+
    ‹°³j»  ã                   ó(   € ^ RI HtHt ^ RIHt R tR# )é    )ÚSingularityFunctionÚ
DiracDelta)Ú	integratec                óú  € V P                  \        4      '       g   R# \        V \        4      '       do   V P                  w  rpVP                  '       g   VP
                  '       d"   \        WV^,           4      V^,           ,          # VR9   d   \        WV^,           4      # V P                  '       g   V P                  '       d6   V P                  \        4      p\        WA4      pVP                  \        4      # R# )aÉ  
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)éÿÿÿÿéþÿÿÿéýÿÿÿéüÿÿÿ)Úhasr   Ú
isinstanceÚargsÚis_positiveÚis_zeroÚis_MulÚis_PowÚrewriter   r   )ÚfÚxÚaÚnÚexprs   &&   Úe/home/luca/screen-checking/.venv/lib/python3.14/site-packages/sympy/integrals/singularityfunctions.pyÚsingularityintegrater      s´   € ðV �5‰5Ô$×%Ò%Ùä�!Ô(×)Ò)Ø—&‘&‰ˆˆaØ�=�=ˆ=˜AŸIŸI˜IÜ& q¨Q°­UÓ3°Q¸µUÕ;Ð;ØÐ"Ô"Ü& q¨Q°­UÓ3Ð3à‡x‡x€x�1—8—8�8à�y‰yœÓ$ˆÜ˜Ó!ˆØ�|‰|Ô/Ó0Ð0Ùó    N)Úsympy.functionsr   r   Úsympy.integralsr   r   © r   r   Ú<module>r      s   ðß ;Ý %ô:r   