~9\ce@sdZddlZddlZddlZddlmZmZmZmZddl m Z ddl m Z m Z ddlmZde fdYZd Zed d d d dddddddddddddddddddd d!d d"d#d$d#d%d&d'd(d)d*d+d,d-d.d/d0d1d2d3d4d5d6d7d6d8d9d:d9d;d<d=d<d>d?d@dAdBdCdDdEdFdGdHdIdJdKdLdMdNdOdPdQdRdSdTdUdVdWdXdYdZd[d\d]d^d_d`dadbdcdddcdedf2Zidgdh6didj6Zidkdl6dmdn6Zdodpdqdrdsdtdudvdwdxdydzd{d|d}d~dddddddddddwdyddgZdZdZidZidZgddZddZegedZgdZ dZ!dZ"dZ#dZ$dZ%dZ&dZ'dZ(dddZ)dS(s Parser for FullForm[Downvalues[]] of Mathematica rules. This parser is customised to parse the output in MatchPy rules format. Multiple `Constraints` are divided into individual `Constraints` because it helps the MatchPy's `ManyToOneReplacer` to backtrack earlier and improve the speed. Parsed output is formatted into readable format by using `sympify` and print the expression using `sstr`. This replaces `And`, `Mul`, 'Pow' by their respective symbols. Mathematica =========== To get the full form from Wolfram Mathematica, type: ``` ShowSteps = False Import["RubiLoader.m"] Export["output.txt", ToString@FullForm@DownValues@Int] ``` The file ``output.txt`` will then contain the rules in parseable format. References ========== [1] http://reference.wolfram.com/language/ref/FullForm.html [2] http://reference.wolfram.com/language/ref/DownValues.html [3] https://gist.github.com/Upabjojr/bc07c49262944f9c1eb0 iN(tsympifytFunctiontSettSymbol(t string_types(tsstrt StrPrinter(tdebugtRubiStrPrintercBseZdZRS(cCsd|j|jdS(NsNot(%s)i(t_printtargs(tselftexpr((sDlib/python2.7/site-packages/sympy/integrals/rubi/parsetools/parse.pyt _print_Not's(t__name__t __module__R (((sDlib/python2.7/site-packages/sympy/integrals/rubi/parsetools/parse.pyR&scKst|j|S(N(Rtdoprint(R tsettings((sDlib/python2.7/site-packages/sympy/integrals/rubi/parsetools/parse.pyt rubi_printer*stTimestMultPlustAddtPowertPowtLogtlogtExptexptSqrttsqrttCostcostSintsintTanttantCots1/tantcottSecs1/costsectCscs1/sintcsctArcSintasintArcCostacostArcCottacottArcSectasectArcCsctacsctSinhtsinhtCoshtcoshtTanhttanhtCoths1/tanhtcothtSechs1/coshtsechtCschs1/sinhtcschtArcSinhtasinhtArcCoshtacoshtArcTanhtatanhtArcCothtacothtArcSechtasechtArcCschtacschtExpandtexpandtImtimtRetretFlattentflattentPolylogtpolylogtCanceltcancelt TrigExpandt expand_trigtSigntsigntSimplifytsimplifytDefertUnevaluatedExprtIdentitytStSumtSum_doittModuletWithtBlocktNulltNonet_gcdtgcdt_jntjnt ImaginaryIs \[ImaginaryI]t _UseGammas $UseGammat BinomialPartstBinomialDegreetTrinomialPartstGeneralizedBinomialPartstGeneralizedTrinomialPartstPseudoBinomialPartstPerfectPowerTesttSquareFreeFactorTestt*SubstForFractionalPowerOfQuotientOfLinearst"FractionalPowerOfQuotientOfLinearst"InverseFunctionOfQuotientOfLinearstFractionalPowerOfSquareQtFunctionOfLineartFunctionOfInverseLineartFunctionOfTrigtFindTrigFactort