Targeting a specific occurence in a string and replacing it - replace

Question

I have a string with multiple / in it and I am trying to convert this string in to LaTeX code. Basically (a)/(b) becomes \\dfrac{a}{b}.
The difficulty is that (a) and/or (b) could contain other /.
To respect the parentheses balancing, I would like to replace the / from left to right, and replacing them accordingly to what it around. I made a try but I don't know how target a specific / and replace. using position and length parameters seems to be very complicated.
function ToFrac (s)
while s:find ("/") ~= nil
do
-- Replace : \dfrac{}{}/() -> \dfrac{\dfrac...}{}
if ( s:find ( '\\dfrac%b{}%b{}/%b()' , j ) ~= nil )
then
x,y,num,den = s:find( '(\\dfrac%b{}%b{})/(%b())' )
den = den:gsub( '.(.+).' , '%1' )
s = s:gsub( '(\\dfrac%b{}%b{})/(%b())',
"\\dfrac{"..num.."}{"..den.."}" , 1 )
end
print ('### -- ', s)
-- Replace : ()/\dfrac{}{} -> \dfrac[}]{\dfrac...}
if ( s:find ( '(%b()/\\dfrac%b{}%b{}' ) ~= nil )
then
x,y,num,den = s:find( '((%b())/(\\dfrac%b{}%b{})' )
num = num:gsub( '.(.+).' , '%1' )
s = s:gsub( '((%b())/()\\dfrac%b{}%b{})',
"\\dfrac{"..num.."}{"..den.."}" , 1 )
end
print ('### -- ', s)
-- Replace : ()/() -> \dfrac{}{}
if ( s:find ( '%b()/%b()' , 1 ) ~= nil )
then
x,y,num,den = s:find( '(%b())/(%b())' )
num = num:gsub( '.(.+).' , '%1' )
den = den:gsub( '.(.+).' , '%1' )
s = s:gsub( '(%b())/(%b())',
"\\dfrac{"..num.."}{"..den.."}" , 1 )
Done = true
end
print ('### -- ', s)
end -- while
return (s)
end
s = "((a)/(b))/(c)"
print (s, ToFrac(s))
s = "(a)/((b)/(c))"
print (s, ToFrac(s))
s = "(a)/(b)/(c)/(d))"
print (s, ToFrac(s))
s = "((a)/(b))/((c)/(d))"
print (s, ToFrac(s))

Answer 1

Amended version of rpattiso's idea:
function to_frac(expr)
local t
return expr == '' and '' or (expr..'()'):gsub('(.-)(%b())',
function(prefix, subexpr)
local replace_with = ''
if not prefix:find'^%s*/%s*$' then
t, replace_with = {}, (not t and ''
or t[2] and '\\dfrac{'..t[1]..'}{'..t[2]..'}'
or '('..t[1]..')')..prefix
elseif t[2] then
t = {'\\dfrac{'..t[1]..'}{'..t[2]..'}'}
end
table.insert(t, to_frac(subexpr:sub(2,-2)))
return replace_with
end
)
end
print(to_frac' (a )/((b) / (c))') --> \dfrac{a }{\dfrac{b}{c}}
print(to_frac'((a)/((b)/(c)))/(e)') --> \dfrac{\dfrac{a}{\dfrac{b}{c}}}{e}
print(to_frac'(a)/(b)/(c)/(d)') --> \dfrac{\dfrac{\dfrac{a}{b}}{c}}{d}

Answer 2

The 'replace' argument of string.gsub can be a function.
Using that function, you can apply the substitution recursively to the numerator and denominator and build the result that way. string.sub can be used to remove the parentheses from the numerator and denominator.
function to_frac(expr)
return (expr:gsub('%s*(%b())%s*/%s*(%b())%s*',
function(num, denom)
return '\\dfrac{'..to_frac(num:sub(2,-2))..'}{'
..to_frac(denom:sub(2,-2))..'}'
end))
end
expr = ' (a )/((b) / (c))' -- \dfrac{a }{\dfrac{b}{c}}
print(to_frac(expr))
expr = '((a)/((b)/(c)))/(e)' -->\dfrac{\dfrac{a}{\dfrac{b}{c}}}{e}
print(to_frac(expr))
If you want to go beyond using parentheses for delimiting arguments and obey precedence rules, then look into LPeg.