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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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&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@mAZAmBZBmCZCmDZDmEZEmFZFmGZGmHZHmIZImJZJmKZKmLZLmMZM d dlNmOZOmPZP d dlQmRZR d dlSmTZT d d	lUmVZV dfd
d„ZWdd„ ZXdd„ ZYdd„ ZZeZG dd„ dƒƒZ[dS )é    )ÚannotationsN)Úproduct)ÚAnyÚCallable)EÚMulÚAddÚPowÚlogÚexpÚsqrtÚcosÚsinÚtanÚasinÚacosÚacotÚasecÚacscÚsinhÚcoshÚtanhÚasinhÚacoshÚatanhÚacothÚasechÚacschÚexpandÚimÚflattenÚpolylogÚcancelÚexpand_trigÚsignÚsimplifyÚUnevaluatedExprÚSÚatanÚatan2ÚModÚMaxÚMinÚrfÚEiÚSiÚCiÚairyaiÚairyaiprimeÚairybiÚprimepiÚprimeÚisprimeÚcotÚsecÚcscÚcschÚsechÚcothÚFunctionÚIÚpiÚTupleÚGreaterThanÚStrictGreaterThanÚStrictLessThanÚLessThanÚEqualityÚOrÚAndÚLambdaÚIntegerÚDummyÚsymbols)ÚsympifyÚ_sympify)Úairybiprime)Úli)Úsympy_deprecation_warningc                 C  s$   t dddd t|ƒ}t| | ¡ƒS )NzóThe ``mathematica`` function for the Mathematica parser is now
deprecated. Use ``parse_mathematica`` instead.
The parameter ``additional_translation`` can be replaced by SymPy's
.replace( ) or .subs( ) methods on the output expression instead.z1.11zmathematica-parser-new)Zdeprecated_since_versionZactive_deprecations_target)rO   ÚMathematicaParserrK   Ú
_parse_old)ÚsÚadditional_translationsÚparser© rU   úb/var/www/html/stable-diffusion-webui/venv/lib/python3.9/site-packages/sympy/parsing/mathematica.pyÚmathematica   s    úrW   c                 C  s   t ƒ }| | ¡S )a±  
    Translate a string containing a Wolfram Mathematica expression to a SymPy
    expression.

    If the translator is unable to find a suitable SymPy expression, the
    ``FullForm`` of the Mathematica expression will be output, using SymPy
    ``Function`` objects as nodes of the syntax tree.

    Examples
    ========

    >>> from sympy.parsing.mathematica import parse_mathematica
    >>> parse_mathematica("Sin[x]^2 Tan[y]")
    sin(x)**2*tan(y)
    >>> e = parse_mathematica("F[7,5,3]")
    >>> e
    F(7, 5, 3)
    >>> from sympy import Function, Max, Min
    >>> e.replace(Function("F"), lambda *x: Max(*x)*Min(*x))
    21

    Both standard input form and Mathematica full form are supported:

    >>> parse_mathematica("x*(a + b)")
    x*(a + b)
    >>> parse_mathematica("Times[x, Plus[a, b]]")
    x*(a + b)

    To get a matrix from Wolfram's code:

    >>> m = parse_mathematica("{{a, b}, {c, d}}")
    >>> m
    ((a, b), (c, d))
    >>> from sympy import Matrix
    >>> Matrix(m)
    Matrix([
    [a, b],
    [c, d]])

    If the translation into equivalent SymPy expressions fails, an SymPy
    expression equivalent to Wolfram Mathematica's "FullForm" will be created:

    >>> parse_mathematica("x_.")
    Optional(Pattern(x, Blank()))
    >>> parse_mathematica("Plus @@ {x, y, z}")
    Apply(Plus, (x, y, z))
    >>> parse_mathematica("f[x_, 3] := x^3 /; x > 0")
    SetDelayed(f(Pattern(x, Blank()), 3), Condition(x**3, x > 0))
    )rP   Úparse)rR   rT   rU   rU   rV   Úparse_mathematica    s    2rY   c                    s¶   t | ƒdkr„| d }tdƒ‰ | ˆ ¡}dd„ |D ƒ}t|ƒ}t|tƒrztd|› td}t|| 	‡ fdd	„t
|ƒD ƒ¡ƒS td
|ƒS t | ƒdkrª| d }| d }t||ƒS tdƒ‚d S )Né   r   ÚSlotc                 S  s   g | ]}|j d  ‘qS )r   )Úargs)Ú.0ÚarU   rU   rV   Ú
<listcomp>[   ó    z#_parse_Function.<locals>.<listcomp>zdummy0:©Úclsc                   s   i | ]\}}ˆ |d  ƒ|“qS )rZ   rU   )r]   ÚiÚv©r[   rU   rV   Ú
<dictcomp>_   r`   z#_parse_Function.<locals>.<dictcomp>rU   é   z&Function node expects 1 or 2 arguments)Úlenr<   ZatomsÚmaxÚ
isinstancerH   rJ   rI   rG   ZxreplaceÚ	enumerateÚSyntaxError)r\   ÚargÚslotsZnumbersZnumber_of_argumentsÚ	variablesÚbodyrU   re   rV   Ú_parse_FunctionV   s    

