~9\c@s\dZddlmZddlmZddlmZmZmZm Z m Z ddl m Z ddl m Z dd d d d d ddddddddddddddddddd d!d"d#d$d%hZd&d'hZd(d)d*hZid+d,6Zid-d-6d.d.6d/d/6d0d06d1d16d2d26d3d36d4d56d6d66d7d76d8d86d9d96d:d:6d;d;6d<d<6d=d=6d>d>6d?d?6d@dA6dBdB6dBdC6dDdD6dEdE6dFdF6dGdG6dHdH6dIdJ6dKdK6dLdL6ZidMdN6dOdP6dMdQ6ZdRZdSZdTe fdUYZdVefdWYZx%ejD]ZeedXeeq*Wx"eD]ZeedXeeqOWdYZdZjZgejD]$\ZZeekreef^qZ e!e id[d[6Z"idOdP6Z#d\efd]YZ$x%e$jD]Zee$dXeeqWx"e#D]Zee$dXeeq!Wd^jZ%gejD]$\ZZee%kr|eef^qXZ&e!e&i d_d-6d`d.6dad/6dbd06dcd16ddd26ded36dfdf6d[d[6Z'dgefdhYZ(x%e(jD]Zee(dXeeqWx%e(j)D]Zee(dXeeqWid8d86d9d96didj6dkdl6dmdn6dodp6d<d<6d>d>6dqdA6drds6dtdu6dvdw6dxdy6dzd{6d|d}6d~d6dd6dd6dd6Z*idd6dOdP6dMdQ6Z+de(fdYZ,x%e,jD]Zee,dXeeqWx%e,j)D]Zee,dXeeq$WdefdYZ-dS(sy Python code printers This module contains python code printers for plain python as well as NumPy & SciPy enabled code. i(t defaultdict(tchain(tStNumbertSymboltMultAddi(t precedence(t CodePrintertandtastasserttbreaktclasstcontinuetdeftdelteliftelsetexcepttfinallytfortfromtglobaltiftimporttintistlambdatnottortpasstraisetreturnttrytwhiletwithtyieldtNonetexectprinttFalsetnonlocaltTruetabstAbstacostacoshtasintasinhtatantatan2tatanhtceiltceilingtcostcoshterfterfctexptexpm1t factorialtfloortgammathypottlgammatloggammatlogtlntlog10tlog1ptlog2tsintsinhtsqrttSqrtttanttanhtetExp1tpitPitEcsPj|jj}djdj|ddjtfd|jS(Ns{name}({args})tnametargss, cs j|S(N(t_print(targ(tself(s4lib/python2.7/site-packages/sympy/printing/pycode.pytFt(tknown_functionst __class__t__name__tformatt_module_formattjointmapRT(RWtexprtknown((RWs4lib/python2.7/site-packages/sympy/printing/pycode.pyt_print_known_funcCscCs |j|jj}|j|S(N(tknown_constantsR[R\R^(RWRaRb((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt_print_known_constIstAbstractPythonCodePrinterc BseZdZdZdZejeZd,Z dZ e e ejgejD]\ZZedef^qOZdejDZidd6dd6dd6Ze ejd id d d ed edeZd,dZdZedZdZdZdZ dZ!dZ"dZ#dZ$dZ%dZ&dZ'dZ(dZ)dZ*dZ+d Z,d!Z-d"Z.d#Z/Z0Z1Z2Z3Z4Z5Z6d$Z7d%Z8d&Z9d'Z:d(Z;d)Z<d*Z=d+Z>RS(-t _pythoncodetPythontpython3s smath.cCs#i|]\}}d||qS(smath.((t.0tktv((s4lib/python2.7/site-packages/sympy/printing/pycode.pys Ys R RRtuser_functionst precisionitinlinetfully_qualified_modulestcontractcCswtt|j|tt|_t|j|p7ijdi|_ t|j |p^ijdi|_ dS(NRmtuser_constants( tsuperRft__init__Rtsettmodule_importstdictt_kftgetRZt_kcRd(RWtsettings((s4lib/python2.7/site-packages/sympy/printing/pycode.pyRtds cCsd||fS(Ns%s = %s((RWRStvalue((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt_declare_number_constlscCs|jd}|rOt|dkrO|jdj|d j|dn|jdr`|S|jddjddjddSdS(Nt.iiRpt(it[(tsplittlenRvR_taddt _settings(RWtfqntregistertparts((s4lib/python2.7/site-packages/sympy/printing/pycode.pyR^os ( cCs|S(N((RWtlines((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt _format_codeyscCs dj|S(Ns{}(R](RWt codestring((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt_get_statement|scCs dj|S(Ns # {0}(R](RWttext((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt _get_commentscCs^t|dkr#|j|dSd|j||j||d |j|dfSdS(s This method expands a fold on binary operations. ``functools.reduce`` is an example of a folded operation. For example, the expression `A + B + C + D` is folded into `((A + B) + C) + D` iis %s(%s, %s)iN(RRUR^t_expand_fold_binary_op(RWtopRT((s4lib/python2.7/site-packages/sympy/printing/pycode.pyRs  cCsqt|dkr#|j|dSt|}|d}d|j||j|| |j||fSdS(s This method expands a reductin on binary operations. Notice: this is NOT the same as ``functools.reduce``. For example, the expression `A + B + C + D` is reduced into: `(A + B) + (C + D)` iiis %s(%s, %s)N(RRUR^t_expand_reduce_binary_op(RWRRTtNtNhalf((s4lib/python2.7/site-packages/sympy/printing/pycode.pyRs   cCsf|j}d}d}d|D}g}xo|D]g}g} xKt|D]=} ||krt| j||n | j||d7}qNW|j| q5Wi} g} g} x|D]} x| D]w}|| krt|}|| |s it,i(t _get_letter_generator_for_einsumtrangetappendtnext(RWtsubrankstcontraction_indicestletterstcontraction_stringtcountertdtindicestrank_argtlindicesRtmappingt letters_freet letters_dumRtl((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt_get_einsum_strings<              cCsdS(Ns float('nan')((RWRa((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt _print_NaNscCsdS(Ns float('inf')((RWRa((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt_print_InfinityscCsdS(Ns float('-inf')((RWRa((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt_print_NegativeInfinityscCs |j|S(N(R(RWRa((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt_print_ComplexInfinityscs1t|djtfd|jS(Ns {0} % {1}csj|S(N(t parenthesize(tx(tPRECRW(s4lib/python2.7/site-packages/sympy/printing/pycode.pyRXRY(RR]R`RT(RWRa((RRWs4lib/python2.7/site-packages/sympy/printing/pycode.pyt _print_Mods cCsg}d}x|jD]}|j}|j}|dkrJ|jdn|jd|j|j||jd|jd|j|j||jd|d7}qW|d }|ddkr|d }|jdn |jd d j|S( NiRt)s if s else iiR+is else None)RY(RTRatcondRRUR_(RWRatresultRRVRNtc((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt_print_Piecewises(          cCsidd6dd6dd6dd6d d 6d d 6}|j|kr|j|j}|j|j}d jd|jd|d|Stt|j|S(s.Relational printer for Equality and Unequalitytequals==t not_equals!=tlesstt greater_equals>=s({lhs} {op} {rhs})Rtlhstrhs(trel_opRURRR]RsRft_print_Relational(RWRaRRR((s4lib/python2.7/site-packages/sympy/printing/pycode.pyRs cCs&ddlm}|j|j|S(Ni(t Piecewise(t$sympy.functions.elementary.piecewiseRRUtrewrite(RWRaR((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt _print_ITE scsDfd|jD}djdj|jddj|S(Nc 3sQ|]G\}}}djdj|dj|dj|VqdS(sfor {i} in range({a}, {b}+1)RtatbN(R]RU(RjRRR(RW(s4lib/python2.7/site-packages/sympy/printing/pycode.pys ss"(builtins.sum({function} {loops}))tfunctiontloopst (tlimitsR]RURR_(RWRaR((RWs4lib/python2.7/site-packages/sympy/printing/pycode.pyt _print_Sums    cCsdS(Nt1j((RWRa((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt_print_ImaginaryUnitscCs>|jj}|jj||}d||j|jfS(Ns%s(%s)(R[R\RZRyRUttolist(RWRaRStfunc((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt_print_MatrixBases