ó ”¼™\c@ srddlmZmZddlmZddlmZmZddlm Z ddl m Z d„Z d„Z dS( i’’’’(tprint_functiontdivision(tMul(t DiracDeltat Heaviside(tdefault_sort_key(tSc C sĆg}d}|jƒ\}}t|dtƒ}|j|ƒx˜|D]}|jr”t|jtƒr”|j |j |j|j dƒƒ|j}n|dkrĒt|tƒrĒ|j |ƒrĒ|}qD|j |ƒqDW|s³g}x›|D]“}t|tƒr"|j |j dtd|ƒƒqė|jrqt|jtƒrq|j |j |jj dtd|ƒ|j ƒƒqė|j |ƒqėW||kr£t|Œj ƒ}nd}d|fS|t|ŒfS(schange_mul(node, x) Rearranges the operands of a product, bringing to front any simple DiracDelta expression. 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 tkeyit diracdeltatwrtN(tNonetargs_cnctsortedRtextendtis_Powt isinstancetbaseRtappendtfunctexpt is_simpletexpandtTrueR( tnodetxtnew_argstdiractctnct sorted_argstargtnnode((s=lib/python2.7/site-packages/sympy/integrals/deltafunctions.pyt change_mul s2$  # *  "4  cC sÄ|jtƒsdSddlm}m}ddlm}|jtkr|j dt d|ƒ}||krš|j |ƒrt |j ƒdks£|j ddkr“t|j dƒSt|j d|j ddƒ|j djƒjƒSqqĄ|||ƒ}|Snŗ|js|jrĄ|j ƒ}||krb|||ƒ}|dk r½t||ƒ r½|SqĄt||ƒ\}} |s™| r½|| |ƒ}|SqĄ|j dt d|ƒ}|jrÜt||ƒ\}} | | } n||j d|ƒd} t |j ƒdkrdn |j d} d} x| dkrµd| | j|| ƒj|| ƒ}|tjkr| d8} | d7} q'| dkr|t|| ƒS|t|| dƒSq'WtjSndS( sÉ deltaintegrate(f, x) 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, Heaviside >>> 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 i’’’’(tIntegralt integrate(tsolveRR iiN(thasRR tsympy.integralsR!R"t sympy.solversR#RRRRtlentargsRtas_polytLCtis_MulRRR tdifftsubsRtZero(tfRR!R"R#thtfhtgt deltatermt rest_multt rest_mult_2tpointtntmtr((s=lib/python2.7/site-packages/sympy/integrals/deltafunctions.pytdeltaintegrateOsT5 (     (&    N(t __future__RRt sympy.coreRtsympy.functionsRRtsympy.core.compatibilityRtsympy.core.singletonRR R:(((s=lib/python2.7/site-packages/sympy/integrals/deltafunctions.pyts  F