"

rq   c                 C  s   |   ¡  | S ©N)Ú_initialize_classra   rU   rU   rV   Ú_decoi   s    rt   c                E   @  sT  e Zd ZU dZdddddddd	d
ddddddddddddddœZedddƒD ]R\ZZZee e d Z	er€de 
¡  e d Zne 
¡ e d Ze e	ei¡ qLdd d!d"d#œZe d$ej¡d%fe d&ej¡d%fe d'ej¡d(fe d)ej¡d*fd+œZe d,ej¡Ze d-ej¡Zd.Zi Zd/ed0< i Zd/ed1< i Zd/ed2< ed3d4„ ƒZdàd6d7„Zed8d9„ ƒZd:d;„ Zd<d=„ Zed>d?„ ƒZed@dA„ ƒZ edBdC„ ƒZ!edDdE„ ƒZ"dFdG„ Z#dHdI„ Z$dJZ%dKZ&dLZ'dMZ(dNZ)dOZ*e'd5dPdQdR„ ife%e(dPdSife%e)dTdUdVdWdXdYdZœfe%e*d[d\dR„ ife'd5d]d^ife%e*d_d`ife%e)dadbdcœfe%e*dddeife%e(dfdgife'd5dhdidjœfe%e(dkdlife%e(dmdnife&d5dodpife%e(dqdrdsœfe%e(dtdudvdwdxdydzœfe%d5d{d|ife%e(d}d}d~œfe%e(ddd€œfe%e(dd‚ife&d5dƒdR„ d„dR„ d…œfe%e)d†d‡ife%e)dˆd‰dŠd‹dR„ dŒœfe'd5ddŽddd‘œfe%d5d’dR„ d“dR„ d”œfe&d5d•dR„ d–dR„ d—œfe%d5d˜d™ife'd5dšdR„ d›dR„ dœdR„ ddR„ džœfe%d5dŸd dR„ ife&d5d¡d¢d£œfgZ+d¤ed¥< d¦dR„ d§dR„ d£œZ,d¨Z-d©Z.g dª¢Z/g d«¢Z0ed¬d­„ ƒZ1ed®d¯„ ƒZ2d5Z3d°d±„ Z4d²d³œd´dµ„Z5d¶d·d¸œd¹dº„Z6d¶d·d¸œd»d¼„Z7d¶d·d¸œd½d¾„Z8d¿dÀœdÁdÂ„Z9d¿d¿d·dÃœdÄdÅ„Z:d¿dÀœdÆdÇ„Z;dád¿d·dÉœdÊdË„Z<d²d²dÌœdÍdÎ„Z=d²dÏœdÐdÑ„Z>d¿dÒœdÓdÔ„Z?e@eAeBdÕdR„ dÖdR„ d×dR„ eCeDeEeFeGeHeIeJeKeLdØdR„ eMeNeOePeQeReSeTeUeVeWeXeYeZe[e\e]e^je_e`eaebecedeeefdÙdR„ egeheiejekelemeneoepeqereseteuevewexeyeze{e|e}e~dÚœDZe€edÛœZ‚dÜdÝ„ ZƒdÞdß„ Z„d5S )ârP   ap  
    An instance of this class converts a string of a Wolfram Mathematica
    expression to a SymPy expression.

    The main parser acts internally in three stages:

    1. tokenizer: tokenizes the Mathematica expression and adds the missing *
        operators. Handled by ``_from_mathematica_to_tokens(...)``
    2. full form list: sort the list of strings output by the tokenizer into a
        syntax tree of nested lists and strings, equivalent to Mathematica's
        ``FullForm`` expression output. This is handled by the function
        ``_from_tokens_to_fullformlist(...)``.
    3. SymPy expression: the syntax tree expressed as full form list is visited
        and the nodes with equivalent classes in SymPy are replaced. Unknown
        syntax tree nodes are cast to SymPy ``Function`` objects. This is
        handled by ``_from_fullformlist_to_sympy(...)``.

