import math
import numbers
import operator

from abc import ABC, abstractproperty, abstractmethod
from collections import OrderedDict, Mapping

from .linexprs import Symbol


__all__ = [
    'GeometricObject',
    'Point',
    'Vector',
]


class GeometricObject(ABC):

    @abstractproperty
    def symbols(self):
        pass

    @property
    def dimension(self):
        return len(self.symbols)

    @abstractmethod
    def aspolyhedron(self):
        pass

    def asdomain(self):
        return self.aspolyhedron()


class Coordinates:

    __slots__ = (
        '_coordinates',
    )

    def __new__(cls, coordinates):
        if isinstance(coordinates, Mapping):
            coordinates = coordinates.items()
        self = object().__new__(cls)
        self._coordinates = OrderedDict()
        for symbol, coordinate in sorted(coordinates,
                key=lambda item: item[0].sortkey()):
            if not isinstance(symbol, Symbol):
                raise TypeError('symbols must be Symbol instances')
            if not isinstance(coordinate, numbers.Real):
                raise TypeError('coordinates must be real numbers')
            self._coordinates[symbol] = coordinate
        return self

    @property
    def symbols(self):
        return tuple(self._coordinates)

    @property
    def dimension(self):
        return len(self.symbols)

    def coordinates(self):
        yield from self._coordinates.items()

    def coordinate(self, symbol):
        if not isinstance(symbol, Symbol):
            raise TypeError('symbol must be a Symbol instance')
        return self._coordinates[symbol]

    __getitem__ = coordinate

    def values(self):
        yield from self._coordinates.values()

    def __bool__(self):
        return any(self._coordinates.values())

    def __hash__(self):
        return hash(tuple(self.coordinates()))

    def __repr__(self):
        string = ', '.join(['{!r}: {!r}'.format(symbol, coordinate)
            for symbol, coordinate in self.coordinates()])
        return '{}({{{}}})'.format(self.__class__.__name__, string)

    def _map(self, func):
        for symbol, coordinate in self.coordinates():
            yield symbol, func(coordinate)

    def _iter2(self, other):
        if self.symbols != other.symbols:
            raise ValueError('arguments must belong to the same space')
        coordinates1 = self._coordinates.values()
        coordinates2 = other._coordinates.values()
        yield from zip(self.symbols, coordinates1, coordinates2)

    def _map2(self, other, func):
        for symbol, coordinate1, coordinate2 in self._iter2(other):
            yield symbol, func(coordinate1, coordinate2)


class Point(Coordinates, GeometricObject):
    """
    This class represents points in space.
    """

    def isorigin(self):
    """
    Return True if a Point is the origin.
    """
        return not bool(self)

    def __hash__(self):
        return super().__hash__()

    def __add__(self, other):
        if not isinstance(other, Vector):
            return NotImplemented
        coordinates = self._map2(other, operator.add)
        return Point(coordinates)

    def __sub__(self, other):
        coordinates = []
        if isinstance(other, Point):
            coordinates = self._map2(other, operator.sub)
            return Vector(coordinates)
        elif isinstance(other, Vector):
            coordinates = self._map2(other, operator.sub)
            return Point(coordinates)
        else:
            return NotImplemented

    def __eq__(self, other):
    """
    Compares two Points for equality.
    """
        return isinstance(other, Point) and \
            self._coordinates == other._coordinates

    def aspolyhedron(self):
    """
    Return a Point as a polyhedron.
    """
        from .polyhedra import Polyhedron
        equalities = []
        for symbol, coordinate in self.coordinates():
            equalities.append(symbol - coordinate)
        return Polyhedron(equalities)


class Vector(Coordinates):
    """
    This class represents displacements in space.
    """

    def __new__(cls, initial, terminal=None):
        if not isinstance(initial, Point):
            initial = Point(initial)
        if terminal is None:
            coordinates = initial._coordinates
        else:
            if not isinstance(terminal, Point):
                terminal = Point(terminal)
            coordinates = terminal._map2(initial, operator.sub)
        return super().__new__(cls, coordinates)

    def isnull(self):
    """
    Returns true if a Vector is null.
    """
        return not bool(self)

    def __hash__(self):
        return super().__hash__()

    def __add__(self, other):
    """
    Adds either a Point or Vector to a Vector.
    """
        if isinstance(other, (Point, Vector)):
            coordinates = self._map2(other, operator.add)
            return other.__class__(coordinates)
        return NotImplemented

    def angle(self, other):
        """
        Retrieve the angle required to rotate the vector into the vector passed in argument. The result is an angle in radians, ranging between -pi and pi.
        """
        if not isinstance(other, Vector):
            raise TypeError('argument must be a Vector instance')
        cosinus = self.dot(other) / (self.norm()*other.norm())
        return math.acos(cosinus)

    def cross(self, other):
        """
        Calculate the cross product of two Vector3D structures.
        """
        if not isinstance(other, Vector):
            raise TypeError('other must be a Vector instance')
        if self.dimension != 3 or other.dimension != 3:
            raise ValueError('arguments must be three-dimensional vectors')
        if self.symbols != other.symbols:
            raise ValueError('arguments must belong to the same space')
        x, y, z = self.symbols
        coordinates = []
        coordinates.append((x, self[y]*other[z] - self[z]*other[y]))
        coordinates.append((y, self[z]*other[x] - self[x]*other[z]))
        coordinates.append((z, self[x]*other[y] - self[y]*other[x]))
        return Vector(coordinates)

    def __truediv__(self, other):
        """
        Divide the vector by the specified scalar and returns the result as a
        vector.
        """
        if not isinstance(other, numbers.Real):
            return NotImplemented
        coordinates = self._map(lambda coordinate: coordinate / other)
        return Vector(coordinates)

    def dot(self, other):
        """
        Calculate the dot product of two vectors.
        """
        if not isinstance(other, Vector):
            raise TypeError('argument must be a Vector instance')
        result = 0
        for symbol, coordinate1, coordinate2 in self._iter2(other):
            result += coordinate1 * coordinate2
        return result

    def __eq__(self, other):
    """
    Compares two Vectors for equality.
    """
        return isinstance(other, Vector) and \
            self._coordinates == other._coordinates

    def __hash__(self):
        return hash(tuple(self.coordinates()))

    def __mul__(self, other):
    """
    Multiplies a Vector by a scalar value.
    """
        if not isinstance(other, numbers.Real):
            return NotImplemented
        coordinates = self._map(lambda coordinate: other * coordinate)
        return Vector(coordinates)

    __rmul__ = __mul__

    def __neg__(self):
    """
    Returns the negated form of a Vector.
    """
        coordinates = self._map(operator.neg)
        return Vector(coordinates)

    def norm(self):
    """
    Normalizes a Vector. 
    """
        return math.sqrt(self.norm2())

    def norm2(self):
        result = 0
        for coordinate in self._coordinates.values():
            result += coordinate ** 2
        return result

    def asunit(self):
        return self / self.norm()

    def __sub__(self, other):
    """
    Subtract a Point or Vector from a Vector. 
    """
        if isinstance(other, (Point, Vector)):
            coordinates = self._map2(other, operator.sub)
            return other.__class__(coordinates)
        return NotImplemented