ó ~9­\c@sňddlmZedƒZddlmZddlmZmZddlZddl Z ddl m Z er|ddlm Z m Z mZmZmZmZddl mZmZmZmZmZmZmZmZdd lmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;m<Z<m=Z=m>Z>m?Z?m@Z@mAZAmBZBmCZCmDZDmEZEmFZFmGZGdd lHmIZImJZJmKZKmLZLmMZMmNZNmOZOdd lPmQZQmRZRed dfƒd „ƒZSeNeƒZTedƒZUeSƒ\ZVZWZXnd„ZYd„ZZd„Z[ed dfƒe\d„ƒZ]ed dfƒe\d„ƒZ^ed dfƒd„ƒZ_dS(i˙˙˙˙(t import_moduletmatchpy(tdoctest_depends_on(tIntegertFloatN(tpowsimp(t OperationtCommutativeOperationtAssociativeOperationtManyToOneReplacertOneIdentityOperationtCustomConstraint(tPowtAddtIntegraltBasictMultStFunctiontE(,tlogtsintcosttantcottcsctsectsqrtterftexptgammatacoshtasinhtatanhtacothtacschtasechtcoshtsinhttanhtcothtsechtcschtatantacsctasintacottacostasectfresnelstfresnelcterfcterfitEit uppergammatpolylogtzetat factorialt polygammatdigammatlitexpinttLambertWtloggamma(tGammatrubi_exptrubi_logt ProductLogt PolyGammatrubi_unevaluated_exprt process_trig(top_itertop_lentmodulescCsEddlm}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}g}|||ƒ7}|||ƒ7}|||ƒ7}|||ƒ7}|||ƒ7}|||ƒ7}|||ƒ7}|||ƒ7}|||ƒ7}|||ƒ7}|| |ƒ7}|| |ƒ7}|| |ƒ7}|| |ƒ7}|| |ƒ7}|||ƒ7}|||ƒ7}t"|Œ}|||fS(s9 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. i˙˙˙˙(tintegrand_simplification(tlinear_products(tquadratic_products(tbinomial_products(ttrinomial_products(tmiscellaneous_algebraic(t exponential(t logarithms(tsine(ttangent(tsecant(tmiscellaneous_trig(t inverse_trig(t hyperbolic(tinverse_hyperbolic(tspecial_functions(tmiscellaneous_integration(#t3sympy.integrals.rubi.rules.integrand_simplificationRJt*sympy.integrals.rubi.rules.linear_productsRKt-sympy.integrals.rubi.rules.quadratic_productsRLt,sympy.integrals.rubi.rules.binomial_productsRMt-sympy.integrals.rubi.rules.trinomial_productsRNt2sympy.integrals.rubi.rules.miscellaneous_algebraicROt&sympy.integrals.rubi.rules.exponentialRPt%sympy.integrals.rubi.rules.logarithmsRQtsympy.integrals.rubi.rules.sineRRt"sympy.integrals.rubi.rules.tangentRSt!sympy.integrals.rubi.rules.secantRTt-sympy.integrals.rubi.rules.miscellaneous_trigRUt'sympy.integrals.rubi.rules.inverse_trigRVt%sympy.integrals.rubi.rules.hyperbolicRWt-sympy.integrals.rubi.rules.inverse_hyperbolicRXt,sympy.integrals.rubi.rules.special_functionsRYt4sympy.integrals.rubi.rules.miscellaneous_integrationRZR (RJRKRLRMRNRORPRQRRRSRTRURVRWRXRYRZtrulest rules_appliedtrubi((s8lib/python2.7/site-packages/sympy/integrals/rubi/rubi.pyt rubi_objectsL  t IntegratecCsktjtdƒdkrtStdtdko^tdko^tdko^tdknrgtSdS(Ni˙˙˙˙iiţ˙˙˙iý˙˙˙iü˙˙˙iű˙˙˙(RmtcounttFalsetTrue(((s8lib/python2.7/site-packages/sympy/integrals/rubi/rubi.pyt _has_cycleMsFcCsL|jtƒr$|jttƒ}n|jtƒrH|jttƒ}n|S(sű