    zsqrt(x)zexp(x)zlog(x)zlog(y,x)zlog(x,2)z	log(x,10)zMod(x,y)zMax(*x)zMin(*x)zrf(x,y)z
atan2(y,x)zEi(x)zSi(x)zCi(x)z	airyai(x)zairyaiprime(x)z	airybi(x)zairybiprime(x)z li(x)z
primepi(x)zprime(x)z
isprime(x))zSqrt[x]zExp[x]zLog[x]zLog[x,y]zLog2[x]zLog10[x]zMod[x,y]zMax[*x]zMin[*x]zPochhammer[x,y]zArcTan[x,y]zExpIntegralEi[x]zSinIntegral[x]zCosIntegral[x]z	AiryAi[x]zAiryAiPrime[x]z	AiryBi[x]zAiryBiPrime[x]zLogIntegral[x]z
PrimePi[x]zPrime[x]z	PrimeQ[x])Ú ZArc)ÚSinÚCosÚTanÚCotÚSecÚCsc)ru   Úhz[x]r^   z(x)ru   z**ú[ú])ú ú^Ú{Ú}zñ
                (?:(?<=[a-zA-Z\d])|(?<=\d\.))     # a letter or a number
                \s+                               # any number of whitespaces
                (?:(?=[a-zA-Z\d])|(?=\.\d))       # a letter or a number
                Ú*zÐ
                (?:(?<=[])\d])|(?<=\d\.))       # ], ) or a number
                                                # ''
                (?=[(a-zA-Z])                   # ( or a single letter
                z¬
                (?<=[a-zA-Z])       # a letter
                \(                  # ( as a character
                (?=.)               # any characters
                z*(z¿
                (?:
                \A|(?<=[^a-zA-Z])
                )
                Pi                  # 'Pi' is 3.14159... in Mathematica
                (?=[^a-zA-Z])
                r>   )Ú
whitespaceúadd*_1úadd*_2ÚPizÞ
                (?:
                \A|(?<=[^a-zA-Z])   # at the top or a non-letter
                )
                [A-Z][a-zA-Z\d]*    # Function
                (?=\[)              # [ as a character
                z(
                \{.*\}
                zº
                (?:
                \A|(?<=[^a-zA-Z])
                )
                {arguments}         # model argument like x, y,...
                (?=[^a-zA-Z])
                z%dict[tuple[str, int], dict[str, Any]]ÚTRANSLATIONSÚcache_originalÚcache_compiledc                 C  s   |   | j¡}| j |¡ d S rr   )Ú_compile_dictionaryÚCORRESPONDENCESrˆ   Úupdate)rb   ÚdrU   rU   rV   rs   ö   s    z#MathematicaParser._initialize_classNc                 C  sl   i | _ | j  | j¡ |d u r i }| jj|krXt|tƒs>tdƒ‚|  |¡}|| j_|| j_	| j  | jj	¡ d S )NzThe argument must be dict type)
Útranslationsr   rˆ   Ú	__class__r‰   rj   ÚdictÚ
ValueErrorr‹   rŠ   )ÚselfrS   rŽ   rU   rU   rV   Ú__init__ü   s    

zMathematicaParser.__init__c                 C  sX  i }|  ¡ D ]D\}}|  |¡ |  |¡ |  |d¡}|  |d¡}|  |d¡}|  |d¡}| j |¡}|d u r‚dj|d}t|ƒ‚| ¡ }|  	|¡\}}	| 
¡ dks°|	t|ƒkrÄdj|d}t|ƒ‚|d d dkrÚd}
nt|ƒ}
||
f}dd	„ |D ƒ}d
d |¡ d }| jj|d}t |tj¡}i ||< ||| d< ||| d< ||| d< q|S )Nr„   r   ú'{f}' function form is invalid.©Úfr   éÿÿÿÿrƒ   c                 S  s$   g | ]}|d  dkr|nd| ‘qS )r   rƒ   ú\rU   )r]   ÚxrU   rU   rV   r_   B  r`   z9MathematicaParser._compile_dictionary.<locals>.<listcomp>z(?:(ú|z)))Ú	argumentsÚfsr\   Úpat)ÚitemsÚ_check_inputÚ_apply_rulesÚ_replaceÚ
FM_PATTERNÚsearchÚformatr’   ÚgroupÚ	_get_argsÚstartrh   ÚjoinÚARGS_PATTERN_TEMPLATEÚreÚcompileÚVERBOSE)rb   ZdicrŽ   Úfmr   ÚmÚerrZfm_namer\   ÚendZkey_argÚkeyZre_argsZxyzZpatStrrž   rU   rU   rV   r‹     s<    

