieUdGJkkjeHBHRiZJI3lwR0YmSSNSU0dGJkYmRiZDJT5GNzwiPyZGM0YlSSV0cnVlR0YoPyZGNEYvRjw/JkY1RiVGPD8mRjZGL0Y8QCQ1My1JI2luR0YoNiQ3JEYzRjVGKjBGM0Y1My9GM0Y1LUZENiQ3JEY0RjZGMT5GNy1JJnVuaW9uR0YoNiRGNzwjNyQ3JEYzRjQ3JEY1RjZGN0YmRiZGJg==

strictrel(XY,RS); strictorderingprod(X,R,Y,S); strictrel(XY,lexorderingprod(X,R,Y,S));

PCc3JDckIiIiSSJiRzYiNyQiIiNGJjckNyRGJUkiYUdGJ0YkNyRGK0YoNyRGKzckRilGLDckRi9GKA==

PCM3JDckIiIiSSJhRzYiNyQiIiNJImJHRic=

PCg3JDckIiIiSSJiRzYiNyQiIiNGJjckNyRGJUkiYUdGJ0YkNyRGK0YoNyRGKzckRilGLDckRi9GKDckRiRGLw==

sort([cc,ca,cb,bb,aa,ab,ba],lexorder);

NylJI2FhRzYiSSNhYkdGJEkjYmFHRiRJI2JiR0YkSSNjYUdGJEkjY2JHRiRJI2NjR0Yk

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

isfunction:=proc(f::set(ordpair),X::set,Y::set) local x,y,S; if not binrel(args) then return false fi; for x in dmn(f) do S:={}; for y in rng(f) do if [x,y] in f then S:=S union {y} fi; od; if nops(S)>1 then return false fi; od; true; end;

Zio2JSdJImZHNiItSSRzZXRHJSpwcm90ZWN0ZWRHNiNJKG9yZHBhaXJHRiYnSSJYR0YmRignSSJZR0YmRig2JUkieEdGJkkieUdGJkkiU0dGJkYmRiZDJUAkNC1JJ2JpbnJlbEdGJjYjJSVhcmdzR09JJmZhbHNlR0YpPyZGMS1JJGRtbkdGJjYjRiVJJXRydWVHRilDJT5GMzwiPyZGMi1JJHJuZ0dGJkZARkFAJC1JI2luR0YpNiQ3JEYxRjJGJT5GMy1JJnVuaW9uR0YpNiRGMzwjRjJAJDIiIiItSSVub3BzR0YpNiNGM0Y7RkFGJkYmRiY=

f:=id({a,b}); isfunction(f); isfunction(f,{a,b,1}); isfunction(f,{a,b},{1,2});f:={[a,1],[b,2],[a,2]}; isfunction(f);

PCQ3JEkiYUc2IkYkNyRJImJHRiVGJw==

SSV0cnVlRyUqcHJvdGVjdGVkRw==

SSV0cnVlRyUqcHJvdGVjdGVkRw==

SSZmYWxzZUclKnByb3RlY3RlZEc=

PCU3JEkiYUc2IiIiIzckSSJiR0YlRiY3JEYkIiIi

SSZmYWxzZUclKnByb3RlY3RlZEc=

isinjective:=proc(f::set(ordpair)) isfunction(f) and isfunction(relinv(f)); end; isinjective({[a,1],[b,2]}); isinjective({[a,1],[b,1]});

Zio2IydJImZHNiItSSRzZXRHJSpwcm90ZWN0ZWRHNiNJKG9yZHBhaXJHRiZGJkYmRiYzLUkraXNmdW5jdGlvbkdGJjYjRiUtRi42Iy1JJ3JlbGludkdGJkYvRiZGJkYm

SSV0cnVlRyUqcHJvdGVjdGVkRw==

SSZmYWxzZUclKnByb3RlY3RlZEc=

issurjective:=proc(f::set(ordpair),Y::set) isfunction(f) and rng(f)=Y; end; issurjective({[a,1],[b,1]},{1,2}); issurjective({[a,1],[b,2]},{1,2});

