OpenEuphoria

Re: simplify math expression

• Posted by David Cuny <dcuny at LANSET.COM> Jun 11, 2002
• 512 views

tone skoda wrote:

> b+(c+(a+d))   --> a+b+c+d
> c+((d+b)+a)   --> a+b+c+d
> (b*a)/c           --> a*b/c
> a/(b/c)            --> a*c/b
> b*(c+a)          --> a*b+a*c

This looks a lot like a Prolog sort of problem. Assuming you represented the 
data in a sequence, such as:

   a --> 'a'
   a+b --> {'a', '+', 'b'}
   b+(c+(a+d)) --> { 'b', '+', { 'c', '+', { 'a', '+', 'd' } } }

you should be able to write a 'simplify' routine to do the work for you. 
Something like this:

   function simp( object o )
      object a, b, tmp
      atom op
      sequence s

      -- a --> a
      if atom( o ) then
         return o

      else
         a = simp(o[1])
         op = o[2]
         b = simp(o[3])

         -- b + a --> a + b
         -- b * a --> a * b
         if atom(a) and (op = '+' or op = '*') and atom(b) and a > b then
               return { b, op, a }

         -- ( (...) + a ) --> (a + (...) )
         -- ( (...) * a ) --> (a * (...) )
         elsif sequence(a) and (op = '+' or op = '*') and atom(b) then
            return simp( { b, op, a } )

         -- ( a + ( b + c ) ) --> (a + ( b + c ) )
         -- ( a * ( b * c ) ) --> (a * ( b * c ) )
         elsif atom(a) and (op = '+' or op = '*') and sequence(b) 
            and atom(b[1]) and b[2] = op and atom(b[3]) then
            s = sort( { a, b[1], b[3] } )
            return { s[1], op, { s[2], op, s[3] } }

         -- a * ( b op c ) --> ( a * b ) op ( a * c )
         elsif atom(a) and op = '*' and sequence(b) then
            tmp = { { a, '*',  b[1] }, b[2], { a, '*', b[3] } }
            return simp( tmp )

         else
             return { a, op, b }

         end if

   end function

This is entirely untested (and incomplete), but captures the general idea.

-- David Cuny