z%MathematicaParser._compile_dictionaryc           
      C  s€   | j }d}d}| |¡}|du r*||7 }q|| ¡ }|  |¡\}}| ¡ }	|  ||||	|¡}|	}||d|… 7 }||d… }q|S )z'Parse Mathematica function to SymPy oneru   r   N)r£   r¤   r¦   r§   r¨   Ú_convert_one_function)
r“   rR   rž   ÚscannedÚcurr¯   r®   r\   r±   ÚbgnrU   rU   rV   Ú_convert_functionT  s    
z#MathematicaParser._convert_functionc                 C  sf  |t |ƒf| jv rB|t |ƒf}| j| d }dd„ t||ƒD ƒ}n‚|df| jv r°|df}| j| d }i }t|ƒD ]:\}	}
|
d dkr d ||	d … ¡||
<  qÄ||	 ||
< qrndj|d}t|ƒ‚| j| d	 }| j| d
 }d}d}| |¡}|d u r||7 }qF| ¡ }
| 	¡ }||d |… ||
  7 }| 
¡ }||d … }qè|d |… | ||d …  }|S )Nr\   c                 S  s   i | ]\}}||“qS rU   rU   )r]   Úkrd   rU   rU   rV   rf   „  r`   z;MathematicaParser._convert_one_function.<locals>.<dictcomp>rƒ   r   ú,z'{f}' is out of the whitelist.r–   r   rž   ru   )rh   r   Úziprk   r©   r¥   r’   r¤   r¦   r¨   r±   )r“   rR   r®   r\   r¶   r±   r²   Zx_argsrŽ   rc   rš   r°   Útemplaterž   r´   rµ   r¯   ZxbgnrU   rU   rV   r³   {  s<    

z'MathematicaParser._convert_one_functionc                 C  sÞ   |j }| ¡ d }g g  }}g }|}t||d… |ƒD ]–\}}	|	dkrh|sh|sh| |||… ¡ |d }|	dkr|| |	¡ n|	dkrŒ| ¡  |	dkr | |	¡ q6|	dkr6|r¶| ¡  q6| |||… ¡  qÎq6|d }
||
fS )z'Get arguments of a Mathematica functionrZ   Nr¹   r   r‚   r}   r~   )Ústringr±   rk   ÚappendÚpop)rb   r¯   rR   ZancZsquareZcurlyr\   rµ   rc   ÚcZfunc_endrU   rU   rV   r§   ½  s,    

zMathematicaParser._get_argsc                 C  s   | j | }| ||¡}|S rr   )ÚREPLACEMENTSÚreplace)rb   rR   ÚbefÚaftrU   rU   rV   r¢   ã  s    
zMathematicaParser._replacec                 C  s   | j | \}}| ||¡S rr   )ÚRULESÚsub)rb   rR   rÂ   rž   rÃ   rU   rU   rV   r¡   é  s    zMathematicaParser._apply_rulesc                 C  sR   dD ]4}|  |d ¡|  |d ¡krdj|d}t|ƒ‚qd|v rNd}t|ƒ‚d S )N))r}   r~   )r   r‚   )ú(ú)r   rZ   r•   r–   r   z Currently list is not supported.)Úcountr¥   r’   )rb   rR   Zbracketr°   rU   rU   rV   r    î  s    
zMathematicaParser._check_inputc                 C  s`   |   |¡ |  |d¡}|  |d¡}|  |d¡}|  |d¡}|  |¡}|  |d¡}|  |d¡}|S )Nr„   r   r…   r†   r€   r‡   )r    r¡   r¢   r·   )r“   rR   rU   rU   rV   rQ   ù  s    

zMathematicaParser._parse_oldc                 C  s"   |   |¡}|  |¡}|  |¡}|S rr   )Ú_from_mathematica_to_tokensÚ_from_tokens_to_fullformlistÚ_from_fullformlist_to_sympy)r“   rR   Ús2Zs3Zs4rU   rU   rV   rX     s    


