a RG5d @sXddlmZddlmZddlmZddlmZmZddl m Z m Z ddZ d d Z d S) )Mul)S)default_sort_key) DiracDelta Heaviside)Integral integratec Cs4g}d}|\}}t|td}|||D]b}|jrdt|jtrd|| |j|j d|j}|durt|tr| |r|}q.||q.|s(g}|D]b}t|tr||j d|dq|jrt|jtr|| |jj d|d|j q||q||krt | }nd}d|fS|t |fS)achange_mul(node, x) Rearranges the operands of a product, bringing to front any simple DiracDelta expression. Explanation =========== If no simple DiracDelta expression was found, then all the DiracDelta expressions are simplified (using DiracDelta.expand(diracdelta=True, wrt=x)). Return: (dirac, new node) Where: o dirac is either a simple DiracDelta expression or None (if no simple expression was found); o new node is either a simplified DiracDelta expressions or None (if it could not be simplified). Examples ======== >>> from sympy import DiracDelta, cos >>> from sympy.integrals.deltafunctions import change_mul >>> from sympy.abc import x, y >>> change_mul(x*y*DiracDelta(x)*cos(x), x) (DiracDelta(x), x*y*cos(x)) >>> change_mul(x*y*DiracDelta(x**2 - 1)*cos(x), x) (None, x*y*cos(x)*DiracDelta(x - 1)/2 + x*y*cos(x)*DiracDelta(x + 1)/2) >>> change_mul(x*y*DiracDelta(cos(x))*cos(x), x) (None, None) See Also ======== sympy.functions.special.delta_functions.DiracDelta deltaintegrate N)keyrTZ diracdeltawrt)args_cncsortedrextendis_Pow isinstancebaserappendfuncexp is_simpleexpandr) nodexnew_argsdiraccncZ sorted_argsargZnnoderZ/var/www/html/django/DPS/env/lib/python3.9/site-packages/sympy/integrals/deltafunctions.py change_muls2'     "  r!c Cs|tsdS|jtkr|jd|d}||kr||rt|jdksT|jddkrbt|jdSt|jd|jdd|jd Snt ||}|SnR|j s|j r|}||krt ||}|durt |ts|Snt||\}}|s|rt ||}|Snddlm}|jd|d}|j rFt||\}}||}||jd|d} t|jdkrndn|jd} d} | dkrtj| ||| || } | jr| d8} | d7} n,| dkr| t|| S| t|| dSq|tjSdS)a deltaintegrate(f, x) Explanation =========== The idea for integration is the following: - If we are dealing with a DiracDelta expression, i.e. DiracDelta(g(x)), we try to simplify it. If we could simplify it, then we integrate the resulting expression. We already know we can integrate a simplified expression, because only simple DiracDelta expressions are involved. If we couldn't simplify it, there are two cases: 1) The expression is a simple expression: we return the integral, taking care if we are dealing with a Derivative or with a proper DiracDelta. 2) The expression is not simple (i.e. DiracDelta(cos(x))): we can do nothing at all. - If the node is a multiplication node having a DiracDelta term: First we expand it. If the expansion did work, then we try to integrate the expansion. If not, we try to extract a simple DiracDelta term, then we have two cases: 1) We have a simple DiracDelta term, so we return the integral. 2) We didn't have a simple term, but we do have an expression with simplified DiracDelta terms, so we integrate this expression. Examples ======== >>> from sympy.abc import x, y, z >>> from sympy.integrals.deltafunctions import deltaintegrate >>> from sympy import sin, cos, DiracDelta >>> deltaintegrate(x*sin(x)*cos(x)*DiracDelta(x - 1), x) sin(1)*cos(1)*Heaviside(x - 1) >>> deltaintegrate(y**2*DiracDelta(x - z)*DiracDelta(y - z), y) z**2*DiracDelta(x - z)*Heaviside(y - z) See Also ======== sympy.functions.special.delta_functions.DiracDelta sympy.integrals.integrals.Integral NTr rr)solve)hasrrrrlenargsras_polyLCr is_Mulrrrr! sympy.solversr"r NegativeOnediffsubsis_zeroZero) frhfhgZ deltatermZ rest_multr"Z rest_mult_2pointnmrrrr deltaintegrateQsT8           r7N)sympy.core.mulrsympy.core.singletonrsympy.core.sortingrsympy.functionsrr integralsrr r!r7rrrr s   I