Find and replace for equations (regex?)

Question

I'm converting some excel formulas to another system and need to do some fairly nifty search and replace magic. I presume Regex are the tools for the job in this case, but if anyone has any other ideas I'd like to hear them.

I'm working on getting these formulas into something resembling SQL syntax. I also have to deal with algebraic symbols so I might have the following:

9^2 will need to become POWER(9,2). (A + 3)^3 will need to become POWER((A+3),3).

Whats the best approach for this?

I'm using C# 3.5 if that makes a difference.

edit: An example of something I have to parse (the power symbol is near the end):

"((({VAL(9286)} / 1000) * {VAL(4648)}) + (({VAL(9609)} / 1000) + ({VAL(6480)} / 1000)) * {VAL(8574)}) / ({VAL(9286)} / 1000 + {VAL(9609)} / 1000 + {VAL(6480)} / 1000) * (({VAL(9286)} / 22.4)*34.38 + {VAL(9609)} + {VAL(6480)}) * ((1.075068 + 0.001*11.17019 * ((({VAL(9286)} / 1000) * {VAL(4648)}) + (({VAL(9609)} / 1000) + ({VAL(6480)} / 1000)) * {VAL(8574)}) / ({VAL(9286)} / 1000 + {VAL(9609)} / 1000 + {VAL(6480)} / 1000)+273.15)) + (100000*0.90755 / ((({VAL(9286)} / 1000) * {VAL(4648)}) + (({VAL(9609)} / 1000) + ({VAL(6480)} / 1000)) * {VAL(8574)}) / ({VAL(9286)} / 1000 + {VAL(9609)} / 1000 + {VAL(6480)} / 1000) + 273.15)^2))*4.1868/32)"

Answer 1

Because of the possibility of nested parenthesis, regex is not a suitable tool for this task. It's better to use a mathematical expression parser.

But it's not impossible. For example, by repeatedly replacing the pattern

((?=[\w.(])[\w.]*\s*(?:\((?>[^()]+|\((?<O1>)|\)(?<-O1>))*(?(O1)(?!))\))?)\s*\^\s*((?=[\w.(])[\w.]*\s*(?:\((?>[^()]+|\((?<O2>)|\)(?<-O2>))*(?(O2)(?!))\))?)

with

"POWER($1,$2)"

until the string does not change, it should be able to turn all a^b into POWER(a,b). Example:

   (a+3)^(b+5^(c+3)) + 9 ^ 2 + (A + 3)^3 + (5^7)^(6^(8^9-1)-3)
-> POWER((a+3),(b+5^(c+3))) + POWER(9 ,2 )+ POWER((A + 3),3 )+ POWER((5^7),(6^(8^9-1)-3))
-> POWER((a+3),(b+POWER(5,(c+3)))) + POWER(9 ,2 )+ POWER((A + 3),3 )+ POWER((POWER(5,7)),(POWER(6,(8^9-1))-3))
-> POWER((a+3),(b+POWER(5,(c+3)))) + POWER(9 ,2 )+ POWER((A + 3),3 )+ POWER((POWER(5,7)),(POWER(6,(POWER(8,9)-1))-3))
-> done

Note that this regex will assume ^ is left-associative instead of right-associative.

   1^2^3
-> POWER(1,2)^3
-> POWER(POWER(1,2),3)
-> done

although 1^2^3 itself isn't well-formed.