o 8Vak@s^dZddlZddlZddlZddlmZmZmZmZddl m Z ddl m Z Gddde Z dd Zedid d d d dddddddddddddddddddd d!d d"d#d$d#d%d&d'd(d)d*d+d,d-d.d/d0d1d2d3d4d5d6d7d6d8d9d:d9d;d<d=d<d>d?d@dAdBdCdDdEdFdGdHdIdJdKdLdMdNdOdPdQdRdSdTdUdVdWdXdYdZd[d\d]d^d_d`dadbdcdddcdedfZdgdhdiZdjdkdlZgdmZdndoZdpdqZifdrdsZifdtduZgdfdvdwZddxdyZdzgdzfd{d|Zdd}d~ZddZddZddZddZddZ ddZ!ddZ"ddZ#dddZ$dS)a 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 N)sympifyFunctionSetSymbol) StrPrinter)debugc@seZdZddZdS)RubiStrPrintercCsd||jdS)NzNot(%s)r)Z_printargs)selfexprr G/usr/lib/python3/dist-packages/sympy/integrals/rubi/parsetools/parse.py _print_Not'szRubiStrPrinter._print_NotN)__name__ __module__ __qualname__rr r r r r&s rcKst||SN)rZdoprint)r Zsettingsr r r rubi_printer+srTimesZMulPlusZAddPowerZPowZLoglogZExpZexpZSqrtZsqrtZCosZcosZSinZsinZTanZtanZCotz1/tanZcotZSecz1/cosZsecZCscz1/sinZcscZArcSinZasinZArcCosZacosZArcCotZacotZArcSecZasecZArcCscZacscZSinhZsinhZCoshZcoshZTanhZtanhZCothz1/tanhZcothZSechz1/coshZsechZCschz1/sinhZcschZArcSinhZasinhZArcCoshZacoshZArcTanhZatanhZArcCothZacothZArcSechZasechZArcCschZacschZExpandexpandZImZimZRereZFlattenZflattenZPolylogZpolylogZCancelZcancelZ TrigExpandZ expand_trigZSignsignZSimplifyZsimplifyZDeferZUnevaluatedExprZIdentitySZSumZSum_doitModuleWithZBlockZNullNoneZ_gcdZ_jn)ZgcdZjnZ ImaginaryIZ _UseGamma)z \[ImaginaryI]z $UseGamma)Z BinomialPartsZBinomialDegreeZTrinomialPartsZGeneralizedBinomialPartsZGeneralizedTrinomialPartsZPseudoBinomialPartsZPerfectPowerTestZSquareFreeFactorTest*SubstForFractionalPowerOfQuotientOfLinearsZ"FractionalPowerOfQuotientOfLinears"InverseFunctionOfQuotientOfLinearsZFractionalPowerOfSquareQZFunctionOfLinearZFunctionOfInverseLinearZFunctionOfTrigZFindTrigFactorZ FunctionOfLogZPowerVariableExpnZFunctionOfSquareRootOfQuadraticZSubstForFractionalPowerOfLinearZFractionalPowerOfLinearZInverseFunctionOfLinearZDividesZDerivativeDividesZ TrigSquareZ SplitProductrr ZFunctionOfHyperbolicZSplitSumcCsxt|tr|D] }t|rdSqdSt|tdks#t|tdkr4tD] }|t|r1dSq%dS|tvr:dSdS)z This function returns whether an expression contains functions which have different return types in diiferent cases. TrrF) isinstancelistcontains_diff_return_typetyperf_diff_return_typehas)air r r r#ys  r#cCsg}|g}td|}d}|D]f}|dur|dS|}|||dddddd}|dkrD|dkrC|d|n-|dkrZ|dkrU|d||n|dkrq|d|g||dd|}q|dS) z@ Parses FullForm[Downvalues[]] generated by Mathematica z[\[\],]rN,][) rfinditerstartreplacestripgroupappendpopend)Zwmexproutstack generatorZlast_posmatchZpositionZ last_exprr r r parse_full_forms. (     r:cCst|ts|S|ddkr$|ddD]}|ddkr#d||dd<q|ddkrA|ddD]}|ddkr@d||dd<q0|ddkr^|ddD]}|ddkr]d||dd<qMt|dkrf|S|D]}t||}qh|S)zD Returns Optional variables and their values in the pattern rrNZOptionalrr)r!r"lenget_default_values)parsedZdefault_valuesr(r r r r=s,         r=c Csg}d}t||}|D]}||dd|d||d}||dq d}t||}|D]}||d|dd}||dq2d}t||}|D]}||d|dd}||dqR||fS)zu Replaces `Pattern(variable)` by `variable` in `string`. Returns the free symbols present in the string. z%(Optional\(Pattern\((\w+), Blank\)\))rWC('{}', S({}))r;z(Pattern\((\w+), Blank\))_z#(Pattern\((\w+), Blank\(Symbol\)\)))rfindallr0formatr3)stringoptionalsymbolspmatchesr(r r r add_wildcardss" $  rHcCs||ddkr$t|ddkr|dg}n|ddd}|d}||fS|ddD]}t|||\}}||fS||fS)z+ Returns list of