Zio2JCdJImZHNiItSSRzZXRHJSpwcm90ZWN0ZWRHNiNJKG9yZHBhaXJHRiYnSSJZR0YmRihGJkYmRiYzLUkraXNmdW5jdGlvbkdGJjYjRiUvLUkkcm5nR0YmRjFGLUYmRiZGJg==

SSZmYWxzZUclKnByb3RlY3RlZEc=

SSV0cnVlRyUqcHJvdGVjdGVkRw==

isbijective:=proc(f::set(ordpair),Y::set) isinjective(f) and issurjective(f,Y); end; isbijective(id({1,2,3}),{1,2,3}); isbijective({[a,1],[b,2]},{1,2,3});

Zio2JCdJImZHNiItSSRzZXRHJSpwcm90ZWN0ZWRHNiNJKG9yZHBhaXJHRiYnSSJZR0YmRihGJkYmRiYzLUksaXNpbmplY3RpdmVHRiY2I0YlLUktaXNzdXJqZWN0aXZlR0YmNiRGJUYtRiZGJkYm

SSV0cnVlRyUqcHJvdGVjdGVkRw==

SSZmYWxzZUclKnByb3RlY3RlZEc=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn f:=x->x^2; f(1);f(2);f(3); eval(f); type(f,procedure);

Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiQpRiQiIiMiIiJGJUYlRiU=

IiIi

IiIl

IiIq

Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiQpRiQiIiMiIiJGJUYlRiU=

SSV0cnVlRyUqcHJvdGVjdGVkRw==

f:='f'; eval(f); whattype(f); f(1):=1; eval(f); f(2):=4; f(3):=8; f(1);f(2);f(3);f(4);

SSJmRzYi

SSJmRzYi

SSdzeW1ib2xHJSpwcm90ZWN0ZWRH

IiIi

Zio2IkYjNiNJKXJlbWVtYmVyR0YjRVxzIiIiIkYnLi0lKXByb2NuYW1lRzYjJSVhcmdzR0YjRiNGIw==

IiIl

IiIp

IiIi

IiIl

IiIp

LUkiZkc2IjYjIiIl

isarrowfromto:=proc(f::procedure,X::set,Y::set) local x; for x in X do if not f(x) in Y then return false fi; od; true; end; isarrowfromto(f,{1,2,3},{1,4,8,10}); isarrowfromto(f,{1,2},{1,8});

Zio2JSdJImZHNiJJKnByb2NlZHVyZUclKnByb3RlY3RlZEcnSSJYR0YmSSRzZXRHRignSSJZR0YmRis2I0kieEdGJkYmRiZDJD8mRi9GKkkldHJ1ZUdGKEAkNC1JI2luR0YoNiQtRiVGLkYtT0kmZmFsc2VHRihGMkYmRiZGJg==

SSV0cnVlRyUqcHJvdGVjdGVkRw==

SSZmYWxzZUclKnByb3RlY3RlZEc=

makefunction:=proc(R::set(ordpair)) local x,y,f; if not isfunction(R) then return NULL fi; for x in dmn(R) do for y in rng(R) do if [x,y] in R then f(x):=y fi; od; od; eval(f); end; f:='f'; R:={[1,1],[2,4],[3,9]}; f(1);f(2);f(3);f(4); f:=makefunction(R);f(1);f(2);f(3);f(4);

Zio2IydJIlJHNiItSSRzZXRHJSpwcm90ZWN0ZWRHNiNJKG9yZHBhaXJHRiY2JUkieEdGJkkieUdGJkkiZkdGJkYmRiZDJUAkNC1JK2lzZnVuY3Rpb25HRiY2I0YlT0klTlVMTEdGKT8mRi0tSSRkbW5HRiZGNUkldHJ1ZUdGKT8mRi4tSSRybmdHRiZGNUY7QCQtSSNpbkdGKTYkNyRGLUYuRiU+LUYvNiNGLUYuLUklZXZhbEdGKTYjRi9GJkYmRiY=