When there is recursion for more than 10 rules or in total 20 rules have been applied rubi returns `Integrate` in order to stop any further matching. After complete integration, Integrate needs to be replaced back to Integral. Also rubi's `exp` need to be replaced back to sympy's general `exp`. Examples ======== >>> from sympy import Function, E >>> from sympy.integrals.rubi.rubi import process_final_integral >>> from sympy.integrals.rubi.utility_function import rubi_unevaluated_expr >>> Integrate = Function("Integrate") >>> from sympy.abc import a, x >>> _E = rubi_unevaluated_expr(E) >>> process_final_integral(Integrate(a, x)) Integral(a, x) >>> process_final_integral(_E**5) exp(5) (thasRptreplaceRt_ER(texpr((s8lib/python2.7/site-packages/sympy/integrals/rubi/rubi.pytprocess_final_integralSs cCs‚g}g}t|tƒr~xF|jD];}t|tttfƒrS|j|ƒq%|j|ƒq%Wtt|Œƒt|ŒS|S(s: 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.rubi import rubi_powsimp >>> from sympy.abc import a, b, x >>> rubi_powsimp(x**a*x**b) x**(a+b) (t isinstanceRtargsR Rtsym_exptappendR(Rxtlst_powt lst_non_powti((s8lib/python2.7/site-packages/sympy/integrals/rubi/rubi.pyt rubi_powsimpnscCsî|jttƒ}gt(t|ƒ}t|ƒ}t|ttfƒs[t|t t fƒrit |ƒ|St|t ƒrĆd}x;|j D]0}gt(|tjt||ƒƒ7}gt(qˆWt|ƒStjt||ƒddƒ}t|ƒS(sW 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. it max_counti (RvR|RRmRFRRztintRtfloatRRR R{RnRRy(Rxtvart showstepstresultstex((s8lib/python2.7/site-packages/sympy/integrals/rubi/rubi.pytrubi_integrate‡s  *  cCsŘt|ƒ}|jttƒ}t|ttfƒsHt|ttfƒrVt |ƒ|St|t ƒrrt ||ƒSt t ƒdkrŻtƒsŸt t ƒdkrŻt||ƒSntjt||ƒddƒ}gt (|S(Ni iR‚(RFRvR|RRzRƒRR„RRR R‰tlenRmRtRpRnR(RxR…R†R‡((s8lib/python2.7/site-packages/sympy/integrals/rubi/rubi.pytutil_rubi_integrate§s * c CsÁtj}|jt||ƒƒ}x™|D]‘\}}dGHtj|ƒGHtj|ƒ\}}d|fGHdj|ƒGHdGHtt jd|dƒj dƒƒ}|j |dGH|GHd GHq(WdS( sš Prints the list or rules which match to `expr`. Parameters ========== expr : integrand expression var : variable of integration sRule matching: s On line: s sPattern matching: s ^\s*rule(\d+)iiN(( RntmatchertmatchRtinspectt getsourcefiletgetsourcelinestjoinRƒtretgrouptpatterns( RxR…RŒtmitertfuntetcodetlinenotpattno((s8lib/python2.7/site-packages/sympy/integrals/rubi/rubi.pytget_matching_rule_definitionśs  %(`tsympy.externalRRtsympy.utilities.decoratorRt sympy.coreRRRŽR’tsympyRRRRR R R R R RRRRRRtsympy.functionsRRRRRRRRRRR|RRR R!R"R#R$R%R&R'R(R)R*R+R,R-R.R/R0R1R2R3R4R5R6R7R8R9R:R;R<R=R>R?t%sympy.integrals.rubi.utility_functionR@RARBRCRDRERFt!sympy.utilities.matchpy_connectorRGRHRoRwRpRnRmRlRtRyRRrR‰R‹R›(((s8lib/python2.7/site-packages/sympy/integrals/rubi/rubi.pyts0 .:˙43