Krdytkyu

The code below defines a macro, Summation, that accepts a comma separated list of integers such as

  Summation{12345, 6543}

  Summation{521725, 256814}

  Summation{523057, 6743}

  Summation{57208,6207}

  Summation[b]{57208,6207,12095}

The macro then adds the integers in a table, as in the OP. The commands above give the output:

There is an optional first argument that becomes the positioning optional argument in the tabular environment (by default, t is used). I haven't really checked, but it is likely ro break with large integers.

All of the integers are printed using the num command from the siunitx package, so their formatting can be customised using siunitx. for example, by adding

sisetup{group-separator={,},group-four-digits}

the numbers will have a comma separating the thousands, millions, ... etc. so that the output becomes

The code is an exercise in using LaTeX3:

documentclass{article}

usepackage{xparse}

usepackage{siunitx}



ExplSyntaxOn

clist_new:N l_int_clist

int_new:N g_total_int

tl_new:N g_summation_tl

NewDocumentCommandSummation {O{t} m}{

  clist_set:Nn l_int_clist {#2}

  int_zero:N g_total_int

  tl_clear:N g_summation_tl

  clist_map_inline:Nn l_int_clist {

    int_gadd:Nn g_total_int {##1}

    tl_gput_right:No g_summation_tl {& num{##1}\}

   }

   begin{tabular}[#1]{r@{space}r}

     + tl_use:N g_summation_tl cline{2-2}

     &num{int_use:N g_total_int}

  end{tabular}

}

ExplSyntaxOff



begin{document}



  Summation{12345, 6543}

  Summation{521725, 256814}

  Summation{523057, 6743}

  Summation{57208,6207}

  Summation[b]{57208,6207,12095}



end{document}

As noted in Latex3 inline mapping produces extra row in tabular, it is necessary to construct the table as a token list because otherwise hrule will complain.

A no-package approach for three term or higher sums as well.

documentclass{article}



newcommand{showsum}[2][c]{%

  $edeforiginalplusmathcode{themathcode`+}%

   begingrouplccode`~=`+ lowercase{endgroupdef~}{\&}%

   mathcode`+ "8000

  begin{array}[#1]{@{}r@{;}r@{}}

   mathcharoriginalplusmathcode& #2 \

  hline

  & thenumexpr#2relax

  end{array}%

  $%

 }



begin{document}



Xquad % to show the baseline

showsum{12345 + 6543}quad

showsum{521725 + 256814}quad

showsum{523057 + 6743}quad

showsum[t]{57208+6207}quad

showsum[b]{57208+6207+12095}quad

X



end{document}

The X are here to indicate baseline. (plagiarized from @egreg)

Variant display:

documentclass{article}



newcommand{showsum}[2][c]{%

  $edeforiginalplusmathcode{themathcode`+}%

   begingrouplccode`~=`+ lowercase{endgroupdef~}{\mathcharoriginalplusmathcode&}%

   mathcode`+ "8000

  begin{array}[#1]{@{}r@{;}r@{}}

   & #2 \

  hline

  =& thenumexpr#2relax

  end{array}%

  $%

 }



begin{document}



Xquad % to show the baseline

showsum{12345 + 6543}quad

showsum{521725 + 256814}quad

showsum{523057 + 6743}quad

showsum[t]{57208+6207+77777}quad

showsum[b]{57208+6207+12095+33333}quad

X



end{document}

We can also sum negative integers:

documentclass{article}



newcommand{showsum}[2][c]{%

  $edeforiginalplusmathcode{themathcode`+}%

   begingrouplccode`~=`+ lowercase{endgroupdef~}{\mathcharoriginalplusmathcode&}%

   edeforiginalminusmathcode{themathcode`-}%

   begingrouplccode`~=`- lowercase{endgroupdef~}{\mathcharoriginalminusmathcode&}%

   mathcode`+ "8000

   mathcode`- "8000

  begin{array}[#1]{@{}r@{;}r@{}}

   & #2 \

  hline

  =& thenumexpr#2relax

  end{array}%

  $%

 }



begin{document}



Xquad % to show the baseline

showsum{12345 - 6543}quad

showsum{521725 + 256814}quad

showsum{523057 - 6743}quad

showsum[t]{57208-6207+77777}quad

showsum[b]{57208-6207+12095-33333}quad

X



end{document}

(there was a missing % after the final $ in all three showsum, fixed now but images not updated)

Here's a LuaLaTeX-based solution. The macro mysum takes two mandatory arguments -- the numbers to be summed -- and one optional argument, which determines how the array environment should be placed vertically relative to the math baseline: centered (the default), top-aligned, or bottom-aligned. (If an optional argument is set, it must be listed first and enclosed in square brackets, per the usual LaTeX macro syntax rules.)