SSJmRzYi

PCU3JCIiIkYkNyQiIiMiIiU3JCIiJCIiKg==

LUkiZkc2IjYjIiIi

LUkiZkc2IjYjIiIj

LUkiZkc2IjYjIiIk

LUkiZkc2IjYjIiIl

Zio2IkYjNiNJKXJlbWVtYmVyR0YjRVxzJCIiIkYnIiIjIiIlIiIkIiIqLi0lKXByb2NuYW1lRzYjJSVhcmdzR0YjRiNGIw==

IiIi

IiIl

IiIq

LUkiZkc2IjYjIiIl

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

makecanonical:=proc(X::set,R::set(ordpair)) local x,rx,y,f; if not isequivalence(X,R) then return FAIL fi; for x in X do rx:={}; for y in X do if [x,y] in R then rx:=rx union {y} fi; od; f(x):=rx od; eval(f) end; f:=makecanonical({1,2,3},{[1,1],[1,2],[2,1],[2,2],[3,3]}); f(1);f(2);f(3);

Zio2JCdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJSR0YmLUYnNiNJKG9yZHBhaXJHRiY2JkkieEdGJkkjcnhHRiZJInlHRiZJImZHRiZGJkYmQyVAJDQtSS5pc2VxdWl2YWxlbmNlR0YmNiRGJUYqT0klRkFJTEdGKD8mRi9GJUkldHJ1ZUdGKEMlPkYwPCI/JkYxRiVGPEAkLUkjaW5HRig2JDckRi9GMUYqPkYwLUkmdW5pb25HRig2JEYwPCNGMT4tRjI2I0YvRjAtSSVldmFsR0YoNiNGMkYmRiZGJg==

Zio2IkYjNiNJKXJlbWVtYmVyR0YjRVxzJCIiIjwkRiciIiNGKUYoIiIkPCNGKi4tJSlwcm9jbmFtZUc2IyUlYXJnc0dGI0YjRiM=

PCQiIiIiIiM=

PCQiIiIiIiM=

PCMiIiQ=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

Az al\303\241bbi k\303\251t f\303\274ggv\303\251nyben R rendez\303\251s X-en, S pedig rendez\303\251s Y-on. isincreasing:=proc(f::procedure,X::set,R::set(ordpair),Y::set,S::set(ordpair)) local x,y; if not isarrowfromto(f,X,Y) then return FAIL fi; if not ispartialordering(X,R) or not ispartialordering(Y,S) then return FAIL fi; for x in X do for y in X do if [x,y] in R and not [f(x),f(y)] in S then return false fi; od; od; true end; X:={1,2,3}; XX:=bincartprod(X,X): R:=select(x->irem(x[2],x[1])=0,XX); Y:=X; S:=select(x->x[1]<=x[2],XX); f:=x->x; isincreasing(f,X,R,Y,S);isincreasing(f,Y,S,X,R);

Zio2JydJImZHNiJJKnByb2NlZHVyZUclKnByb3RlY3RlZEcnSSJYR0YmSSRzZXRHRignSSJSR0YmLUYrNiNJKG9yZHBhaXJHRiYnSSJZR0YmRisnSSJTR0YmRi42JEkieEdGJkkieUdGJkYmRiZDJkAkNC1JLmlzYXJyb3dmcm9tdG9HRiY2JUYlRipGMk9JJUZBSUxHRihAJDQzLUkyaXNwYXJ0aWFsb3JkZXJpbmdHRiY2JEYqRi0tRkQ2JEYyRjRGPj8mRjZGKkkldHJ1ZUdGKD8mRjdGKkZJQCQzLUkjaW5HRig2JDckRjZGN0YtNC1GTjYkNyQtRiU2I0Y2LUYlNiNGN0Y0T0kmZmFsc2VHRihGSUYmRiZGJg==

