restart;

#==================================================================

#  Author: Dmitry K Demskoi
#  Email: ddemskoy@csu.edu.au
#  The following procedure produces a LaTex code which illustrates the process of dividing A by B using long division.
#  Usage: LongDivision(A,B);
#  Here A and B are positive integers and A>B. For example the following command LongDivision(1460912312,273)
#  should produce the following output
#==================================================================

$${\setlength\tabcolsep{0.5mm}
\begin{tabular}{ccccccccccccccc}
&&&&&&&5 & 3 & 5 & 1 & 3 & 2 & 7\\\cline{4-14}
2 & 7 & 3&$)$&1 & 4 & 6 & 0 & 9 & 1 & 2 & 3 & 1 & 2\\
&&&\textbf{--}&1 & 3 & 6 & 5\\\cline{5-8}
&&&&&&9 & 5 & 9\\
&&&&&\textbf{--}&8 & 1 & 9\\\cline{7-9}
&&&&&&1 & 4 & 0 & 1\\
&&&&&\textbf{--}&1 & 3 & 6 & 5\\\cline{7-10}
&&&&&&&&3 & 6 & 2\\
&&&&&&&\textbf{--}&2 & 7 & 3\\\cline{9-11}
&&&&&&&&&8 & 9 & 3\\
&&&&&&&&\textbf{--}&8 & 1 & 9\\\cline{10-12}
&&&&&&&&&&7 & 4 & 1\\
&&&&&&&&&\textbf{--}&5 & 4 & 6\\\cline{11-13}
&&&&&&&&&&1 & 9 & 5 & 2\\
&&&&&&&&&\textbf{--}&1 & 9 & 1 & 1\\\cline{11-14}
&&&&&&&&&&&&4 & 1\\
\end{tabular}}$$

#==================================================================
# This code when compiled in LaTex will look somthing like

#==================================================================

LongDivision:=proc(a,b)
local i,l,la,lb,dvdn,dvdns,dvsr,dvsrs,s,shft,ashft,basespace,crct,crct2,flag,Is,substrng,BreakNumber,NumberToArrayString,unionlists;
Is:=proc(a,b,c) if a then RETURN(b) else RETURN(c);fi; end;
substrng:=proc() parse(substring(convert(args[1],string),args[2]));end;
BreakNumber := proc (a) local i, b; if a=0 then RETURN([0]);fi;b := []; for i to length(a) do b := unionlists(b,substrng(a,i .. i)) end do end;
NumberToArrayString := proc (a) local i, b, s; s := ""; b := BreakNumber(a); for i to nops(b)-1 do s := cat(s,b[i]," & ") end do; RETURN(cat(s,b[nops(b)])) end proc;
unionlists := proc () RETURN([seq(op(args[i]),i = 1 .. nargs)]) end proc;
if a<=0 or b<=0 or a<b then ERROR(`Invalid argument!`);fi;
la:=length(a);
lb:=length(b);
l:=la+lb;
dvdn:=substrng(a,1..1);
#dvsrs:=[];
if dvdn>b then
   flag:=true;dvdns:=[dvdn];dvsrs:=[floor(dvdn/b)];
   else dvdns:=[];dvsrs:=[];flag:=false;
fi;
for i from 2 to la+1 do
 if dvdn<b then
    dvdn:=parse(cat(dvdn,substrng(a,i..i)));
    dvsr:=0;
    else dvsr:=floor(dvdn/b);
         dvdn:=parse(cat(dvdn-dvsr*b,substrng(a,i..i)));
 fi;
 dvdns:=unionlists(dvdns,dvdn);
 dvsrs:=unionlists(dvsrs,dvsr);
od;
dvsrs:=unionlists(dvsrs,0);
while dvsrs[2]=0 do
      dvsrs:=[0,seq(dvsrs[i],i=3..nops(dvsrs))];
      dvdns:=dvdns[2..nops(dvdns)];
od;
s:=cat("{\\setlength\\tabcolsep{0.5mm}
\\begin{tabular}{",seq("c",i=1..l+2),"}\n");
s:=cat(s,seq("&",i=1..la+lb-nops(dvsrs)+3),NumberToArrayString(parse(cat(op(dvsrs[Is(flag,2,1)..nops(dvsrs)-1])))),"\\\\\\cline{",lb+1,"-",l+1,"}\n");
s:=cat(s,NumberToArrayString(b),"&$)$&",NumberToArrayString(a),"\\\\\n");
basespace:=lb+1+length(dvdns[1])-length(b*dvsrs[2]);
s:=cat(s,seq("&",i=1..basespace-1),"\\textbf{--}&",NumberToArrayString(b*dvsrs[2]),"\\\\\\cline{",basespace+1,"-",basespace+length(dvdns[1]),"}\n");
ashft:=lb+1;
crct:=0;crct2:=0;
for i from 2 to nops(dvdns) do
   if dvdns[i-1]-b*dvsrs[i]=0 then crct:=1;
      else crct:=0;
   fi;
   shft:=length(dvdns[i-1])-length(dvdns[i-1]-b*dvsrs[i]);
   ashft:=ashft+shft;
   s:=cat(s,seq("&",j=1..ashft-crct),Is(crct=0,"","0 &"),Is(i=nops(dvdns) and dvdns[i]=0,"",NumberToArrayString(dvdns[i])),"\\\\\n");
   if i<nops(dvdns) then
      if dvsrs[i+1]=0 then crct2:=1;
        else crct2:=0;
      fi;    s:=cat(s,seq("&",j=1..ashft-crct2-1+length(dvdns[i])-length(b*dvsrs[i+1])),"\\textbf{--}&",NumberToArrayString(b*dvsrs[i+1]),"\\\\\\cline{",ashft+1,"-",min(ashft+length(dvdns[i]),l+1),"}\n");
   fi;
od;
RETURN(printf("$$%s$$",cat(s,"\\end{tabular}}")));
end;

#==================================================================

# Example

LongDivision(1460912312,273);

$${\setlength\tabcolsep{0.5mm}
\begin{tabular}{ccccccccccccccc}
&&&&&&&5 & 3 & 5 & 1 & 3 & 2 & 7\\\cline{4-14}
2 & 7 & 3&$)$&1 & 4 & 6 & 0 & 9 & 1 & 2 & 3 & 1 & 2\\
&&&\textbf{--}&1 & 3 & 6 & 5\\\cline{5-8}
&&&&&&9 & 5 & 9\\
&&&&&\textbf{--}&8 & 1 & 9\\\cline{7-9}
&&&&&&1 & 4 & 0 & 1\\
&&&&&\textbf{--}&1 & 3 & 6 & 5\\\cline{7-10}
&&&&&&&&3 & 6 & 2\\
&&&&&&&\textbf{--}&2 & 7 & 3\\\cline{9-11}
&&&&&&&&&8 & 9 & 3\\
&&&&&&&&\textbf{--}&8 & 1 & 9\\\cline{10-12}
&&&&&&&&&&7 & 4 & 1\\
&&&&&&&&&\textbf{--}&5 & 4 & 6\\\cline{11-13}
&&&&&&&&&&1 & 9 & 5 & 2\\
&&&&&&&&&\textbf{--}&1 & 9 & 1 & 1\\\cline{11-14}
&&&&&&&&&&&&4 & 1\\
\end{tabular}}$$