zMathematicaParser.parseZInfixZPrefixZPostfixZFlatZRightZLeftú;c                 C  s.   t | tƒr$| r$| d dkr$| dg S d| dgS )Nr   ÚCompoundExpressionÚNull)rj   Úlist©rš   rU   rU   rV   Ú<lambda>$  r`   zMathematicaParser.<lambda>rÎ   ÚSetZ
SetDelayedZAddToZSubtractFromZTimesByZDivideBy)ú=z:=z+=z-=z*=z/=z//c                 C  s   | |gS rr   rU   ©rš   ÚyrU   rU   rV   rÒ   '  r`   ú&r<   z/.Z
ReplaceAllZRuleZRuleDelayed)z->z:>z/;Ú	Conditionr›   ZAlternativesZRepeatedZRepeatedNull)z..z...z||rE   z&&rF   ú!ÚNotZSameQZUnsameQ)z===z=!=ÚEqualZUnequalÚ	LessEqualÚLessÚGreaterEqualÚGreater)z==z!=z<=ú<z>=ú>z;;ZSpanÚPlus©ú+ú-ÚTimes)rƒ   ú/Ú.ZDotc                 C  s
   t  | ¡S rr   )rP   Ú_get_negrÑ   rU   rU   rV   rÒ   7  r`   c                 C  s   | S rr   rU   rÑ   rU   rU   rV   rÒ   8  r`   )rå   rä   r€   ÚPowerÚApplyZMapZMapAllc                 C  s   d| |ddggS )Nrë   ÚListÚ1rU   rÕ   rU   rU   rV   rÒ   :  r`   )z@@z/@z//@z@@@Z
DerivativeZ	FactorialZ
Factorial2Z	Decrement)ú'rÙ   z!!z--c                 C  s
   | g|¢S rr   rU   rÕ   rU   rU   rV   rÒ   <  r`   c                 C  s   d| g|¢S )NZPartrU   rÕ   rU   rU   rV   rÒ   <  r`   )r}   ú[[c                 C  s
   dg| ¢S )Nrì   rU   rÑ   rU   rU   rV   rÒ   =  r`   c                 C  s   | d S )Nr   rU   rÑ   rU   rU   rV   rÒ   =  r`   )r   rÆ   ú?ZPatternTestc                 C  s   d| dggS ©NÚPatternÚBlankrU   rÑ   rU   rU   rV   rÒ   @  r`   c                 C  s   dd| dgggS )NÚOptionalrò   ró   rU   rÑ   rU   rU   rV   rÒ   A  r`   c                 C  s   d| dggS )Nrò   ZBlankSequencerU   rÑ   rU   rU   rV   rÒ   B  r`   c                 C  s   d| dggS )Nrò   ZBlankNullSequencerU   rÑ   rU   rU   rV   rÒ   C  r`   )Ú_z_.Ú__Z___rõ   c                 C  s   d| d|ggS rñ   rU   rÕ   rU   rU   rV   rÒ   E  r`   r[   ÚSlotSequence)ú#z##z7list[tuple[str, str | None, dict[str, str | Callable]]]Ú_mathematica_op_precedencec                   C  s   ddgS )Nr[   rí   rU   rU   rU   rU   rV   rÒ   J  r`   c                   C  s   ddgS )Nr÷   rí   rU   rU   rU   rU   rV   rÒ   K  r`   z[A-Za-z][A-Za-z0-9]*z (?:[0-9]+(?:\.[0-9]*)?|\.[0-9]+))rÆ   r}   rï   r   )rÇ   r~   ú]]r‚   c                 C  s,   t |tƒr"t tj|¡r"d|› S dd|gS )Nrå   ræ   ú-1)rj   Ústrr«   ÚmatchrP   Ú_number©rb   rš   rU   rU   rV   ré   T  s    zMathematicaParser._get_negc                 C  s
   d|dgS )Nrê   rû   rU   rÿ   rU   rU   rV   Ú_get_invX  s    zMathematicaParser._get_invc                 C  s¸   | j d ur| j S | j| jg}| jd d … | jd d …  }| jD ]\}}}|D ]}| |¡ qLq>|jdd„ d | t	t
j|ƒ¡ | d¡ | d¡ t
 dd |¡ d ¡}|| _ | j S )	Nc                 S  s
   t | ƒ S rr   )rh   rÑ   rU   rU   rV   rÒ   g  r`   z2MathematicaParser._get_tokenizer.<locals>.<lambda>)r²   r¹   Ú
rÆ   r›   rÇ   )Ú_regex_tokenizerÚ_literalrþ   Ú_enclosure_openÚ_enclosure_closerù   r½   ÚsortÚextendÚmapr«   Úescaper¬   r©   )r“   ÚtokensZtokens_escapeÚtypZstratZsymdictr¸   Ú	tokenizerrU   rU   rV   Ú_get_tokenizer^  s    


