separate terms of a polynomial

We can create a function to separate the terms of a polynomial.
The idea is to go through the polynomial and read all the characters one by one (sequentially).
And what the function does is depends on which character we are reading at the moment.

We need three key variables:

1. currentTerm ( a string )

When we pass through polynomial, we store each character in CurrentTerm until an integer term is formed and store it in the variable terminos. And then, we reset CurrentTerm to save new characters and to find another whole term.

2. terms ( a list of string )

This is the result of the function, saving all the terms in the polynomial. The content is like this:['3x^2','+x(2-4)','-1']

3. numberParenthesis ( an integer )

This variable checks if we are inside a pair of parentheses. It works like this: if a is found (, the value is added by 1. And if it is found ), the value is subtracted by 1. So, if parenthesisNumber is equal to 0, it means that we are not inside a pair of parentheses and vice versa.

It is useful when we find operators ( +or -). If we are out of parentheses, we create a new term. Otherwise, we do not create a new term.

The code:

def separarTerminos(polinomio:str) -> []:

    # quitar los space
    polinomio = polinomio.replace(' ','')

    terminoActual = ''
    terminos = []
    numeroParentesis = 0

    # Por cada caracter en polinomio
    for i in range(len(polinomio)):
        caracterActual = polinomio[i]

        # El primero caracter, siempre se agrega a terminoActual
        if i == 0:
            terminoActual = terminoActual + caracterActual

        # El ultimo caracter
        elif i == len(polinomio) - 1:
            terminoActual = terminoActual + caracterActual
            terminos.append(terminoActual)

        # Otros caracteres
        else:

            # Si se encuentra parentesis, actualizamos el valor de numeroParentesis
            if caracterActual == '(':
                numeroParentesis += 1
                terminoActual = terminoActual + caracterActual
            elif caracterActual == ')':
                numeroParentesis -= 1
                terminoActual = terminoActual + caracterActual

            # Si se encuentra operador '+' o '-'
            elif caracterActual == '+' or caracterActual == '-':

                # Si estamos dentro de parentesis
                if numeroParentesis > 0:
                    terminoActual = terminoActual + caracterActual

                # Si estamos fuera de parentesis, crea un nuevo termino
                else:
                    terminos.append(terminoActual)
                    terminoActual = caracterActual

            # Otros caracteres
            else:
                terminoActual = terminoActual + caracterActual

    return terminos

You can test the function with this code:

polinomio = '3x^2+x(2-4)-1'

terminos = separarTerminos(polinomio)
for i in terminos:
    print(i)

The result is:

3x^2
+x(2-4)
-1

You can use the following regular expression "([+-]?[^-+]+)" . I think the grace is in its simplicity although it can be improved.

It is a regular expression to obtain each of the terms of the polynomial (sequence of characters) whose initial character is an empty string ('') or the character '+' or the character '-' and whose final character group (not included) does not contain neither + nor - . For example '3x^2' or '+3x^2' would fit in your regular expression.

Here you can test it better.

An example with code is as follows:

import re

#polinomios para el test
p = "3x^2+x(2-4)-1"
p2 = "5x^3-1x^2+6x+33"

#expresion regular para obtener cada uno de los terminos del polinomio cuyo caracter inicial sea "" o bien +,- y cuyo grupo de caracteres final (no incluido) no contenga ni + ni -
rExpr = "([+-]?[^-+]+)"

pAsList = re.split(rExpr, p)
p2AsList = re.split(rExpr, p2)

#Eliminamos de la lista obtenida los strings vacios
print(list(filter(None,pAsList)))
print(list(filter(None,p2AsList)))