symbols in FreeQ. rFreeQr;N)r<seperate_freeq)sZ variablesxr(r r r rKs   rKc sg}d}|D]}t|trOd|||vr=|d7}d|||} | 7} | d|d|7} d|} || <ned} tfdd t|D} nSt|trttt ||} d | } dt |||vr|d7}d || } | 7} | d|d|7} d|} || <nd} tfd d |D} | |vr| | | | || 7}q|gkrd d |||fSd||fS) z< Converts FreeQ constraints into MatchPy constraint r*z return FreeQ({}, {})r;z def cons_f{}({}, {}): $ cons{} = CustomConstraint({}) cons_f{}cons{}c3 |] \}}|kr|VqdSrr .0keyvaluerr r zparse_freeq..,  def cons_f{}({}): c3rQrr rRrVr r rXrY) r!strrBvaluesnextsorteditemsr"setget_free_symbolsjoingenerate_sympy_from_parsedr3) lrM cons_index cons_dict cons_importrEresconsr(c cons_namerLr rVr parse_freeqsD                rmFc s"d}t|ts"z t|d|WSY|vr r |dS|S|ddkr>dt|ddt|d dS|dtvrM|t|d7}n|dd krZrZ|d 7}n||d7}t|dkrh|Sfd d |ddD}d|vr|d|d7}|d|7}|d7}|S)a  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). r*zS({})r@rZRationalz S({})/S({})r;wildrE replace_IntrJZIntZIntegralcsg|] }t|dqS)rn)rdrSr(rprEror r Gsz.generate_sympy_from_parsed..N(rZ)) r!r"floatrBrd replacementsr<removerc)r>rorErpr6resultr rrr rd#s6   ,     rdcCsB|pg}t|ts||vr|||S|D]}t|||}q|S)z. Returns free_symbols present in `s`. )r!r"r3rb)rLrE free_symbolsr(r r r rbRs  rbc Cs@g}d}t|tr|ddkr||}t|i}t|dd}t||d\}}tt|}t|tdtdtd d d }|j d j d}|j d j d } t |dd }t |}d |d || }|d ||7}|d ||7}|d |j d7}d|fS|D]} t| trt| |}||d|d }q~|| q~||fS)z] Takes care of the case, when a pattern matching has to be done inside a constraint. r*rMatchQTrprDOrAndNotr~rrlocalsr;Zsympy_integersz2 def _cons_f_{}({}): return {} rZz0 _cons_{} = CustomConstraint(_cons_f_{}) z8 pat = Pattern(UtilityOperator({}, x), _cons_{}) z= result_matchq = is_match(UtilityOperator({}, x), pat)Z result_matchq)r!r"r=rdrHr_rarrr rsetWCrBrcset_matchq_in_constraintr3) r'rflstrirLrDrWrzpatternrjr(r r r rbs4           rc shttt||g}t|}t|tdtdtddd}|tdrLt||}|ddt tt|d tdtdtdddd d 7nt |rZd t |d d n d t |d d | vr|d7}d|d |}d|vr~|d7}|7}|d|d|7}d|} || <nd}t fdd|D} | |vr|| | ||fS)Nr~rrrrr{r;z return {}rTrzg try: return {} except (TypeError, AttributeError): return Falsez return {}r[rZrMzQ if isinstance(x, (int, Integer, float, Float)): return False rNrOrPr*c3rQrr rRrir r rXrYz%_divide_constriant..)r_rarbrdrrr&rrBrr#r]rcr^r`r3) rLrErfrgrhZlambda_symbolsrWZ match_resrjrlr rr _divide_constriants0  <     rc Csg}d}|ddkr3|ddD]!}|ddkr1t|||||}||d||d7}|d}qnt|||||}||d||d7}|d}dg} |D] }|dkr\| |qQd| ||fS) z Divides multiple constraints into smaller constraints. Parameters ========== s : constraint as list symbols : all the symbols present in the expression r*rrr;NrIrJrZ)rr3rc) rLrErfrgrhryrjr(r'rWr r r divide_constraints*      rc Cs>d}t||}|D]}||dd|d|d}q |S)z0 Replaces `WC(a, b)` by `WC('a', S(b))` z(WC\((\w+), S\(([-+]?\d)\)\))rr?r;rJ)rrAr0rB)rCrFrGr(r r r rs  "rc Cs t|d}d}d}d}t|tdkst|tdkr|jD]k}|jD]}t|trA||vrA|d|jdt|jddd 7}q$t|td td fvrZ|td sZ|}d}qt|td krj|jd }d}qt|jdtd kr|jd}d |j |jd |jd}d}q|||fS)z] Functions like `Set`, `With` and `CompoundExpression` has to be taken special care. r;r*Frrz {} = {}rTrListCompoundExpressionr-z {}({}, {})) rr$rr r!rrBrr&func) Za1Lr'rMZ processedZ return_valuer(rLCr r r process_return_types,    $&   rcCsRg}t|tr||vr|||Sz|jD] }|t||7}qW|SY|S)z4 this function extracts all `Set` functions )r!rr3r extract_set)rLrrr(r r r rs  rc s`d}d}t|tdkst|tdkr'd}d|d}t|jdtd kr4t|jdj}n|jdg}g}|jd dD] } |t| |7}qC||7}|D]'} t| trm|d | jdt | jd d d 7}qSt| t rz|d| | 7}qSt|jd tdkr|jd } ||7}t| jdtr|d | jdjd| jdjd 7}|dt | jd d d 7}|||fSt|jd tdkrl|jd } t | jdkrbt fdddd| j DDr||7}|dt | jdd d 7}ngdvr|d7}t|r'|dd} |d| t | jd d d 7}|d7}|d7}n||7}|dt | jd d d 7}|t | jdd d f}t||} | drZ|| dt | d f}|d7}|d 7}d!