PCUiIiIiIiMiIiQ=

PCc3JCIiIiIiIzckRiRGJDckIiIkRig3JEYkRig3JEYlRiU=

PCUiIiIiIiMiIiQ=

PCg3JCIiIiIiIzckRiRGJDckIiIkRig3JEYkRig3JEYlRiU3JEYlRig=

Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlRiRGJUYlRiU=

SSV0cnVlRyUqcHJvdGVjdGVkRw==

SSZmYWxzZUclKnByb3RlY3RlZEc=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

issetfamily:=proc(Iset::set,f::procedure) local i; for i in Iset do if not type(f(i),set) then return false fi; od; true; end; f:='f'; f(1):={a,b};f(2):={b,c,d}; issetfamily({1,2},f); issetfamily({1,2,3},f);

Zio2JCdJJUlzZXRHNiJJJHNldEclKnByb3RlY3RlZEcnSSJmR0YmSSpwcm9jZWR1cmVHRig2I0kiaUdGJkYmRiZDJD8mRi1GJUkldHJ1ZUdGKEAkNC1JJXR5cGVHRig2JC1GKkYsRidPSSZmYWxzZUdGKEYwRiZGJkYm

SSJmRzYi

PCRJImJHNiJJImFHRiQ=

PCVJImJHNiJJImNHRiRJImRHRiQ=

SSV0cnVlRyUqcHJvdGVjdGVkRw==

SSZmYWxzZUclKnByb3RlY3RlZEc=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

`union`();

PCI=

`intersect`();

Error, invalid input: `intersect` expects 1 or more arguments, but received 0

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

s:=x,y; s[1]; s[2]; t:=y,x; evalb(s=t);

NiRJInhHNiJJInlHRiQ=

SSJ4RzYi

SSJ5RzYi

NiRJInlHNiJJInhHRiQ=

SSZmYWxzZUclKnByb3RlY3RlZEc=

descartesprod:=proc(L::list(set)) local x,y,i,S,SS; if nops(L)=0 then return {} fi; S:=map(x->[x],L[1]); for i from 2 to nops(L) do SS:={}; for x in S do for y in L[i] do SS:=SS union {[op(x),y]} od; od; S:=SS od; S; end; descartesprod([]); descartesprod([{1,2}]); descartesprod([{1,2},{a,b}]); descartesprod([{1,2},{}]); descartesprod([{1,2},{a},{x,y}]); descartesprod([{1,2},{a,b,c},{x,y}]);

Zio2IydJIkxHNiItSSVsaXN0RyUqcHJvdGVjdGVkRzYjSSRzZXRHRik2J0kieEdGJkkieUdGJkkiaUdGJkkiU0dGJkkjU1NHRiZGJkYmQyZAJC8tSSVub3BzR0YpNiNGJSIiIU88Ij5GMC1JJG1hcEdGKTYkZio2I0YtRiY2JEkpb3BlcmF0b3JHRiZJJmFycm93R0YmRiY3I0YtRiZGJkYmJkYlNiMiIiI/KEYvIiIjRkdGNUkldHJ1ZUdGKUMlPkYxRjo/JkYtRjBGSj8mRi4mRiU2I0YvRko+RjEtSSZ1bmlvbkdGKTYkRjE8IzckLUkjb3BHRilGQEYuPkYwRjFGMEYmRiZGJg==

PCI=

PCQ3IyIiIjcjIiIj

PCY3JCIiIkkiYkc2IjckRiRJImFHRiY3JCIiI0YlNyRGKkYo

PCI=

PCY3JSIiIkkiYUc2IkkieEdGJjclRiRGJUkieUdGJjclIiIjRiVGJzclRitGJUYp

PC43JSIiIkkiYUc2IkkieEdGJjclRiRGJUkieUdGJjclIiIjRiVGJzclRitGJUYpNyVGJEkiYkdGJkYnNyVGJEYuRik3JUYrRi5GJzclRitGLkYpNyVGJEkiY0dGJkYnNyVGJEYzRik3JUYrRjNGJzclRitGM0Yp

isselection:=proc(Iset::set,f::procedure,x::procedure) local i; if not issetfamily(Iset,f) then return FAIL fi; for i in Iset do if not x(i) in f(i) then return false fi; od; true end; Iset:={a,b,c}; f:='f'; f(a):={1,2};f(b):={1,3};f(c):={2,3}; x(a):=1;x(b):=3;x(c):=3; isselection(Iset,f,x); x(b):=2; isselection(Iset,f,x);