cCs |j|S(N(R(RWRa((s4lib/python2.7/site-packages/sympy/printing/pycode.pyRX+RYcCs0djg|jdD]}|j|^qS(Ns (R_Rttab(RWRtline((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt_indent_codestring-sc sdjtfd|j}djdj|jddjg|jD]}j|j^qOdj|S(Ns cs j|S(N(RU(RV(RW(s4lib/python2.7/site-packages/sympy/printing/pycode.pyRX1RYs def {name}({parameters}): {body}RSt parameterss, tbody( R_R`RR]RURSRtsymbolR(RWtfdRtvar((RWs4lib/python2.7/site-packages/sympy/printing/pycode.pyt_print_FunctionDefinition0s $ 1csOdjtfd|j}djdj|jdj|S(Ns cs j|S(N(RU(RV(RW(s4lib/python2.7/site-packages/sympy/printing/pycode.pyRX9RYswhile {cond}: {body}RR(R_R`RR]RUt conditionR(RWtwhlR((RWs4lib/python2.7/site-packages/sympy/printing/pycode.pyt _print_While8s$ cCs,d|j|jj|j|jjfS(Ns%s = %s(RUtvariableRR|(RWtdecl((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt_print_Declaration?scCs|j\}d|j|S(Ns return %s(RTRU(RWtretRV((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt _print_ReturnEs csdjtfd|j}|jdkrTdjj|j|}n|jdkr|dj|j7}nd|S(Ns, cs j|S(N(RU(RV(RW(s4lib/python2.7/site-packages/sympy/printing/pycode.pyRXJRYs {0} % ({1})s , file=%ss print(%s)(R_R`t print_argst format_stringR&R]RUtfile(RWtprntR((RWs4lib/python2.7/site-packages/sympy/printing/pycode.pyt _print_PrintIs$cCsXt|jdkr"|jdSt|jdkrD|jdS|j|jSdS(Ntstdouts sys.stdouttstderrs sys.stderr(tstrRSR^RU(RWtstrm((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt _print_StreamRs   cCsdS(NR&((RWRV((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt_print_NoneTokenZsN(?R\t __module__t printmethodtlanguagetstandardt _kw_py2and3tuniont _kw_only_py3treserved_wordsR&tmodulesRRwRt_known_functionstitemst_known_functions_mathRkRlRxt_known_constants_mathRzt _operatorsRt_default_settingsR+R)RtR}R^RRRRRRRRRRRRRRRRRt_print_SparseMatrixt_print_MutableSparseMatrixt_print_ImmutableSparseMatrixt _print_Matrixt_print_DenseMatrixt_print_MutableDenseMatrixt_print_ImmutableMatrixt_print_ImmutableDenseMatrixRRRRRRRR(((s4lib/python2.7/site-packages/sympy/printing/pycode.pyRfNs^ 5          #          %      tPythonCodePrintercBseZdZdZRS(cCs/djd|jdd|j|jdS(Ns"(0.0 if {e} == 0 else {f}(1, {e}))tfs math.copysignRNi(R]R^RURT(RWRN((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt _print_sign`s cCs.t|}|jd|j|jd|S(NRi(RRRRT(RWRaR((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt _print_Notds (R\RRR(((s4lib/python2.7/site-packages/sympy/printing/pycode.pyR^s s _print_%scKst|j|S(s Converts an expr to a string of Python code Parameters ========== expr : Expr A SymPy expression. fully_qualified_modules : bool Whether or not to write out full module names of functions (``math.sin`` vs. ``sin``). default: ``True``. Examples ======== >>> from sympy import tan, Symbol >>> from sympy.printing.pycode import pycode >>> pycode(tan(Symbol('x')) + 