documentclass{article}

usepackage{booktabs} % for "midrule" macro

newcommand{mysum}[3][c]{%

   begin{array}[#1]{@{}r@{}}

      #2 \ {+}: #3 \ midrule directlua{tex.sprint(#2+#3)}

   end{array}}

usepackage{newtxtext,newtxmath} % optional (Times Roman text and math fonts)

begin{document}

[

mysum{12345}{6543}       qquad

mysum{511725}{256814}    qquad

mysum[b]{523057}{6743}   qquad

mysum[t]{57208}{6207}

]

end{document}

Addendum to allow an arbitrary number of summands. The preceding code dealt with the case outlined in the original query, which involved exactly two terms in the summation. The following solution, which is still LuaLaTeX-based, works as follows:

• The LaTeX macro mysum takes one optional argument (the position indicator, see above) and one mandatory argument: a string of comma-separated numbers. Whitespace is allowed inside the string. Thus, mysum{12345,6543}, mysum{12345, 6543}, mysum{ 12345 , 6543 }, and mysum{12345,6543 }, are all equally valid -- and produce the same output, viz, the number 18888.




• The mysum macro sets up an array environment, calls the Lua function perform_summation to perform most of the actual work, and terminates the array.



• 
  

  The perform_summation function begins by splitting the comma-delimited string of numbers into a Lua table, using , as the separator. (The auxiliary function that performs the splitting was obtained from stackoverflow.) perform_summation then iterates over the table entries to (a) compute the sum of the entries and (b) print out each entry on a separate row. Finally, it prints the value of the sum of the entries.

  
  
  

  It is entirely valid, from a syntactic point of view, to execute mysum with just one entry, e.g., mysum{10}.

  
  

In the following screenshot, the 3 - symbols at the left-hand and right-hand edged serve to indicate the location of the math axis.

documentclass{article}

usepackage{newtxtext,newtxmath} % optional: Times Roman text and math fonts

usepackage{booktabs} % for "midrule" macro

usepackage{luacode}  % for "luacode" environment



%% Lua-side code:

begin{luacode}

-- Obtained from https://stackoverflow.com/a/19263313

function string:split( inSplitPattern, outResults )

  if not outResults then

    outResults = { }

  end

  local theStart = 1

  local theSplitStart, theSplitEnd = string.find( self, inSplitPattern, theStart )

  while theSplitStart do

    table.insert( outResults, string.sub( self, theStart, theSplitStart-1 ) )

    theStart = theSplitEnd + 1

    theSplitStart, theSplitEnd = string.find( self, inSplitPattern, theStart )

  end

  table.insert( outResults, string.sub( self, theStart ) )

  return outResults

end



function perform_summation ( s )

  t = s:split(",")

  sum = 0 -- initialize "sum" variable

  tex.sprint ( "+\:" ) -- print the "+" symbol

  for i=1,#t do

    sum = sum+t[i]

    tex.sprint ( t[i] .. "\\" )

  end

  tex.sprint ( "\midrule" .. sum )

end

end{luacode}



%% LaTeX-side code:

newcommand{mysum}[2][c]{%

   begin{array}[#1]{@{}r@{}}

      directlua{perform_summation("#2")}

   end{array}}



begin{document}

[

---quad  % indicate math axis

mysum{12345,6543}       qquad

mysum{1234567891234,9876543219877} qquad

mysum{1,2,3,4} qquad

mysum[t]{ 57208 , 6207 , 12095 } qquad

mysum[b]{12345,67890}

quad---{}   % indicate math axis

]

end{document}

Let TeX do the calculations

documentclass{article}

usepackage{xparse}



ExplSyntaxOn

NewDocumentCommand{showsum}{O{c}m}

 {

  ensuremath

   {

    simeon_showsum:nn { #1 } { #2 }

   }

 }



seq_new:N l__simeon_showsum_seq



cs_new_protected:Nn simeon_showsum:nn

 {

  seq_set_split:Nnn l__simeon_showsum_seq { + } { #2 }

  begin{array}[#1]{@{}r@{;}r@{}}

  + & seq_use:Nn l__simeon_showsum_seq { \ & } \

  hline

  & int_eval:n { #2 }

  end{array}

 }

ExplSyntaxOff



begin{document}



Xquad % to show the baseline

showsum{12345 + 6543}quad

showsum{521725 + 256814}quad

showsum{523057 + 6743}quad

showsum[t]{57208+6207}quad

showsum[b]{57208+6207+12095}quad

X



end{document}