|}|||fSt|jd tdkst|jd tdkr|jd } ||7}|t | d d f}t||} | dr|| dt | d f}|| d7}|dt | d 7}||dfS|jd tdr|jd jd} ||7}t| jdtr|d | jdjd| jdjd 7}|d"|jd j| jd#|jd jd 7}||dfS||7}|dt |jd d d 7}|||fSt |d d d|fS)$z: Replaces `With` and `Module by python functions` Nr*rr z def With{}({}):rZrrr;z {} = {}Trz {} = Symbol('{}')rz return {} ConditionrJc3s|]}|vVqdSrr )rSjrEr r rX$szreplaceWith..cSsg|]}t|qSr )r\rqr r r rs$szreplaceWith..rMzI if isinstance(x, (int, Integer, float, Float)): return False z z try:{} res = {}z= except (TypeError, AttributeError): return Falsez if res:z if {}:z return Truez return Falsez, CustomConstraint(With{})z return {}({}, {})r-)r$rrBrcr r"rr!rrrr<allrzr#r0rr&r) rLrEindex return_typeZ with_valueZ constraintsryrrr(rZ n_with_valueZ return_type1r rr replaceWiths"  &  (  "        0     (,  rcCsd}d}d}d}g} |D]} td|| d| ddddkr0| ddd} n| dd} t| i} t| dd } t| | d \} }tt|}| d ddkrt | d d |||| \}}}t | d d \}}t| d d|d }nd}d}gg}}t| d |d }t ||||| |\}}}t | t d t dt ddd} t| dd} t| } t |t d t dt ddd}||}||7}|d7}t|t dkst|t dkrt|||\}}}|dur.|d|7}|dt|d| d|d|d7}|dt|ddt|ddd|d7}n|d|7}|dt|d| d|d||d7}|d|d ||dd!||d7}|dt|ddt|ddd"|d7}nCt|dd}|dt|d| d|d|d7}|d#|d |||7}|dt|ddt|ddd"|d7}|d$|7}q |d%7}|d&|d'7}|d(d d)d*| D7}|||}||||fS)+zp Function which generates parsed rules by substituting all possible combinations of default values. r,z r*zparsing rule {}r;rrTr|r}rJrr~rrrrrrrNz{}z patternz = Pattern(ruz rulez = ReplacementRule(rz, With{}z) z def replacement{}({}): rZz return z, replacement{}z% def replacement{}({}): return zrule{}, r+z return rz1 from sympy.integrals.rubi.constraints import css|]}|VqdSrr )rSZwordr r r rXsz#downvalues_rules..)rrBrcopyr=rdrHr_rarrKrmrrrrr$rr\rc)rWheaderrgrfrrulesr>Z repl_funcsrjrhr(rFrDrrzZ constriantZconstraint_defZ FreeQ_varsZFreeQ_xZ transformedZFreeQ_constraintZ free_cons_defZWith_constraintsrr r r downvalues_rulesXst       " ,40 4 ,2  r rubi_objectc Cs0|dur#tjtjtt}ttj|d }| |}i}d}d}d}t D] }| |t |}q-t D] }| |t |}q:g} t|D] }|ddkrX| |qKt| ||||} | dd} || d7}t D]}| t ||}| t ||} qqd|dddd|}| |fS) a Parses rules in MatchPy format. Parameters ========== fullform : FullForm of the rule as string. header : Header imports for the file. Uses default imports if None. module_name : name of RUBI module References ========== [1] http://reference.wolfram.com/language/ref/FullForm.html [2] http://reference.wolfram.com/language/ref/DownValues.html [3] https://gist.github.com/Upabjojr/bc07c49262944f9c1eb0 Nz header.py.txtrr*Z RuleDelayedrrJ)ospathdirnameabspathinspectZgetfileZ currentframeopenrcreadrBtemporary_variable_replacementr0permanent_variable_replacementr:r3rr1split) ZfullformrZ module_nameZ path_headerrgrfrrjr(rr>ryr r r rubi_rule_parsers2      rr r)Nr)%__doc__rrrZsympyrrrrZsympy.printingrZsympy.utilities.miscrrrdictrwrrr%r#r:r=rHrKrmrdrbrrrrrrrrrr r r r s         !"#$%&'()*,-./012348   / /#"  XG