Zio2JSdJJUlzZXRHNiJJJHNldEclKnByb3RlY3RlZEcnSSJmR0YmSSpwcm9jZWR1cmVHRignSSJ4R0YmRis2I0kiaUdGJkYmRiZDJUAkNC1JLGlzc2V0ZmFtaWx5R0YmNiRGJUYqT0klRkFJTEdGKD8mRi9GJUkldHJ1ZUdGKEAkNC1JI2luR0YoNiQtRi1GLi1GKkYuT0kmZmFsc2VHRihGOUYmRiZGJg==

PCVJImJHNiJJImNHRiRJImFHRiQ=

SSJmRzYi

PCQiIiIiIiM=

PCQiIiIiIiQ=

PCQiIiMiIiQ=

IiIi

IiIk

IiIk

SSV0cnVlRyUqcHJvdGVjdGVkRw==

IiIj

SSZmYWxzZUclKnByb3RlY3RlZEc=

agent:={[D209,"Peti"],[KISZ1,"Fleto"],[Puf3,"Gyula"]}; event:={[KISZ1,"Balaton",19930706],[Puf3,"Nyugati",19561108],[KISZ1,"Motim",19961231],[D209,"Paks",20000103],[KISZ1,"Fittelina",19980320],[D209,"Gresham",20010908],[KISZ1,"Nomentana",19951122]}; descartesprod([agent,event]):select(x->x[1][1]=x[2][1],%):map(x->[x[1][2],x[2][2],x[2][3],x[2][1]],%):active:=select(x->x[3]>19891023,%);

PCU3JEklRDIwOUc2IlElUGV0aUYlNyRJJktJU1oxR0YlUSZGbGV0b0YlNyRJJVB1ZjNHRiVRJkd5dWxhRiU=

PCk3JUkmS0lTWjFHNiJRKEJhbGF0b25GJSIpMTIkKj43JUklUHVmM0dGJVEoTnl1Z2F0aUYlIikzNmM+NyVGJFEmTW90aW1GJSIpSjcnKj43JUklRDIwOUdGJVElUGFrc0YlIikuLCs/NyVGJFEqRml0dGVsaW5hRiUiKT8uKSo+NyVGMFEoR3Jlc2hhbUYlIikzNCw/NyVGJFEqTm9tZW50YW5hRiUiKUE2Jio+

PCg3JlElUGV0aTYiUSVQYWtzRiUiKS4sKz9JJUQyMDlHRiU3JkYkUShHcmVzaGFtRiUiKTM0LD9GKDcmUSZGbGV0b0YlUShCYWxhdG9uRiUiKTEyJCo+SSZLSVNaMUdGJTcmRi1RJk1vdGltRiUiKUo3Jyo+RjA3JkYtUSpGaXR0ZWxpbmFGJSIpPy4pKj5GMDcmRi1RKk5vbWVudGFuYUYlIilBNiYqPkYw

isselection:=proc(Iset::set,f::procedure,x::procedure) local i; if not issetfamily(Iset,f) then return FAIL fi; for i in Iset do if not x(i) in f(i) then return false fi; od; true end; Iset:={a,b,c}; f:='f'; f(a):={1,2};f(b):={1,3};f(c):={2,3}; x(a):=1;x(b):=3;x(c):=3; isselection(Iset,f,x); x(b):=2; isselection(Iset,f,x);

Zio2JSdJJUlzZXRHNiJJJHNldEclKnByb3RlY3RlZEcnSSJmR0YmSSpwcm9jZWR1cmVHRignSSJ4R0YmRis2I0kiaUdGJkYmRiZDJUAkNC1JLGlzc2V0ZmFtaWx5R0YmNiRGJUYqT0klRkFJTEdGKD8mRi9GJUkldHJ1ZUdGKEAkNC1JI2luR0YoNiQtRi1GLi1GKkYuT0kmZmFsc2VHRihGOUYmRiZGJg==

