[Python] Splitting a mathematical string into a list while keeping everything in matching...

Problem


I am trying to get any mathematical string to split into a list by operators (i.e. "+", "-", "/", "*"), while keeping anything in a matching number of brackets together as one list element.

Examples and desired outputs


Here are some very random examples and the desired outputs of what I want to achieve:

import math

equation = "5+5*10"
equation_segmented = ["5", "+", "5", "*", "10"]

equation = "(2*2)-5*(math.sqrt(9)+2)"
equation_segmented = ["(2*2)", "-", "5", "*", "(math.sqrt(9)+2)"]

equation = "(((5-3)/2)*0.5)+((2*2))*(((math.log(5)+2)-2))"
equation_segmented = ["(((5-3)/2)*0.5)", "+", "((2*2))", "*", "(((math.log(5)+2)-2))"]


Note: alphabetical letters (or symbols like "π") should be included in the brackets too

Finding a solution


My first thought was using a regex :

import re

equation_segmented = re.split("([\+|\-|\*|\/]|\(.*\))", equation)


The problem here, however, is that it does not account for matching brackets.

I then thought of iterating through the string manually and keeping track of the parentheses with a counter, but did not get it to work (I was pretty much only able to write my own 're.split'-function).

Lastly I went back to regex (equation_segmented = re.split("([\+|\-|\*|\/])", equation)) and thought about just splitting the string by operators, to then "".join() all the list elements in matching brackets afterwards - yet again to no avail.

I am not sure if this might be a problem for a parser, but I do not have any experience with that at all, so I am not sure where to start.

Help would be much appreciated - thank you!

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