o
    i                     @   s(   d dl mZmZ d dlmZ dd ZdS )    )SingularityFunction
DiracDelta)	integratec                 C   s   |  tsdS t| tr0| j\}}}|js|jr$t|||d |d  S |dv r0t|||d S | js6| jrE| t	}t
||}|tS dS )aI  
    This function handles the indefinite integrations of Singularity functions.
    The ``integrate`` function calls this function internally whenever an
    instance of SingularityFunction is passed as argument.

    Explanation
    ===========

    The idea for integration is the following:

    - If we are dealing with a SingularityFunction expression,
      i.e. ``SingularityFunction(x, a, n)``, we just return
      ``SingularityFunction(x, a, n + 1)/(n + 1)`` if ``n >= 0`` and
      ``SingularityFunction(x, a, n + 1)`` if ``n < 0``.

    - If the node is a multiplication or power node having a
      SingularityFunction term we rewrite the whole expression in terms of
      Heaviside and DiracDelta and then integrate the output. Lastly, we
      rewrite the output of integration back in terms of SingularityFunction.

    - If none of the above case arises, we return None.

    Examples
    ========

    >>> from sympy.integrals.singularityfunctions import singularityintegrate
    >>> from sympy import SingularityFunction, symbols, Function
    >>> x, a, n, y = symbols('x a n y')
    >>> f = Function('f')
    >>> singularityintegrate(SingularityFunction(x, a, 3), x)
    SingularityFunction(x, a, 4)/4
    >>> singularityintegrate(5*SingularityFunction(x, 5, -2), x)
    5*SingularityFunction(x, 5, -1)
    >>> singularityintegrate(6*SingularityFunction(x, 5, -1), x)
    6*SingularityFunction(x, 5, 0)
    >>> singularityintegrate(x*SingularityFunction(x, 0, -1), x)
    0
    >>> singularityintegrate(SingularityFunction(x, 1, -1) * f(x), x)
    f(1)*SingularityFunction(x, 1, 0)

    N   ))hasr   
isinstanceargsZis_positiveis_zeroZis_MulZis_PowZrewriter   r   )fxanexpr r   s/var/www/html/eduruby.in/lip-sync/lip-sync-env/lib/python3.10/site-packages/sympy/integrals/singularityfunctions.pysingularityintegrate   s   
+



r   N)Zsympy.functionsr   r   Zsympy.integralsr   r   r   r   r   r   <module>   s    