FunctionOfLogtPowerVariableExpntFunctionOfSquareRootOfQuadratictSubstForFractionalPowerOfLineartFractionalPowerOfLineartInverseFunctionOfLineartDividestDerivativeDividest TrigSquaret SplitProducttFunctionOfHyperbolictSplitSumcCst|tr3x|D]}t|rtSqWnmt|tdksct|tdkrx:tD]}|jt|rjtSqjWn|tkrtStS(s This function returns whether an expression contains functions which have different return types in diiferent cases. RfRe( t isinstancetlisttcontains_diff_return_typetTruettypeRtf_diff_return_typethastFalse(tati((sDlib/python2.7/site-packages/sympy/integrals/rubi/parsetools/parse.pyRws   0   c Cs[g}|g}tjd|}d}x)|D]!}|dkrDPn|j}|||!jddjddjddj}|jdkr|dkrC|dj|qCn|jdkr|dkr|dj|n|j|d}n>|jdkrC|dj|g|j|ddn|j }q.W|dS( s@ Parses FullForm[Downvalues[]] generated by Mathematica s[\[\],]it,tt]t[iN( RRtfinditerRitstarttreplacetstriptgrouptappendtpoptend( twmexprtouttstackt generatortlast_postmatchtpositiont last_exprt current_pos((sDlib/python2.7/site-packages/sympy/integrals/rubi/parsetools/parse.pytparse_full_forms,    7    cCs4t|ts|S|ddkr`x:|dD]+}|ddkr.d||ddss, s def cons_f{}({}): c3s'|]\}}|kr|VqdS(N((RRR(R(sDlib/python2.7/site-packages/sympy/integrals/rubi/parsetools/parse.pys s( RRRtvaluestnexttitemsRtsettget_free_symbolstjointgenerate_sympy_from_parsedR( tlRt cons_indext cons_dictt cons_importRtrestconsRtct cons_nameR((RsDlib/python2.7/site-packages/sympy/integrals/rubi/parsetools/parse.pyt parse_freeqsD    %   %   c Csd}t|ts[yt|dj|SWnnX||krW|rW|dSn|S|ddkrdjt|dd|d |d |t|d d|d |d |S|dtkr|t|d7}n1|dd kr|r|d 7}n||d7}t|dkr|Sg|dD]$}t|d|d |d |^q*}d|krp|jdn|d7}|dj|7}|d7}|S(s  Parses list into Python syntax. Parameters ========== wild : When set to True, the symbols are replaced as wild symbols. symbols : Symbols already present in the pattern. replace_Int: when set to True, `Int` is replaced by `Integral`(used to parse pattern). RsS({})RitRationals S({})/S({})itwildRt replace_IntitInttIntegralt(s, t)( RRtfloatRRt replacementsRtremoveR(RRRRRRtresult((sDlib/python2.7/site-packages/sympy/integrals/rubi/parsetools/parse.pyRs6    H 5   cCsVt|ts/||kr+|j|n|Sx |D]}t|||}q6W|S(s. Returns free_symbols present in `s`. (RRRR(RRt free_symbolsR((sDlib/python2.7/site-packages/sympy/integrals/rubi/parsetools/parse.pyRJs  c Csg}d}t|tr|ddkri|}t|i}t|dt}t|d|\}}tt|}t|ditdd6tdd6td d 6}|j d j d}|j d j d } t |d t}t |}d j |d j || }|dj ||7}|dj ||7}|dj |j d7}d|fSxZ|D]O} t| trt| |}|j|d|d }qp|j| qpWn||fS(s] Takes care of the case, when a pattern matching has to be done inside a constraint. RitMatchQRRtlocalstOrtAndtNotitsympy_integerss2 def _cons_f_{}({}): return {} s, s0 _cons_{} = CustomConstraint(_cons_f_{}) s8 pat = Pattern(UtilityOperator({}, x), _cons_{}) s= result_matchq = is_match(UtilityOperator({}, x), pat)t