#! /usr/bin/env python
# -*- coding: utf-8 -*-
# vim:fenc=utf-8
#
# Copyright © 2017 lafrite <lafrite@Poivre>
#
# Distributed under terms of the MIT license.

"""
Adding MO
"""

from functools import wraps
from multipledispatch import Dispatcher
from ..tree import Tree
from ..MO.mo import MO, MOnumber, MOstr
from ..MO.fraction import MOFraction
from ..MO.monomial import MOstrPower, MOMonomial
from .exceptions import AddError
from .arithmetic import lcm
from .filters import special_case

add_doc = """ Adding MOs

:param left: left MO
:param right: right MO
:return: Tree or MO

"""

add = Dispatcher("add", doc=add_doc)

def add_filter(left, right):
    """ Automatic add on MO

    :param left: MO
    :param right: MO
    :returns: MO if it is a special case, nothing other wise

    >>> a = MOnumber(0)
    >>> b = MOFraction(1, 2)
    >>> add(a, b)
    <MOFraction 1 / 2>
    >>> add(b, a)
    <MOFraction 1 / 2>
    """
    try:
        if left == 0:
            return right
    except TypeError:
        pass
    try:
        if right == 0:
            return left
    except TypeError:
        pass

@add.register(MOnumber, MOnumber)
@special_case(add_filter)
def monumber_monumber(left, right):
    """ Simply add MO value

    >>> a = MOnumber(4)
    >>> b = MOnumber(6)
    >>> add(a, b)
    <MOnumber 10>

    """
    return MO.factory(left.value + right.value)

@add.register(MOnumber, MOFraction)
@special_case(add_filter)
def monumber_mofraction(left, right):
    """ Return a tree with the MOnumber transformed into a MOFraction

    >>> a = MOnumber(4)
    >>> b = MOFraction(6, 5)
    >>> print(add(a, b))
    +
     > /
     | > 4
     | > 1
     > /
     | > 6
     | > 5
    """
    left_fraction = MOFraction(left, MOnumber(1))
    return Tree("+", left_fraction, right)

@add.register(MOFraction, MOnumber)
@special_case(add_filter)
def mofraction_monumber(left, right):
    """ Return a tree with the MOnumber transformed into a MOFraction

    >>> a = MOFraction(6, 5)
    >>> b = MOnumber(4)
    >>> print(add(a, b))
    +
     > /
     | > 6
     | > 5
     > /
     | > 4
     | > 1
    """
    right_fraction = MOFraction(right, MOnumber(1))
    return Tree("+", left, right_fraction)

@add.register(MOFraction, MOFraction)
@special_case(add_filter)
def mofraction_mofraction(left, right):
    """ 3 differents cases:

    Fractions have same denomintor -> add numerator Tree

    >>> a = MOFraction(1, 5)
    >>> b = MOFraction(4, 5)
    >>> print(add(a, b))
    /
     > +
     | > 1
     | > 4
     > 5
    >>> a = MOFraction(1, 5, True)
    >>> b = MOFraction(4, 5)
    >>> print(mofraction_mofraction(a, b))
    /
     > +
     | > -
     | | > None
     | | > 1
     | > 4
     > 5
    >>> a = MOFraction(1, 5)
    >>> b = MOFraction(4, 5, True)
    >>> print(mofraction_mofraction(a, b))
    /
     > +
     | > 1
     | > -
     | | > None
     | | > 4
     > 5

    A denominator is a multiple of the other

    >>> a = MOFraction(1, 2)
    >>> b = MOFraction(1, 4)
    >>> print(mofraction_mofraction(a, b))
    +
     > /
     | > *
     | | > 1
     | | > 2
     | > *
     | | > 2
     | | > 2
     > /
     | > 1
     | > 4

    Denominators are coprime

    >>> a = MOFraction(1, 2)
    >>> b = MOFraction(1, 5)
    >>> print(mofraction_mofraction(a, b))
    +
     > /
     | > *
     | | > 1
     | | > 5
     | > *
     | | > 2
     | | > 5
     > /
     | > *
     | | > 1
     | | > 2
     | > *
     | | > 5
     | | > 2
    """
    if left.denominator == right.denominator:
        num = Tree("+", left.numerator, right.numerator)
        return Tree("/", num, left.denominator)

    denom_lcm = lcm(left.denominator.value, right.denominator.value)

    if left.denominator.value == denom_lcm:
        left_frac = left
    else:
        multiply_by = MO.factory(denom_lcm // left.denominator.value)
        left_num = Tree("*", left.numerator, multiply_by)
        left_denom = Tree("*", left.denominator, multiply_by)
        left_frac = Tree("/", left_num, left_denom)

    if right.denominator.value == denom_lcm:
        right_frac = right
    else:
        multiply_by = MO.factory(denom_lcm // right.denominator.value)
        right_num = Tree("*", right.numerator, multiply_by)
        right_denom = Tree("*", right.denominator, multiply_by)
        right_frac = Tree("/", right_num, right_denom)

    return Tree("+", left_frac, right_frac)

@add.register(MOstr, MOstr)
@special_case(add_filter)
def mostr_mostr(left, right):
    """ Add 2 MOstr

    :example:
    >>> a = MOstr("x")
    >>> b = MOstr("x")
    >>> add(a, b)
    <MOMonomial 2x>
    """
    if left != right:
        raise NotImplementedError("Can't add 2 MOstr with not same letter")
    return MOMonomial(2, left)

@add.register(MOstrPower, MOstrPower)
@special_case(add_filter)
def mostrpower_mostrpower(left, right):
    """ Add 2 MOstrPower

    :example:
    >>> a = MOstrPower("x", 2)
    >>> b = MOstrPower("x", 2)
    >>> add(a, b)
    <MOMonomial 2x^2>
    """
    if left.variable != right.variable:
        raise NotImplementedError("Can't add 2 MOstrPower with not same letter")
    if left.power != right.power:
        raise NotImplementedError("Can't add 2 MOstrPower with not same power")
    return MOMonomial(2, left.variable, left.power)

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