(self, *indices)
return Sum(e * self.function, *limits)
Reverse the order of a limit in a Sum.

        Usage
        =====

        ``reverse_order(self, *indices)`` reverses some limits in the expression
        ``self`` which can be either a ``Sum`` or a ``Product``. The selectors in
        the argument ``indices`` specify some indices whose limits get reversed.
        These selectors are either variable names or numerical indices counted
        starting from the inner-most limit tuple.

        Examples
        ========

        >>> from sympy import Sum
        >>> from sympy.abc import x, y, a, b, c, d

        >>> Sum(x, (x, 0, 3)).reverse_order(x)
        Sum(-x, (x, 4, -1))
        >>> Sum(x*y, (x, 1, 5), (y, 0, 6)).reverse_order(x, y)
        Sum(x*y, (x, 6, 0), (y, 7, -1))
        >>> Sum(x, (x, a, b)).reverse_order(x)
        Sum(-x, (x, b + 1, a - 1))
        >>> Sum(x, (x, a, b)).reverse_order(0)
        Sum(-x, (x, b + 1, a - 1))

        While one should prefer variable names when specifying which limits
        to reverse, the index counting notation comes in handy in case there
        are several symbols with the same name.

        >>> S = Sum(x**2, (x, a, b), (x, c, d))
        >>> S
        Sum(x**2, (x, a, b), (x, c, d))
        >>> S0 = S.reverse_order( 0)
        >>> S0
        Sum(-x**2, (x, b + 1, a - 1), (x, c, d))
        >>> S1 = S0.reverse_order( 1)
        >>> S1
        Sum(x**2, (x, b + 1, a - 1), (x, d + 1, c - 1))

        Of course we can mix both notations:

        >>> Sum(x*y, (x, a, b), (y, 2, 5)).reverse_order( x, 1)
        Sum(x*y, (x, b + 1, a - 1), (y, 6, 1))
        >>> Sum(x*y, (x, a, b), (y, 2, 5)).reverse_order( y, x)
        Sum(x*y, (x, b + 1, a - 1), (y, 6, 1))

        See Also
        ========

        index, reorder_limit, reorder

        References
        ==========

        .. [1] Michael Karr, "Summation in Finite Terms", Journal of the ACM,
               Volume 28 Issue 2, April 1981, Pages 305-350
               http://dl.acm.org/citation.cfm?doid=322248.322255
Reverse the order of a limit in a Sum.
Reverse the order of a limit in a Sum .
def reverse_order(self, *indices):
        """
        Reverse the order of a limit in a Sum.

        Usage
        =====

        ``reverse_order(self, *indices)`` reverses some limits in the expression
        ``self`` which can be either a ``Sum`` or a ``Product``. The selectors in
        the argument ``indices`` specify some indices whose limits get reversed.
        These selectors are either variable names or numerical indices counted
        starting from the inner-most limit tuple.

        Examples
        ========

        >>> from sympy import Sum
        >>> from sympy.abc import x, y, a, b, c, d

        >>> Sum(x, (x, 0, 3)).reverse_order(x)
        Sum(-x, (x, 4, -1))
        >>> Sum(x*y, (x, 1, 5), (y, 0, 6)).reverse_order(x, y)
        Sum(x*y, (x, 6, 0), (y, 7, -1))
        >>> Sum(x, (x, a, b)).reverse_order(x)
        Sum(-x, (x, b + 1, a - 1))
        >>> Sum(x, (x, a, b)).reverse_order(0)
        Sum(-x, (x, b + 1, a - 1))

        While one should prefer variable names when specifying which limits
        to reverse, the index counting notation comes in handy in case there
        are several symbols with the same name.

        >>> S = Sum(x**2, (x, a, b), (x, c, d))
        >>> S
        Sum(x**2, (x, a, b), (x, c, d))
        >>> S0 = S.reverse_order( 0)
        >>> S0
        Sum(-x**2, (x, b + 1, a - 1), (x, c, d))
        >>> S1 = S0.reverse_order( 1)
        >>> S1
        Sum(x**2, (x, b + 1, a - 1), (x, d + 1, c - 1))

        Of course we can mix both notations:

        >>> Sum(x*y, (x, a, b), (y, 2, 5)).reverse_order( x, 1)
        Sum(x*y, (x, b + 1, a - 1), (y, 6, 1))
        >>> Sum(x*y, (x, a, b), (y, 2, 5)).reverse_order( y, x)
        Sum(x*y, (x, b + 1, a - 1), (y, 6, 1))

        See Also
        ========

        index, reorder_limit, reorder

        References
        ==========

        .. [1] Michael Karr, "Summation in Finite Terms", Journal of the ACM,
               Volume 28 Issue 2, April 1981, Pages 305-350
               http://dl.acm.org/citation.cfm?doid=322248.322255
        """
        l_indices = list(indices)

        for i, indx in enumerate(l_indices):
            if not isinstance(indx, int):
                l_indices[i] = self.index(indx)

        e = 1
        limits = []
        for i, limit in enumerate(self.limits):
            l = limit
            if i in l_indices:
                e = -e
                l = (limit[0], limit[2] + 1 , limit[1] - 1)
            limits.append(l)

        return Sum(e * self.function, *limits)
def reverse_order ( self , * indices ) : l_indices = list ( indices ) for i , indx in enumerate ( l_indices ) : if not isinstance ( indx , int ) : l_indices [ i ] = self . index ( indx ) e = 1 limits = [ ] for i , limit in enumerate ( self . limits ) : l = limit if i in l_indices : e = - e l = ( limit [ 0 ] , limit [ 2 ] + 1 , limit [ 1 ] - 1 ) limits . append ( l ) return Sum ( e * self . function , * limits )