result_matchq(RRRRRRRRRR RtsetWCRRtset_matchq_in_constraintR( RRtlstRRRRRtpatternRR((sDlib/python2.7/site-packages/sympy/integrals/rubi/parsetools/parse.pyRXs49    c sttt||g}t|}t|ditdd6tdd6tdd6}|jtdrt||}|ddjt tt|dditdd6tdd6tdd6d t 7nEt |rd jt |d t nd jt |d t |j kr|d7}d j|d j |}d|kr|d7}n|7}|dj|dj|7}dj|} || s(RRRRRRRRRRRRRRRRR( RRRRRtlambda_symbolsRt match_resRR((RsDlib/python2.7/site-packages/sympy/integrals/rubi/parsetools/parse.pyt_divide_constriant{s0 9 _      " c Csg}d}|ddkrx|dD]Z}|ddkr't|||||}|j|d||d7}|d}q'q'WnAt|||||}|j|d||d7}|d}dg} x*|D]"}|dkr| j|qqWdj| ||fS(s Divides multiple constraints into smaller constraints. Parameters ========== s : constraint as list symbols : all the symbols present in the expression RiRiRis, (RRR( RRRRRRRRRR((sDlib/python2.7/site-packages/sympy/integrals/rubi/parsetools/parse.pytdivide_constraints$     cCsWd}tj||}x8|D]0}|j|ddj|d|d}qW|S(s0 Replaces `WC(a, b)` by `WC('a', S(b))` s(WC\((\w+), S\(([-+]?\d)\)\))isWC('{}', S({}))ii(RRRRR(RRRR((sDlib/python2.7/site-packages/sympy/integrals/rubi/parsetools/parse.pyRs  .c Cst|d}d}t}d}t|tdksRt|tdkrxH|jD]:}x_|jD]T}t|trl||krl|dj|jdt|jddt 7}qlqlWt|tdtd fkr |j td  r |}t }q\t|td kr;|jd }t }q\t|jdtd kr\|jd}d j|j |jd |jd}t }q\q\Wn|||fS( s] Functions like `Set`, `With` and `CompoundExpression` has to be taken special care. iRRfRes {} = {}iRtListtCompoundExpressionis {}({}, {})( RRRRR RRRRRRtfunc( ta1tLRRt processedt return_valueRRtC((sDlib/python2.7/site-packages/sympy/integrals/rubi/parsetools/parse.pytprocess_return_types(07:    &cCsjg}t|tr1||kr1|j|n5y+x$|jD]}|t||7}q>WWnnX|S(s4 this function extracts all `Set` functions (RRRR t extract_set(RRRR((sDlib/python2.7/site-packages/sympy/integrals/rubi/parsetools/parse.pyRsc sd}d}t|tdks<t|tdkrd}dj|dj}t|jdtdkrt|jdj}n|jdg}g}x(|jd D]} |t| |7}qW||7}xx|D]p} t| t r/|d j| jdt | jd d t 7}qt| t r|d j| | 7}qqWt|jd td kr|jd } ||7}t| jdt r|d j| jdjd| jdjd 7}n|dj|t | jd d t 7}|||fSt|jd tdkr|jd } t | jdkrtfdg| jD]} t| ^qlDr||7}|dj|t | jdd t 7}qdkr|d7}nt|r8|jdd} |dj| t | jd d t 7}|d7}|d7}n0||7}|djt | jd d t 7}|t | jdd t f}t||} | dr|| dt | d f}n|d7}|d7}ndj|}|||fSt|jd tdks2t|jd tdkr|jd } ||7}|t | d t f}t||} | dr|| dt | d f}n|| d7}|dj|t | d 7}||dfS|jd jtd r|jd jd} ||7}t| jdt r[|d j| jdjd| jdjd 7}n|dj|jd j| jd|jd jd 7}||dfS||7}|dj|t |jd d t 7}|||fSt |d t d|fSdS( s: Replaces `With` and `Module by python functions` RRfRet s def With{}({}):s, iRis {} = {}Rs {} = Symbol('{}')Rs* rubi.append({}) return {}t Conditionic3s|]}|kVqdS(N((Rtj(R(sDlib/python2.7/site-packages/sympy/integrals/rubi/parsetools/parse.pys sRsQ if isinstance(x, (int, Integer, float, Float)): return Falses s s$ try:{} res = {}sE except (TypeError, AttributeError): return Falses if res:s if {}:s return Trues return Falses, CustomConstraint(With{})s return {}({}, {})iN(RiRRRRR RRRRRRRRtallRtstrRRRRR( RRtindext return_typet with_valuet constraintsRRRRRt n_with_valuet return_type1((RsDlib/python2.7/site-packages/sympy/integrals/rubi/parsetools/parse.pyt replaceWiths0  3  5)  8 ,   )   & !   >   !   58  ) cCsd}d}d}g}x|D]} tdj|j| d| ddddkrx| dddj} n| ddj} t| i} t| jdt} t| d | \} } tt | } | d ddkr]t | d d | |||\}}}t | d d j\}}t| d djd | }n5d}d}gg}}t| d jd | }t |||||| \}}}t | d itd d 6tdd6tdd6} t| dt} t| } t |d itd d 6tdd6tdd6}||}||7}|d7}t|tdkst|tdkrt|| |\}}}|d)kr>|dj|7}|dt|d| d|d|d7}|d*t|ddt|dtdj|d7}q|dj|7}|dt|d| d|d||d7}|dj|dj| |ddj||d7}|d+t|ddt|dtd j|d7}nt|dt}|d!t|d| d|d|d7}|d"j|dj| ||7}|d,t|ddt|dtd j|d7}|d#j|7}qW|d$7}|d%|d&7}|d'djd(|D7}||}||||fS(-sp Function which generates parsed rules by substituting all possible combinations of default values. Rs Rsparsing rule {}iiRRRiRRRRRRRfRes{}s patterns = Pattern(Rs trules = ReplacementRule(Rs, With{}s) s def replacement{}({}): s, s( rubi.append({}) return s, replacement{}s patternsC def replacement{}({}): rubi.append({}) return srule{}, Rs return s s1 from sympy.integrals.rubi.constraints import css|] }|VqdS(N((Rtword((sDlib/python2.7/site-packages/sympy/integrals/rubi/parsetools/parse.pys sNs rules rules rule(RRRtcopyRRRRRRRRRRRRRRRRiRR(RtheaderRRRtrulesRRRRRRRRt constrianttconstraint_deft FreeQ_varstFreeQ_xt transformedtFreeQ_constraintt free_cons_deftWith_constraintsR((sDlib/python2.7/site-packages/sympy/integrals/rubi/parsetools/parse.pytdownvalues_rulesIsb  ) # $9 9   0 0@4<@0&= ! t rubi_objectc Cs|d krotjjtjjtjtj}ttjj |ddj }|j |}ni}d}d}d}x$t D]}|j |t |}qWx$tD]}|j |t|}qWg} x4t|D]&}|ddkr| j|qqWt| ||||} | djd} | d}|| d7}| d }x:t D]2}|j t ||}| j t ||} qgWdj |jdd d|}| |fS( s Parses rules in MatchPy format. Parameters ========== fullform : FullForm of the rule as string. header : Header imports for the file. Uses default imports if None. module_name : name of RUBI module References ========== [1] http://reference.wolfram.com/language/ref/FullForm.html [2] http://reference.wolfram.com/language/ref/DownValues.html [3] https://gist.github.com/Upabjojr/bc07c49262944f9c1eb0 s header.py.txtRiRt RuleDelayeds iiiiN(Ritostpathtdirnametabspathtinspecttgetfilet currentframetopenRtreadRttemporary_variable_replacementRtpermanent_variable_replacementRRRRtsplit( tfullformRt module_namet path_headerRRRRRRRR((sDlib/python2.7/site-packages/sympy/integrals/rubi/parsetools/parse.pytrubi_rule_parsers4 -$     $(*t__doc__RRRRtsympyRRRRtsympy.core.compatibilityRtsympy.printingRRtsympy.utilities.miscRRRtdictRRRRRRRRRiRRRRRRRRRRRRRR#(((sDlib/python2.7/site-packages/sympy/integrals/rubi/parsetools/parse.pyts   "           ..  # !   W D