o *ήcd @snddlmZddlmZddlmZmZddlmZddl m Z ddl m Z ddl mZddlmZdd lmZdd lmZdd lmZdd lZdd lZdd lmZedZerddlmZmZddlm Z m!Z!m"Z"ddl#m$Z$m%Z%eddddZ&e!eZ'GdddZ(eddddZ)eddddZ*eddd$ddZ+eddd%d d!Z,eddd"d#Z-d S)&) import_module)doctest_depends_on)IntegerFloat)Add)Function)Mul)E)Pow)S)Integral)expN)powsimpmatchpy)ManyToOneReplacerManyToOneMatcher)rubi_exprubi_unevaluated_expr process_trig)op_iterop_len)r)modulescCsddlm}ddlm}ddlm}ddlm}ddlm }ddl m }ddl m }dd lm}dd lm}dd lm} dd lm} dd lm} ddlm} ddlm} ddlm}ddlm}ddl m!}g}||7}||7}||7}||7}||7}||7}||7}||7}||7}||7}|| 7}|| 7}|| 7}|| 7}|| 7}||7}||7}t"|}||fS)a9 Returns rubi ManyToOneReplacer by adding all rules from different modules. Uncomment the lines to add integration capabilities of that module. Currently, there are parsing issues with special_function, derivative and miscellaneous_integration. Hence they are commented. r)integrand_simplification)linear_products)quadratic_products)binomial_products)trinomial_products)miscellaneous_algebraic) exponential) logarithms)sine)tangent)secant)miscellaneous_trig) inverse_trig) hyperbolic)inverse_hyperbolic)special_functions)miscellaneous_integration)#3sympy.integrals.rubi.rules.integrand_simplificationr*sympy.integrals.rubi.rules.linear_productsr-sympy.integrals.rubi.rules.quadratic_productsr,sympy.integrals.rubi.rules.binomial_productsr-sympy.integrals.rubi.rules.trinomial_productsr2sympy.integrals.rubi.rules.miscellaneous_algebraicr&sympy.integrals.rubi.rules.exponentialr%sympy.integrals.rubi.rules.logarithmsrsympy.integrals.rubi.rules.siner "sympy.integrals.rubi.rules.tangentr!!sympy.integrals.rubi.rules.secantr"-sympy.integrals.rubi.rules.miscellaneous_trigr#'sympy.integrals.rubi.rules.inverse_trigr$%sympy.integrals.rubi.rules.hyperbolicr%-sympy.integrals.rubi.rules.inverse_hyperbolicr&,sympy.integrals.rubi.rules.special_functionsr'4sympy.integrals.rubi.rules.miscellaneous_integrationr(r)rrrrrrrrr r!r"r#r$r%r&r'r(rulesrubir<D/tmp/pip-target-vg8gfxp4/lib/python/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=rCXs  zLoadRubiReplacer.__new__cCs*|jdur|jSt\}}||_||_|SN)rDr>rE)selfr;r:r<r<r=loadds  zLoadRubiReplacer.loadcCLddl}|}t|d}|||WddS1swYdSNrwb)picklerJopendump)rIfilenamerNr;foutr<r<r= to_picklel  "zLoadRubiReplacer.to_picklecCrKrL)dillrJrOrP)rIrQrUr;rRr<r<r=to_dillrrTzLoadRubiReplacer.to_dillcCHddl}t|d}|||_Wd|jS1swY|jSNrrb)rNrOrJrD)rIrQrNfinr<r<r= from_picklex  zLoadRubiReplacer.from_picklecCrWrX)rUrOrJrD)rIrQrUrZr<r<r= from_dill~r\zLoadRubiReplacer.from_dill) __name__ __module__ __qualname____doc__rArCrJrSrVr[r]r<r<r<r=r?Qs  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) )has_Ereplacer )exprr<r<r=process_final_integrals  rfcCs\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) ) isinstancerargsr rsym_expappendr)relst_pow lst_non_powir<r<r= rubi_powsimps    rnFcCst}|tt}t|}t|}t|tt t t fr"t ||St|t r=d}|jD] }||t||7}q,t|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?rJrdrirrrnrgintrfloatrr rrhr rfutil_rubi_integrate)revar showstepsr;resultsexr<r<r=rubi_integrates     rv csXtt|}|tt}t|D]}|ddfdd}||kr)|Sq|S)NcSs t|tSrH)rgr xr<r<r=s z%util_rubi_integrate..csj|ddS)Nrw) max_count)rdrxr;r<r=rzs)r?rJrrdrirrange)rersmax_looprmrtr<r|r=rqs    rqc 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?matchermatchr r@inspect getsourcefilegetsourcelinesjoinroregrouppatterns) rerrr;rmiterfunecodelinenopattnor<r<r=get_matching_rule_definitions   r)F)Frw).sympy.externalrsympy.utilities.decoratorr sympy.corerrsympy.core.addrsympy.core.functionrsympy.core.mulrsympy.core.numbersr sympy.core.powerr sympy.core.singletonr sympy.integrals.integralsr sympy.functionsr rirrsympy.simplify.powsimprrrr%sympy.integrals.rubi.utility_functionrrr!sympy.utilities.matchpy_connectorrrr>rcr?rfrnrvrqrr<r<r<r=sB           44