1) 'math.tan(x) + 1' (Rtdoprint(RaR{((s4lib/python2.7/site-packages/sympy/printing/pycode.pytpycodepss log1p log2tsignt MpmathPrintercBseZdZdZeeejgejD]\Z Z e de f^q.Z dZ dZ dZdZdZdZRS( sH Lambda printer for mpmath which maintains precision for floats t _mpmathcodesmpmath.cCs=tttt|j}djd|jdd|S(Ns{func}({args})Rs mpmath.mpfRT(RttupleR`tintt_mpf_R]R^(RWRNRT((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt _print_FloatscCs"dj|jd|j|jS(Ns{0}({1})/{0}({2})s mpmath.mpf(R]R^tptq(RWRN((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt_print_Rationals cCsHdj|jd|j|jd|j|jd|jdS(Ns{0}({1}, {2}, {3})smpmath.gammainciis mpmath.inf(R]R^RURT(RWRN((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt_print_uppergammas  cCs<dj|jd|j|jd|j|jdS(Ns{0}({1}, 0, {2})smpmath.gammaincii(R]R^RURT(RWRN((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt_print_lowergammas cCs)dj|jd|j|jdS(Ns{0}({1})/{0}(2)s mpmath.logi(R]R^RURT(RWRN((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt _print_log2scCs)dj|jd|j|jdS(Ns {0}({1}+1)s mpmath.logi(R]R^RURT(RWRN((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt _print_log1ps(R\Rt__doc__RRwRRRt_known_functions_mpmathRkRlRxRRRRRR(((s4lib/python2.7/site-packages/sympy/printing/pycode.pyR s 5    s!erf erfc factorial gamma loggammatarccostarccoshtarcsintarcsinhtarctantarctan2tarctanhtexp2t NumPyPrintercBsIeZdZdZeeejjge jD]\Z Z e de f^q1Zde jDZ dZdZdZdZdZd Zd Zd Zd Zd ZdZdZdZdZdZdZdZdZdZ dZ!dZ"dZ#dZ$dZ%RS(sa Numpy printer which handles vectorized piecewise functions, logical operators, etc. t _numpycodesnumpy.cCs#i|]\}}d||qS(snumpy.((RjRkRl((s4lib/python2.7/site-packages/sympy/printing/pycode.pys s cs,d}dj|jfd|DS(s+General sequence printer: converts to tuples, s({},)c3s|]}j|VqdS(N(RU(Rjtitem(RW(s4lib/python2.7/site-packages/sympy/printing/pycode.pys s(R]R_(RWtseqt delimiter((RWs4lib/python2.7/site-packages/sympy/printing/pycode.pyt _print_seqscs|jdtdk rc|jd|jdg}djdjfd|DSdjdjfd|jDS(sMatrix multiplication printeriis({0})s).dot(c3s|]}j|VqdS(N(RU(RjR(RW(s4lib/python2.7/site-packages/sympy/printing/pycode.pys sc3s|]}j|VqdS(N(RU(RjR(RW(s4lib/python2.7/site-packages/sympy/printing/pycode.pys s(tas_coeff_matricesRR]R_RT(RWRat expr_list((RWs4lib/python2.7/site-packages/sympy/printing/pycode.pyt _print_MatMuls!&cCs<dj|jd|j|jd|j|jdS(sMatrix power printers {0}({1}, {2})snumpy.linalg.matrix_powerii(R]R^RURT(RWRa((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt _print_MatPowscCs)dj|jd|j|jdS(sMatrix inverse printers{0}({1})snumpy.linalg.invi(R]R^RURT(RWRa((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt_print_InversescCsy|j\}}|jddkr.|j}n|jddkrM|j}nd|jd|j||j|fS(Niis %s(%s, %s)s numpy.dot(RTtshapetTR^RU(RWRatarg1targ2((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt_print_DotProducts   csrdjdjfd|jD}djdjfd|jD}djjd||S(sPiecewise function printers[{0}]Rc3s!