PCVJImJHNiJJImNHRiRJImFHRiQ=

SSJmRzYi

PCQiIiIiIiM=

PCQiIiIiIiQ=

PCQiIiMiIiQ=

IiIi

IiIk

IiIk

SSV0cnVlRyUqcHJvdGVjdGVkRw==

IiIj

SSZmYWxzZUclKnByb3RlY3RlZEc=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

isbinop:=proc(X::set,f::procedure) local x,y; for x in X do for y in X do if not f(x,y) in X then return false fi; od; od; true end; f:='f'; f(0,0):=0;f(0,1):=1;f(1,0):=1;f(1,1):=0; isbinop({0,1},f); isbinop({0,1,2},f);

Zio2JCdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJmR0YmSSpwcm9jZWR1cmVHRig2JEkieEdGJkkieUdGJkYmRiZDJD8mRi1GJUkldHJ1ZUdGKD8mRi5GJUYxQCQ0LUkjaW5HRig2JC1GKkYsRiVPSSZmYWxzZUdGKEYxRiZGJkYm

SSJmRzYi

IiIh

IiIi

IiIi

IiIh

SSV0cnVlRyUqcHJvdGVjdGVkRw==

SSZmYWxzZUclKnByb3RlY3RlZEc=

&+(0,0):=0;&+(0,1):=1;&+(1,0):=1;&+(1,1):=0; 0&+1;1&+1;&+(0,1); isbinop({0,1},(x,y)->x &+ y);

IiIh

IiIi

IiIi

IiIh

IiIi

IiIh

IiIi

SSV0cnVlRyUqcHJvdGVjdGVkRw==

isunop:=proc(X::set,f::procedure) local x; for x in X do if not f(x) in X then return false fi; od; true end; f:='f'; f(0):=1;f(1):=0; isunop({0,1},f); isunop({0,1,2},f);

Zio2JCdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJmR0YmSSpwcm9jZWR1cmVHRig2I0kieEdGJkYmRiZDJD8mRi1GJUkldHJ1ZUdGKEAkNC1JI2luR0YoNiQtRipGLEYlT0kmZmFsc2VHRihGMEYmRiZGJg==

SSJmRzYi

IiIi

IiIh

SSV0cnVlRyUqcHJvdGVjdGVkRw==

SSZmYWxzZUclKnByb3RlY3RlZEc=

&inc(0):=1;&inc(1):=0; &inc 0; &inc 1; isunop({0,1},x->&inc x);

IiIi

IiIh

IiIi

IiIh

SSV0cnVlRyUqcHJvdGVjdGVkRw==

9();9(x);9(x,y);

IiIq

IiIq

IiIq

isnullop:=proc(X::set,f::procedure) evalb(f() in X) end; f:='f'; f():=1; eval(f); isnullop({0,1},f); isnullop({0,2},f);

Zio2JCdJIlhHNiJJJHNldEclKnByb3RlY3RlZEcnSSJmR0YmSSpwcm9jZWR1cmVHRihGJkYmRiYtSSZldmFsYkdGKDYjLUkjaW5HRig2JC1GKkYmRiVGJkYmRiY=

SSJmRzYi

IiIi

Zio2IkYjNiNJKXJlbWVtYmVyR0YjRVxzIkYjIiIiLi0lKXByb2NuYW1lRzYjJSVhcmdzR0YjRiNGIw==

SSV0cnVlRyUqcHJvdGVjdGVkRw==

SSZmYWxzZUclKnByb3RlY3RlZEc=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

X:={1,2,3}; P:=combinat[powerset](X); isbinop(P,(x,y)->x union y);

PCUiIiIiIiMiIiQ=

PCo8IjwjIiIiPCMiIiM8JEYlRic8IyIiJDwkRiVGKjwlRiVGJ0YqPCRGJ0Yq

SSV0cnVlRyUqcHJvdGVjdGVkRw==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

true and true; true and false; false and true; false and false; T:=table(); T[true,true]:=true;T[true,false]:=false; T[false,true]:=true;T[false,false]:=false; print(T);

