Question

I need to add two simple polynomials (represented as strings). The following example would clarify my requirement.

input1 = '5a+6b'
input2 = '2a+3b+9c'

The required sum should be as follows:

 '7a+9b+9c'

Currently I have created a function (of 20 lines) to perform this task for me, but I think this can be improved.

EDIT: Adding my code

def add_domain_strings():
    input_list = ['5a+6b', '2a+3b+9c']
    vars_dict = {}
    for input in input_list:
        temp_list = input.split('+')
        for i in temp_list:
            split_index = None
            for j in i:
                if not j.isdigit():
                    split_index = i.index(j)
                    break
            if i[split_index:] in vars_dict:
                vars_dict[i[split_index:]] += int(i[:split_index])
            else:
                vars_dict[i[split_index:]] = int(i[:split_index])
    sum_string = ''
    for k,v in vars_dict.iteritems():
        if sum_string:
            sum_string += '+%s%s' % (v,k)
        else:
            sum_string += '%s%s' % (v,k)
    return sum_string

Answer 1

You could either use sympy:

>>> import sympy
>>> from sympy import *
>>> a = Symbol('a')
>>> b = Symbol('b')
>>> c = Symbol('c')
>>> eval('5*a+6*b')
5*a + 6*b
>>> eval('5*a+6*b') + eval('2*a+3*b+9*c')
7*a + 9*b + 9*c

Or write a simple parser:

>>> input1 = '5a+6b'
>>> input2 = '2a+3b+9c'
>>> s = "+".join((input1, input2))
>>> s
'5a+6b+2a+3b+9c'
>>> d = {}
>>> for i in s.split("+"):
...     d[i[-1]] = d.get(i[-1], 0) + int(i[:-1])
... 
>>> d
{'a': 7, 'c': 9, 'b': 9}
>>> "+".join("".join((str(j),i)) for i, j in d.items())
'7a+9c+9b'