from __future__ import print_function, division

from sympy.core.basic import C
from sympy.core.expr import Expr
from sympy.core.relational import Eq
from sympy.core.sets import Interval
from sympy.core.singleton import S
from sympy.core.symbol import (Dummy, Wild, Symbol)
from sympy.core.sympify import sympify
from sympy.core.compatibility import is_sequence, xrange
from sympy.core.containers import Tuple
from sympy.functions.elementary.piecewise import piecewise_fold, Piecewise
from sympy.utilities import flatten




def _process_limits(*symbols):
    """Process the list of symbols and convert them to canonical limits,
    storing them as Tuple(symbol, lower, upper). The orientation of
    the function is also returned when the upper limit is missing
    so (x, 1, None) becomes (x, None, 1) and the orientation is changed.
    """
    limits = []
    orientation = 1
    for V in symbols:
        if isinstance(V, Symbol):
            limits.append(Tuple(V))
            continue
        elif is_sequence(V, Tuple):
            V = sympify(flatten(V))
            if V[0].is_Symbol:
                newsymbol = V[0]
                if len(V) == 2 and isinstance(V[1], Interval):
                    V[1:] = [V[1].start, V[1].end]

                if len(V) == 3:
                    if V[1] is None and V[2] is not None:
                        nlim = [V[2]]
                    elif V[1] is not None and V[2] is None:
                        orientation *= -1
                        nlim = [V[1]]
                    elif V[1] is None and V[2] is None:
                        nlim = []
                    else:
                        nlim = V[1:]
                    limits.append(Tuple(newsymbol, *nlim ))
                    continue
                elif len(V) == 1 or (len(V) == 2 and V[1] is None):
                    limits.append(Tuple(newsymbol))
                    continue
                elif len(V) == 2:
                    limits.append(Tuple(newsymbol, V[1]))
                    continue

        raise ValueError('Invalid limits given: %s' % str(symbols))

    return limits, orientation

class ExprWithLimits(Expr):
    __slots__ = ['is_commutative']

    def __new__(cls, function, *symbols, **assumptions):
        # Any embedded piecewise functions need to be brought out to the
        # top level so that integration can go into piecewise mode at the
        # earliest possible moment.
        function = piecewise_fold(sympify(function))

        if function is S.NaN:
            return S.NaN

        if symbols:
            limits, orientation = _process_limits(*symbols)
        else:
            # symbol not provided -- we can still try to compute a general form
            free = function.free_symbols
            if len(free) != 1:
                raise ValueError(
                    "specify dummy variables for %s" % function)
            limits, orientation = [Tuple(s) for s in free], 1

        # denest any nested calls
        while cls == type(function):
            limits = list(function.limits) + limits
            function = function.function

        # Only limits with lower and upper bounds are supported; the indefinite form
        # is not supported
        if any(len(l) != 3 or None in l for l in limits):
            raise ValueError('ExprWithLimits requires values for lower and upper bounds.')

        obj = Expr.__new__(cls, **assumptions)
        arglist = [function]
        arglist.extend(limits)
        obj._args = tuple(arglist)
        obj.is_commutative = function.is_commutative  # limits already checked

        return obj

    @property
    def function(self):
        """Return the function applied across limits.

        Examples
        ========

        >>> from sympy import Integral
        >>> from sympy.abc import x
        >>> Integral(x**2, (x,)).function
        x**2

        See Also
        ========

        limits, variables, free_symbols
        """
        return self._args[0]

    @property
    def limits(self):
        """Return the limits of expression.

        Examples
        ========

        >>> from sympy import Integral
        >>> from sympy.abc import x, i
        >>> Integral(x**i, (i, 1, 3)).limits
        ((i, 1, 3),)

        See Also
        ========

        function, variables, free_symbols
        """
        return self._args[1:]

    @property
    def variables(self):
        """Return a list of the dummy variables

        >>> from sympy import Sum
        >>> from sympy.abc import x, i
        >>> Sum(x**i, (i, 1, 3)).variables
        [i]

        See Also
        ========

        function, limits, free_symbols