z MathematicaParser._get_tokenizerrü   )Úcodec                   s¤  |   ¡ ‰ g }| d¡}|dkr6t|ƒdkr¼| |¡ q¼t d||d d … ¡}|d u r^tdƒ‚|| ¡  d }|dkrˆ| |d |… ¡ | d||d |…  dd¡g¡ ||d d … }qt	|ƒD ]v\}}t
|tƒrØqÄ| d	¡}|dkrîq2| d
¡}	|	dks|	|k rtdƒ‚|d |… ||	d d …  }qØ|||< qÄ‡ fdd„|D ƒ}
dd„ |
D ƒ}|r~|d dkr~| d¡ q\|r |d dkr | d¡ q~|S )Nú"r˜   r   z(?<!\\)"rZ   z"mismatch in string "  " expressionZ_Strz\"z(*z*)zmismatch in comment (*  *) coderg   c                   s.   g | ]&}t |tƒr$| ¡ r$ˆ  |¡n|g‘qS rU   )rj   rü   ÚisasciiÚfindall)r]   rc   ©r  rU   rV   r_   ’  r`   zAMathematicaParser._from_mathematica_to_tokens.<locals>.<listcomp>c                 S  s   g | ]}|D ]}|‘qqS rU   rU   )r]   rc   ÚjrU   rU   rV   r_   “  r`   r  )r  Úfindrh   r½   r«   r¤   rl   r¨   rÁ   rk   rj   rÐ   r¾   )r“   r  Zcode_splitsZstring_startZ	match_endZ
string_endrc   Z
code_splitZpos_comment_startZpos_comment_endZtoken_listsr
  rU   r  rV   rÉ   o  sB    

"



z-MathematicaParser._from_mathematica_to_tokensz
str | listÚbool)ÚtokenÚreturnc                 C  s:   t |tƒrdS t | j|¡r dS t d| j |¡r6dS dS )NFz-?T)rj   rÐ   r«   rý   r  rþ   ©r“   r  rU   rU   rV   Ú_is_opž  s    
zMathematicaParser._is_opc                 C  s   |dv rdS |   |¡ S )N)rÇ   r‚   T©r  r  rU   rU   rV   Ú_is_valid_star1§  s    z!MathematicaParser._is_valid_star1c                 C  s   |dv rdS |   |¡ S )N)rÆ   r   Tr  r  rU   rU   rV   Ú_is_valid_star2¬  s    z!MathematicaParser._is_valid_star2rÐ   )r
  c           
      C  sz  g g}g }d}|t |ƒk rZ|| }|| jv rT|d  |¡ | |¡ | g ¡ nü|dkr°t |d ƒdkr|d d |d krtd|d  ƒ‚|  |d ¡|d< | g ¡ n || jv rB| j |¡}| j| |d kr„tdƒ}|dkr€|d dkr€|d dkr| |d	 d
¡ nb|d dkr„||d	  d
krJd||d	 < n4||d	  dkrzd||d	 < | |d d
¡ n|‚n|‚t |d ƒdkr°|d d dkr°tdƒ‚|  |d d¡}||d< g }	|d d |d krô|	 | ¡ ¡ qÌ|	 	¡  |d dkr(t |	ƒd	kr(tdt |	ƒ ƒ‚|d  |	¡ | d¡ n|d  |¡ |d	7 }qt |ƒd	kslJ ‚|  |d ¡S )Nr   r˜   r¹   éþÿÿÿz %s cannot be followed by comma ,zunmatched enclosurerú   r}   rZ   r~   rï   rg   rÆ   z( ) not valid syntaxTz1( must be followed by one expression, %i detected)
rh   r  r½   rl   Ú_parse_after_bracesr  ÚindexÚinsertr¾   Úreverse)
r“   r
  ÚstackZopen_seqÚpointerr  ÚindZunmatched_enclosureZ
last_stackZnew_stack_elementrU   rU   rV   rÊ   ±  sZ    

$$
z.MathematicaParser._from_tokens_to_fullformlist)Úlinesr
  Úinside_enclosurec           	      C  s  d}t |ƒ}||k r|| }|dkr|r@| |¡ |d8 }q|dkr\| d¡ |d8 }q|dkr¨z|  |d |… |¡}W q° ty¤   | |¡ |d8 }Y qY q°0 n|d }t |ƒdkrÜ|d dkrÜ| |dd … ¡ n
| |¡ t|ƒD ]}| d¡ qî||8 }d}q|d7 }qd S )Nr   r  rZ   rÎ   )rh   r¾   r  rl   r  r½   Úrange)	r“   r%  r
  r&  r#  Úsizer  Z	prev_exprrc   rU   rU   rV   Ú_util_remove_newlinesç  s<    





