o 8Va@s>ddlmZddlmZddlmZmZddlmZm Z m Z m Z m Z m Z mZddlmZddlZddlZddlmZedZergdd lmZmZdd lmZmZmZdd lmZmZed d ddZeeZ GdddZ!ed d ddZ"ed d ddZ#ed d dddZ$ed d dddZ%ed d ddZ&dS) ) import_module)doctest_depends_on)IntegerFloat)PowAddIntegralMulSFunctionE)expN)powsimpmatchpy)ManyToOneReplacerManyToOneMatcher)rubi_exprubi_unevaluated_expr process_trig)op_iterop_len)r)modulescCsddlm}ddlm}ddlm}ddlm}ddlm }ddl m }ddl m }dd lm}dd lm}dd lm} dd lm} dd lm} ddlm} ddlm} ddlm}ddlm}ddl m!}g}||7}||7}||7}||7}||7}||7}||7}||7}||7}||7}|| 7}|| 7}|| 7}|| 7}|| 7}||7}||7}t"|}||fS)a9 Returns rubi ManyToOneReplacer by adding all rules from different modules. Uncomment the lines to add integration capabilities of that module. Currently, there are parsing issues with special_function, derivative and miscellaneous_integration. Hence they are commented. r)integrand_simplification)linear_products)quadratic_products)binomial_products)trinomial_products)miscellaneous_algebraic) exponential) logarithms)sine)tangent)secant)miscellaneous_trig) inverse_trig) hyperbolic)inverse_hyperbolic)special_functions)miscellaneous_integration)#Z3sympy.integrals.rubi.rules.integrand_simplificationrZ*sympy.integrals.rubi.rules.linear_productsrZ-sympy.integrals.rubi.rules.quadratic_productsrZ,sympy.integrals.rubi.rules.binomial_productsrZ-sympy.integrals.rubi.rules.trinomial_productsrZ2sympy.integrals.rubi.rules.miscellaneous_algebraicrZ&sympy.integrals.rubi.rules.exponentialrZ%sympy.integrals.rubi.rules.logarithmsrZsympy.integrals.rubi.rules.siner Z"sympy.integrals.rubi.rules.tangentr!Z!sympy.integrals.rubi.rules.secantr"Z-sympy.integrals.rubi.rules.miscellaneous_trigr#Z'sympy.integrals.rubi.rules.inverse_trigr$Z%sympy.integrals.rubi.rules.hyperbolicr%Z-sympy.integrals.rubi.rules.inverse_hyperbolicr&Z,sympy.integrals.rubi.rules.special_functionsr'Z4sympy.integrals.rubi.rules.miscellaneous_integrationr(r)rrrrrrrrr r!r"r#r$r%r&r'r(rulesrubir+?/usr/lib/python3/dist-packages/sympy/integrals/rubi/rubimain.pyget_rubi_objectsJ                                 r-c@sDeZdZdZdZddZddZddZd d Zd d Z d dZ dS)LoadRubiReplacerz- Class trick to load RUBI only once. NcCsDtdur tddStjdurtjSt|}d|_d|_|t_|S)NzMatchPy library not found)rprintr. _instanceobject__new___rubi_rules)clsobjr+r+r,r2Rs  zLoadRubiReplacer.__new__cCs*|jdur|jSt\}}||_||_|SN)r3r-r4)selfr*r)r+r+r,load^s  zLoadRubiReplacer.loadcCLddl}|}t|d}|||WddS1swYdSNrwb)pickler9opendump)r8filenamer=r*foutr+r+r, to_picklef  "zLoadRubiReplacer.to_picklecCr:r;)dillr9r>r?)r8r@rDr*rAr+r+r,to_dilllrCzLoadRubiReplacer.to_dillcCHddl}t|d}|||_Wd|jS1swY|jSNrrb)r=r>r9r3)r8r@r=finr+r+r, from_pickler  zLoadRubiReplacer.from_picklecCrFrG)rDr>r9r3)r8r@rDrIr+r+r, from_dillxrKzLoadRubiReplacer.from_dill) __name__ __module__ __qualname____doc__r0r2r9rBrErJrLr+r+r+r,r.Ks  r.cCs|tr |tt}|S)a Rubi's `rubi_exp` need to be replaced back to SymPy's general `exp`. Examples ======== >>> from sympy import Function, E, Integral >>> from sympy.integrals.rubi.rubimain import process_final_integral >>> from sympy.integrals.rubi.utility_function import rubi_unevaluated_expr >>> from sympy.abc import a, x >>> _E = rubi_unevaluated_expr(E) >>> process_final_integral(Integral(a, x)) Integral(a, x) >>> process_final_integral(_E**5) exp(5) )Zhas_Ereplacer )exprr+r+r,process_final_integrals  rTcCs\g}g}t|tr,|jD]}t|tttfr||q ||q tt|t|S|S)a@ This function is needed to preprocess an expression as done in matchpy `x^a*x^b` in matchpy auotmatically transforms to `x^(a+b)` Examples ======== >>> from sympy.integrals.rubi.rubimain import rubi_powsimp >>> from sympy.abc import a, b, x >>> rubi_powsimp(x**a*x**b) x**(a + b) ) isinstancer argsrrsym_expappendr)rSZlst_powZ lst_non_powir+r+r, rubi_powsimps    rZFcCst}|tt}t|}t|}t|tt fs!t|t t fr't ||St|t rBd}|jD] }||t||7}q1t|Stt||}t|S)aW Rule based algorithm for integration. Integrates the expression by applying transformation rules to the expression. Returns `Integrate` if an expression cannot be integrated. Parameters ========== expr : integrand expression var : variable of integration Returns Integral object if unable to integrate. r)r.r9rRrWrrrZrUintrfloatrr rrVrrTutil_rubi_integrate)rSvar showstepsr*resultsexr+r+r,rubi_integrates     rb csXtt|}|tt}t|D]}|ddfdd}||kr)|Sq|S)NcSs t|tSr7)rUrxr+r+r,s z%util_rubi_integrate..csj|ddS)Nrc)Z max_count)rRrdr*r+r,rfs)r.r9rrRrWrrange)rSr_Zmax_looprYr`r+rgr,r]s    r]c Cst}|j}|t||}|D]C\}}tdtt|t|\}}td|td|tdt t d|d d} t|j | dt|tqdS) z Prints the list or rules which match to `expr`. Parameters ========== expr : integrand expression var : variable of integration zRule matching: z On line:  zPattern matching: z ^\s*rule(\d+)rN) r.matchermatchrr/inspectZ getsourcefileZgetsourcelinesjoinr[regrouppatterns) rSr^r*rkZmiterZfunecodelinenoZpattnor+r+r,get_matching_rule_definitions   ru)F)Frc)'Zsympy.externalrZsympy.utilities.decoratorrZ sympy.corerrZsympyrrrr r r r Zsympy.functionsr rWrmrorrrrZ%sympy.integrals.rubi.utility_functionrrrZ!sympy.utilities.matchpy_connectorrrr-rQr.rTrZrbr]rur+r+r+r,s6 $   44