SSV0cnVlRyUqcHJvdGVjdGVkRw==

SSZmYWxzZUclKnByb3RlY3RlZEc=

SSZmYWxzZUclKnByb3RlY3RlZEc=

SSZmYWxzZUclKnByb3RlY3RlZEc=

PTYiSSZmYWxzZUclKnByb3RlY3RlZEdFXFtsIQ==

SSV0cnVlRyUqcHJvdGVjdGVkRw==

SSZmYWxzZUclKnByb3RlY3RlZEc=

SSV0cnVlRyUqcHJvdGVjdGVkRw==

SSZmYWxzZUclKnByb3RlY3RlZEc=

LUkmVEFCTEVHJSpwcm90ZWN0ZWRHNiM3Ji82JEkmZmFsc2VHRiRGKUYpLzYkSSV0cnVlR0YkRilGKS82JEYsRixGLC82JEYpRixGLA==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

f:=x->x^2; g:=x->x^3; (f*g)(2); (f*g)(3); (f/g)(2); (f/g)(0); (g/f)(0);

Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiQpRiQiIiMiIiJGJUYlRiU=

Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiQpRiQiIiQiIiJGJUYlRiU=

IiNL

IiRWIw==

IyIiIiIiIw==

Error, numeric exception: division by zero

Error, numeric exception: division by zero

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

f:=[true,true,false,false]; g:=[true,false,true,false]; zip((x,y)->x and y,f,g);

NyZJJXRydWVHJSpwcm90ZWN0ZWRHRiNJJmZhbHNlR0YkRiU=

NyZJJXRydWVHJSpwcm90ZWN0ZWRHSSZmYWxzZUdGJEYjRiU=

NyZJJXRydWVHJSpwcm90ZWN0ZWRHSSZmYWxzZUdGJEYlRiU=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

ishom:=proc(phi::procedure,X::set,f::procedure,Y::set,g::procedure) local x,y; if not isarrowfromto(phi,X,Y) then return FAIL fi; if not isbinop(X,f) then return FAIL fi; if not isbinop(Y,g) then return FAIL fi; for x in X do for y in X do if phi(f(x,y))<>g(phi(x),phi(y)) then return false fi; od; od; true end; X:={true,false}; Y:=X; ishom(x->x,X,(x,y)->x and y,Y,(x,y)->x or y); ishom(x-> not x,X,(x,y)->x and y,Y,(x,y)->x or y);

Zio2JydJJHBoaUc2IkkqcHJvY2VkdXJlRyUqcHJvdGVjdGVkRydJIlhHRiZJJHNldEdGKCdJImZHRiZGJydJIllHRiZGKydJImdHRiZGJzYkSSJ4R0YmSSJ5R0YmRiZGJkMnQCQ0LUkuaXNhcnJvd2Zyb210b0dGJjYlRiVGKkYvT0klRkFJTEdGKEAkNC1JKGlzYmlub3BHRiY2JEYqRi1GO0AkNC1GQDYkRi9GMUY7PyZGM0YqSSV0cnVlR0YoPyZGNEYqRkdAJDAtRiU2Iy1GLUYyLUYxNiQtRiU2I0YzLUYlNiNGNE9JJmZhbHNlR0YoRkdGJkYmRiY=

PCRJJmZhbHNlRyUqcHJvdGVjdGVkR0kldHJ1ZUdGJA==

PCRJJmZhbHNlRyUqcHJvdGVjdGVkR0kldHJ1ZUdGJA==

SSZmYWxzZUclKnByb3RlY3RlZEc=

SSV0cnVlRyUqcHJvdGVjdGVkRw==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

a:='a'; a^(x+y); expand(%);

SSJhRzYi

KUkiYUc2IiwmSSJ4R0YkIiIiSSJ5R0YkRic=

KiYpSSJhRzYiSSJ4R0YlIiIiKUYkSSJ5R0YlRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn