� ��g��(�ddlmZmZddlmZd�ZdS)�)�SingularityFunction� DiracDelta)� integratec��|�t��sdSt|t��rK|j\}}}|js|jrt|||dz��|dzzS|dvrt|||dz��S|js|jrD|�t��}t||��}|�t��SdS)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�args�is_positive�is_zero�is_Mul�is_Pow�rewriterr)�f�x�a�n�exprs �t/home/asafur/pinokio/api/open-webui.git/app/env/lib/python3.11/site-packages/sympy/integrals/singularityfunctions.py�singularityintegraters��V �5�5�$�%�%��t��!�(�)�)�4��&��1�a��=� 4�A�I� 4�&�q�!�Q��U�3�3�Q��U�;�;� �"� "� "�&�q�!�Q��U�3�3�3��x�1�1�8�1��y�y��$�$��q�!�!��|�|�/�0�0�0��4�N)�sympy.functionsrr�sympy.integralsrr�rr�<module>rsH��;�;�;�;�;�;�;�;�%�%�%�%�%�%�:�:�:�:�:r