|]}j|jVqdS(N(RURa(RjRV(RW(s4lib/python2.7/site-packages/sympy/printing/pycode.pys sc3s!|]}j|jVqdS(N(RUR(RjRV(RW(s4lib/python2.7/site-packages/sympy/printing/pycode.pys ss {0}({1}, {2}, default=numpy.nan)s numpy.select(R]R_RTR^(RWRatexprstconds((RWs4lib/python2.7/site-packages/sympy/printing/pycode.pyR s++cCsidd6dd6dd6dd6d d 6d d 6}|j|kr|j|j}|j|j}d jd|jd||jd|d|Stt|j|S(s.Relational printer for Equality and UnequalityRs==Rs!=RRRs<=RRRs>=s{op}({lhs}, {rhs})Rsnumpy.RR( RRURRR]R^RsR#R(RWRaRRR((s4lib/python2.7/site-packages/sympy/printing/pycode.pyRs # cs5djjddjfd|jDS(sLogical And printers{0}.reduce(({1}))snumpy.logical_andRc3s|]}j|VqdS(N(RU(RjR(RW(s4lib/python2.7/site-packages/sympy/printing/pycode.pys ,s(R]R^R_RT(RWRa((RWs4lib/python2.7/site-packages/sympy/printing/pycode.pyt _print_And'scs5djjddjfd|jDS(sLogical Or printers{0}.reduce(({1}))snumpy.logical_orRc3s|]}j|VqdS(N(RU(RjR(RW(s4lib/python2.7/site-packages/sympy/printing/pycode.pys 3s(R]R^R_RT(RWRa((RWs4lib/python2.7/site-packages/sympy/printing/pycode.pyt _print_Or.scs5djjddjfd|jDS(sLogical Not printers{0}({1})snumpy.logical_notRc3s|]}j|VqdS(N(RU(RjR(RW(s4lib/python2.7/site-packages/sympy/printing/pycode.pys :s(R]R^R_RT(RWRa((RWs4lib/python2.7/site-packages/sympy/printing/pycode.pyR5scs5djjddjfd|jDS(Ns {0}(({1}))s numpy.aminRc3s|]}j|VqdS(N(RU(RjR(RW(s4lib/python2.7/site-packages/sympy/printing/pycode.pys =s(R]R^R_RT(RWRa((RWs4lib/python2.7/site-packages/sympy/printing/pycode.pyt _print_Min<scs5djjddjfd|jDS(Ns {0}(({1}))s numpy.amaxRc3s|]}j|VqdS(N(RU(RjR(RW(s4lib/python2.7/site-packages/sympy/printing/pycode.pys @s(R]R^R_RT(RWRa((RWs4lib/python2.7/site-packages/sympy/printing/pycode.pyt _print_Max?scCsN|jdkr4dj|jd|j|jStt|j|SdS(Ng?s{0}({1})s numpy.sqrt(R;R]R^RUtbaseRsR#t _print_Pow(RWRa((s4lib/python2.7/site-packages/sympy/printing/pycode.pyR:Bs%cCs'd|jd|j|jdfS(Ns%s(%s)s numpy.anglei(R^RURT(RWRa((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt _print_argHscCs'd|jd|j|jdfS(Ns%s(%s)s numpy.imagi(R^RURT(RWRa((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt _print_imKscs5djddjtfd|jfS(Ns%s(%s)s numpy.mods, cs j|S(N(RU(RV(RW(s4lib/python2.7/site-packages/sympy/printing/pycode.pyRXPRY(R^R_R`RT(RWRa((RWs4lib/python2.7/site-packages/sympy/printing/pycode.pyRNscCs'd|jd|j|jdfS(Ns%s(%s)s numpy.reali(R^RURT(RWRa((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt _print_reRscCs.d|jd|j|jdtjfS(Ns%s(%s)s numpy.sinci(R^RURTRRQ(RWRa((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt _print_sincUscCsV|jj|jjd}|dkr9|jd}nd||j|jfS(Ns numpy.arrays%s(%s)(RZRyR[R\R&R^RUR(RWRaR((s4lib/python2.7/site-packages/sympy/printing/pycode.pyRXs cCszgt|jD]D\}}|j|dd|d|dffD] }|^qEq}d|jddj|fS(Ns[%i, %i]iis%s(%s)s numpy.einsums, (t enumerateRTRUR^R_(RWRaRRVRt array_list((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt _print_CodegenArrayTensorProduct^s>cCs@ddlm}|j}|j}|s5|j|St||r3d}d|D}g}xr|jD]g}g} xKt|D]=} ||kr| j||n | j||d7}qW|j| qjWgt |j |D]%\} } d|j| | f^q} d|j dd j | fSt dS( Ni(tCodegenArrayTensorProducticSs,i|]"}|D]}t||qqS((R(RjRR((s4lib/python2.7/site-packages/sympy/printing/pycode.pys ks is%s, %ss%s(%s)s numpy.einsums, (tsympy.codegen.array_utilsRBRaRRUt isinstanceRRRtzipRTR^R_tNotImplementedError(RWRaRBR9RRRRRRRRVtindtelems((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt_print_CodegenArrayContractioncs,     > cCst|j}t|dkr*tnt|ddkrItnd|jd|j|j|dd|ddfS(Niiis%s(%s, 0, axis1=%s, axis2=%s)snumpy.diagonal(tlisttdiagonal_indicesRRFR^RURa(RWRaRK((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt_print_CodegenArrayDiagonal}s    cCs9d|jd|j|j|j|jjdfS(Ns %s(%s, %s)snumpy.transposei(R^RURat permutationRT(RWRa((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt_print_CodegenArrayPermuteDimss cCs|jd|jS(Ns numpy.add(RRT(RWRa((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt!_print_CodegenArrayElementwiseAdds(&R\RRRRwRRRxRt_known_functions_numpyRkRlRRzR(R+R,R-R2RRR5R6RR7R8R:R;R<RR=R>RRARIRLRNRO(((s4lib/python2.7/site-packages/sympy/printing/pycode.pyR#s< 5                     tjvtbesseljtyvtbesselytivtbesselitkvtbesselktgammalntpsitdigammatpochtRisingFactorialt eval_jacobitjacobiteval_gegenbauert gegenbauert eval_chebytt chebyshevtt eval_chebyut chebyshevut eval_legendretlegendret eval_hermitethermitet eval_laguerretlaguerreteval_genlaguerretassoc_laguerret golden_ratiot GoldenRatiot SciPyPrintercBs}eZeeejjgejD]\ZZ ede f^q%Zde jDZ dZ e Z dZRS(sscipy.special.cCs#i|]\}}d||qS(sscipy.constants.((RjRkRl((s4lib/python2.7/site-packages/sympy/printing/pycode.pys s c Csggg}}}xJ|jjD]9\\}}}|j||j||j|q$Wdjd|jdd|d|d|d|jS(Ns){name}({data}, ({i}, {j}), shape={shape})RSsscipy.sparse.coo_matrixtdataRRR.(t_smatRRR]R^R.(RWRaRRRqtrRRl((s4lib/python2.7/site-packages/sympy/printing/pycode.pyRs"   cCsOdj|jd|j|jd|j|jd|j|jdS(Ns{0}({2}, {1}, {3})sscipy.special.lpmviii(R]R^RURT(RWRa((s4lib/python2.7/site-packages/sympy/printing/pycode.pyt_print_assoc_legendres  (R\RRwRR#RxRt_known_functions_scipy_specialRkRlt _known_constants_scipy_constantsRzRRRt(((s4lib/python2.7/site-packages/sympy/printing/pycode.pyRps 5 t SymPyPrintercBs6eZdeejejDZdZRS(cCs#i|]\}}d||qS(ssympy.((RjRkRl((s4lib/python2.7/site-packages/sympy/printing/pycode.pys s csa|jjpd}dj||r*dnd|jjdjtfd|jfS(NRYs%s(%s)R~s, cs j|S(N(RU(RV(RW(s4lib/python2.7/site-packages/sympy/printing/pycode.pyRXRY(RRR^R\R_R`RT(RWRatmod((RWs4lib/python2.7/site-packages/sympy/printing/pycode.pyt_print_Functions)(R\RRRRRRxRy(((s4lib/python2.7/site-packages/sympy/printing/pycode.pyRws  N(.Rt collectionsRt itertoolsRt sympy.coreRRRRRRt codeprinterRRt _kw_only_py2RRRRRcReRfRRxRktsetattrR Rt_not_in_mpmathRRlt _in_mpmathRwRt_known_constants_mpmathR t _not_in_numpyt _in_numpyRPR#RzRuRvRpRw(((s4lib/python2.7/site-packages/sympy/printing/pycode.pyts(          7   1  7