z'MathematicaParser._util_remove_newlinesc                 C  s”   t |ƒ}d}||k r|dkr†|  ||d  ¡r†|  || ¡r†|| dkrjd||< ||d  d ||d < n| |d¡ |d7 }|d7 }|d7 }qd S )Nr   rZ   rÆ   rƒ   )rh   r  r  r   )r“   r
  r(  r#  rU   rU   rV   Ú_util_add_missing_asterisks
  s    ÿþz-MathematicaParser._util_add_missing_asterisksF)r
  r&  c                 C  s  d}g }|   |||¡ t| jƒD ]R\}}}d|v r>|  |¡ t|ƒ}d}	|	|k r ||	 }
t|
tƒrj|
|v rj||
 }t|tƒrŽ|g}d}ng }d}|
dv rÌ|| jkrÌ|	dkrÌ|  ||	d  ¡sÌ|	d7 }	qJ|| j	kr"|	dks|	|d ks|  ||	d  ¡s|  ||	d  ¡r"|	d7 }	qJd}|||	< || j	krH| 
|	d ¡}| 
|	¡}|
dkrh|  |¡}n|
dkr||  |¡}|	d8 }	|d	8 }| |¡ |}|| jkr4|	d	 |k r&|  ||	d  |
¡r&| |¡ | 
|	d ¡}| 
|	d ¡}|dkr|  |¡}n|dkr|  |¡}|d	8 }q¦| |¡ q"|| jkrª|	d	 |k rž||	d  |
krž| ||g¡ |d
 }| 
|	d ¡ | 
|	d ¡}|d	8 }q@| |¡ nœ|| jkr<|	d |k r0||	d  |
kr0t|tƒrö||| |g||< n||| |ƒ||< | 
|	d ¡ | 
|	d ¡}|d	8 }q¶| |¡ n
| |¡ nÚ|| jkr´|d u sbJ ‚|	|d ks„|  ||	d  ¡r–| j|
 ƒ ||	< n| | 
|	d ¡¡ |d8 }nn|| jkr"|d u sÎJ ‚|	dksì|  ||	d  ¡rþ| j|
 ƒ ||	< n$| | 
|	d ¡¡ |	d8 }	|d8 }t|tƒrjt t|¡}||Ž }| ¡  t|tƒrb| |¡ n|||	< |	d7 }	qJq t|ƒdks t|ƒdkrºt|ƒdkrº|r²|  ||¡S tdƒ‚t|ƒdkr|d rô|d d dkrô|d dd … }dg|¢|¢}|S |d S )NFrƒ   r   rZ   rã   Trç   rå   rg   r˜   z0unable to create a single AST for the expressionrÎ   )r)  Úreversedrù   r*  rh   rj   rü   ÚPREFIXr  ÚINFIXr¾   r   ré   r½   ÚFLATÚ_check_op_compatibleÚRIGHTÚLEFTÚ_missing_arguments_defaultÚPOSTFIXr   ÚtypingÚcastÚclearrÐ   r  r  rl   )r“   r
  r&  Úchangedr%  Zop_typeZgrouping_stratZop_dictr(  r#  r  Zop_nameÚnodeZfirst_indexZarg1Zarg2Znode_pZother_opZop_callÚnew_nodeZcompound_expressionrU   rU   rV   r    sÂ    

,@




$



  "
*z%MathematicaParser._parse_after_braces)Úop1Úop2c                 C  sH   ||krdS ddh}ddh}||v r0||v r0dS ||v rD||v rDdS dS )NTrƒ   rç   rä   rå   FrU   )r“   r:  r;  ZmuldivZaddsubrU   rU   rV   r/  –  s    z&MathematicaParser._check_op_compatible)Úwmexprc           	      C  sî   g }|g}t  d|¡}d}|D ]Æ}|du r. qæ| ¡ }|||…  dd¡ dd¡ dd¡ ¡ }| ¡ dkr‚|dkrÜ|d  |¡ nZ| ¡ dkr®|dkr¤|d  |¡ | ¡  n.| ¡ dkrÜ|d  |g¡ | |d d ¡ | ¡ }q|d S )	zH
        Parses FullForm[Downvalues[]] generated by Mathematica
        z[\[\],]r   Nr¹   ru   r~   r}   r˜   )	r«   Úfinditerr¨   rÁ   Ústripr¦   r½   r¾   r±   )	r“   r<  Úoutr"  Ú	generatorZlast_posrý   ÚpositionÚ	last_exprrU   rU   rV   Ú_from_fullform_to_fullformlist¡  s*    (

z0MathematicaParser._from_fullform_to_fullformlist)Úpylistc                   s(   ddl m‰ m‰ ‡ ‡‡fdd„‰ˆ|ƒS )Nr   )r<   ÚSymbolc                   sl   t | tƒrNt| ƒdkrD| d }‡fdd„| dd … D ƒ}ˆ |ƒ|Ž S tdƒ‚nt | tƒr`ˆ| ƒS t| ƒS d S )Nr   c                   s   g | ]}ˆ |ƒ‘qS rU   rU   ©r]   rm   )Ú	converterrU   rV   r_   Ã  r`   z\MathematicaParser._from_fullformlist_to_fullformsympy.<locals>.converter.<locals>.<listcomp>rZ   zEmpty list of expressions)rj   rÐ   rh   r’   rü   rL   )ÚexprÚheadr\   ©r<   rE  rG  rU   rV   rG  ¿  s    


