from decimal import Decimal, getcontext
from vector import Vector

getcontext().prec = 30


class MyDecimal(Decimal):
    def is_near_zero(self, eps=1e-10):
        return abs(self) < eps


class Hyperplane(object):

    NO_NONZERO_ELTS_FOUND_MSG = 'No nonzero elements found'
    EITHER_DIM_OR_NORMAL_VEC_MUST_BE_PROVIDED_MSG = (
        'Either the dimension of the hyperplane or the normal vector '
        'must be provided')

    def __init__(self, dimension=None, normal_vector=None, constant_term=None):
        if not dimension and not normal_vector:
            raise Exception(self.EITHER_DIM_OR_NORMAL_VEC_MUST_BE_PROVIDED_MSG)

        elif not normal_vector:
            self.dimension = dimension
            all_zeros = ['0'] * self.dimension
            normal_vector = Vector(all_zeros)
        else:
            self.dimension = normal_vector.dimension

        self.normal_vector = normal_vector

        if not constant_term:
            constant_term = Decimal('0')
        self.constant_term = Decimal(constant_term)

        self.set_basepoint()

    def set_basepoint(self):
        try:
            n = self.normal_vector
            c = self.constant_term
            basepoint_coords = ['0'] * self.dimension

            initial_index = Hyperplane.first_nonzero_index(n)
            initial_coefficient = n[initial_index]

            basepoint_coords[initial_index] = c / initial_coefficient
            self.basepoint = Vector(basepoint_coords)

        except Exception as e:
            if str(e) == Hyperplane.NO_NONZERO_ELTS_FOUND_MSG:
                self.basepoint = None
            else:
                raise e

    def __str__(self):

        num_decimal_places = 3

        def write_coefficient(coefficient, is_initial_term=False):
            coefficient = round(coefficient, num_decimal_places)
            if coefficient % 1 == 0:
                coefficient = int(coefficient)

            output = ''

            if coefficient < 0:
                output += '-'
            if coefficient > 0 and not is_initial_term:
                output += '+'

            if not is_initial_term:
                output += ' '

            if abs(coefficient) != 1:
                output += '{}'.format(abs(coefficient))

            return output

        n = self.normal_vector

        try:
            initial_index = Hyperplane.first_nonzero_index(n)
            terms = [write_coefficient(
                     n[i], is_initial_term=(i == initial_index)) +
                     'x_{}'.format(i + 1)
                     for i in range(self.dimension)
                     if round(n[i], num_decimal_places) != 0]
            output = ' '.join(terms)

        except Exception as e:
            if str(e) == self.NO_NONZERO_ELTS_FOUND_MSG:
                output = '0'
            else:
                raise e

        constant = round(self.constant_term, num_decimal_places)
        if constant % 1 == 0:
            constant = int(constant)
        output += ' = {}'.format(constant)

        return output

    def is_parallel(self, plane2):
        return self.normal_vector.is_parallel(plane2.normal_vector)

    def __eq__(self, plane2):
        if self.normal_vector.is_zero():
            if not plane2.normal_vector.is_zero():
                return False

            diff = self.constant_term - plane2.constant_term
            return MyDecimal(diff).is_near_zero()

        elif plane2.normal_vector.is_zero():
            return False

        if not self.is_parallel(plane2):
            return False

        basepoint_difference = self.basepoint.minus(plane2.basepoint)
        return basepoint_difference.is_orthogonal(self.normal_vector)

    def __iter__(self):
        self.current = 0
        return self

    def next(self):
        if self.current >= len(self.normal_vector):
            raise StopIteration
        else:
            current_value = self.normal_vector[self.current]
            self.current += 1
            return current_value

    def __len__(self):
        return len(self.normal_vector)

    def __getitem__(self, i):
        return self.normal_vector[i]

    @staticmethod
    def first_nonzero_index(iterable):
        for k, item in enumerate(iterable):
            if not MyDecimal(item).is_near_zero():
                return k
        raise Exception(Hyperplane.NO_NONZERO_ELTS_FOUND_MSG)