number_list.py

def arr_get(lst, i):
    return lst[i] if i < len(lst) else 0


class BasicNumberList:
    def __init__(self, lst):
        self.lst = lst
        self.simplify()

    def raised_to_exponent(self, exponent):
        if exponent < 0:
            raise ValueError("we do not support negative exponents")

        if exponent == 0:
            return BasicNumberList([1])
        if exponent == 1:
            return self
        return BasicNumberList.mul(self, self.raised_to_exponent(exponent - 1))

    def simplify(self):
        self.lst = BasicNumberList.simplify_list(self.lst)

    @staticmethod
    def add(basic_number_list1, basic_number_list2):
        lst1 = basic_number_list1.lst
        lst2 = basic_number_list2.lst
        # do the analog of elementary school arithmetic
        new_size = max(len(lst1), len(lst2))
        return BasicNumberList(
            [arr_get(lst1, i) + arr_get(lst2, i) for i in range(new_size)]
        )

    @staticmethod
    def equal(basic_number_list1, basic_number_list2):
        return basic_number_list1.lst == basic_number_list2.lst

    @staticmethod
    def mul(basic_number_list1, basic_number_list2):
        lst1 = basic_number_list1.lst
        lst2 = basic_number_list2.lst
        # do the analog of elementary school arithmetic
        result = BasicNumberList([])
        for i, elem in enumerate(lst1):
            sub_result = BasicNumberList.mul_by_constant(elem, [0] * i + lst2)
            result = BasicNumberList.add(result, sub_result)
        return result

    @staticmethod
    def mul_by_constant(c, lst):
        return BasicNumberList([c * elem for elem in lst])

    @staticmethod
    def negate(basic_number_list):
        lst = basic_number_list.lst
        return BasicNumberList([-elem for elem in lst])

    @staticmethod
    def simplify_list(lst):
        while lst and lst[-1] == 0:
            lst = lst[:-1]
        return lst


class NumberList:
    def __init__(self, lst):
        self.bnl = BasicNumberList(lst)

    def __add__(self, other):
        return NumberList(BasicNumberList.add(self.bnl, other.bnl).lst)

    def __eq__(self, other):
        return BasicNumberList.equal(self.bnl, other.bnl)

    def __mul__(self, other):
        return NumberList(BasicNumberList.mul(self.bnl, other.bnl).lst)

    def __neg__(self):
        return NumberList(BasicNumberList.negate(self.bnl).lst)

    def __pow__(self, n):
        return NumberList(self.bnl.raised_to_exponent(n).lst)

    def __str__(self):
        return str(self.bnl.lst)

    def list(self):
        return self.bnl.lst