zHMathematicaParser._from_fullformlist_to_fullformsympy.<locals>.converter)Úsympyr<   rE  )r“   rD  rU   rJ  rV   Ú#_from_fullformlist_to_fullformsympy¼  s    z5MathematicaParser._from_fullformlist_to_fullformsympyc                  G  s   t t| ƒŽ S rr   )r	   r+  ©r^   rU   rU   rV   rÒ   Ò  r`   c                 C  s
   t | dƒS ©Nrg   ©r	   rÑ   rU   rU   rV   rÒ   Ó  r`   c                 C  s
   t | dƒS )Né
   rO  rÑ   rU   rU   rV   rÒ   Ô  r`   c                  G  s    t | ƒdkrtt| ƒŽ S t| Ž S rN  )rh   r(   r+  r'   rM  rU   rU   rV   rÒ   á  r`   c                  G  s   t jS rr   )r&   ZZerorM  rU   rU   rV   rÒ     r`   )Dræ   râ   rê   ÚLogZLog2ZLog10ZExpZSqrtrv   rw   rx   ry   rz   r{   ZArcSinZArcCosZArcTanZArcCotZArcSecZArcCscZSinhZCoshZTanhZCothZSechZCschZArcSinhZArcCoshZArcTanhZArcCothZArcSechZArcCschZExpandZImZReZFlattenZPolylogZCancelZ
TrigExpandZSignZSimplifyZDeferZIdentityrÏ   r)   r*   r+   Z
PochhammerZExpIntegralEiZSinIntegralZCosIntegralZAiryAiZAiryAiPrimeZAiryBiZAiryBiPrimeZLogIntegralZPrimePiÚPrimeZPrimeQrì   rß   rÞ   rÝ   rÜ   rÛ   rE   rF   r<   )r=   r‡   c                   s   ‡ ‡fdd„‰ ˆ |ƒS )Nc                   st   t | tƒr^t | d tƒr&ˆ | d ƒ}nˆj | d t| d ƒ¡}|‡ fdd„| dd … D ƒŽ S ˆj | t| ƒ¡S d S )Nr   c                   s   g | ]}ˆ |ƒ‘qS rU   rU   rF  )ÚrecurserU   rV   r_   -  r`   zRMathematicaParser._from_fullformlist_to_sympy.<locals>.recurse.<locals>.<listcomp>rZ   )rj   rÐ   Ú_node_conversionsÚgetr<   Ú_atom_conversionsrK   )rH  rI  ©rS  r“   rU   rV   rS  '  s    
z>MathematicaParser._from_fullformlist_to_sympy.<locals>.recurserU   )r“   Zfull_form_listrU   rW  rV   rË   %  s    
z-MathematicaParser._from_fullformlist_to_sympyc                 C  s,   |}| j  ¡ D ]\}}| t|ƒ|¡}q|S rr   )rT  rŸ   rÁ   r<   )r“   ZmformrH  Zmma_formZ
sympy_noderU   rU   rV   Ú_from_fullformsympy_to_sympy3  s    z.MathematicaParser._from_fullformsympy_to_sympy)N)F)…Ú__name__Ú
__module__Ú__qualname__Ú__doc__rŒ   r   ZarcZtrir|   r®   Úlowerr   r   rÀ   r«   r¬   r­   rÄ   r£   ZARG_MTRX_PATTERNrª   rˆ   Ú__annotations__r‰   rŠ   Úclassmethodrs   r”   r‹   r·   r³   r§   r¢   r¡   r    rQ   rX   r-  r,  r3  r.  r0  r1  rù   r2  r  rþ   r  r  ré   r   r  r  rÉ   r  r  r  rÊ   r)  r*  r  r/  rC  rL  r   r   r   r
   r   r   r   r   r6   r7   r8   r   r   r   r   r   r   r   r   r;   r:   r9   r   r   r   r   r   r   r   r   rK  r   r    r!   r"   r#   r$   r%   r&   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   rM   rN   r3   r4   r5   r?   rA   r@   rB   rC   rD   rE   rF   rq   rT  r=   r>   rV  rË   rX  rU   rU   rU   rV   rP   n   sÄ  
êÿü
üú
üú
üú
úøã)ú	þ	


?'B
%




ÿüÝ'þ

/	6#w±SþrP   )\Ú
__future__r   r«   r4  Ú	itertoolsr   r   r   rK  r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   Zsympy.core.sympifyrK   rL   Zsympy.functions.special.besselrM   Z'sympy.functions.special.error_functionsrN   Zsympy.utilities.exceptionsrO   rW   rY   rq   rt   rP   rU   rU   rU   rV   Ú<module>   s"   ÿ 6