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This module contains query handlers responsible for calculus queries:
infinitesimal, finite, etc.
é    )ÚQÚask)ÚExprÚAddÚMulÚPowÚSymbol)ÚNegativeInfinityÚGoldenRatioÚInfinityÚExp1ÚComplexInfinityÚImaginaryUnitÚNaNÚNumberÚPiÚEÚTribonacciConstant)ÚcosÚexpÚlogÚsignÚsin)Ú	conjunctsé   )ÚFinitePredicateÚInfinitePredicateÚPositiveInfinitePredicateÚNegativeInfinitePredicatec                 C   s*   | j dur| j S t | ¡t|ƒv rdS dS )z
    Handles Symbol.
    NT)Ú	is_finiter   Úfiniter   ©ÚexprÚassumptions© r$   úc/home/air/sanwanet/gpt-api/venv/lib/python3.10/site-packages/sympy/assumptions/handlers/calculus.pyÚ_   s
   
r&   c                 C   sx   d}d}| j D ]2}tt |¡|ƒ}|rqtt |¡|ƒ}|dkr$||ks.|du r1d||fv r1 dS |}|dur9|}q|S )ab  
    Return True if expr is bounded, False if not and None if unknown.

    Truth Table:

    +-------+-----+-----------+-----------+
    |       |     |           |           |
    |       |  B  |     U     |     ?     |
    |       |     |           |           |
    +-------+-----+---+---+---+---+---+---+
    |       |     |   |   |   |   |   |   |
    |       |     |'+'|'-'|'x'|'+'|'-'|'x'|
    |       |     |   |   |   |   |   |   |
    +-------+-----+---+---+---+---+---+---+
    |       |     |           |           |
    |   B   |  B  |     U     |     ?     |
    |       |     |           |           |
    +---+---+-----+---+---+---+---+---+---+
    |   |   |     |   |   |   |   |   |   |
    |   |'+'|     | U | ? | ? | U | ? | ? |
    |   |   |     |   |   |   |   |   |   |
    |   +---+-----+---+---+---+---+---+---+
    |   |   |     |   |   |   |   |   |   |
    | U |'-'|     | ? | U | ? | ? | U | ? |
    |   |   |     |   |   |   |   |   |   |
    |   +---+-----+---+---+---+---+---+---+
    |   |   |     |           |           |
    |   |'x'|     |     ?     |     ?     |
    |   |   |     |           |           |
    +---+---+-----+---+---+---+---+---+---+
    |       |     |           |           |
    |   ?   |     |           |     ?     |
    |       |     |           |           |
    +-------+-----+-----------+---+---+---+

        * 'B' = Bounded

        * 'U' = Unbounded

        * '?' = unknown boundedness

        * '+' = positive sign

        * '-' = negative sign

        * 'x' = sign unknown

        * All Bounded -> True

        * 1 Unbounded and the rest Bounded -> False

        * >1 Unbounded, all with same known sign -> False

        * Any Unknown and unknown sign -> None

        * Else -> None

    When the signs are not the same you can have an undefined
    result as in oo - oo, hence 'bounded' is also undefined.
    éÿÿÿÿTNF)Úargsr   r   r    Úextended_positive)r"   r#   r   ÚresultÚargÚ_boundedÚsr$   r$   r%   r&       s   >
€c                 C   s    d}d}| j D ]F}tt |¡|ƒ}|r'tt |¡|ƒdur&|du r$ dS d}q|du rF|du r2 dS tt |¡|ƒdu r? dS |durEd}q|rK dS d}q|S )a)  
    Return True if expr is bounded, False if not and None if unknown.

    Truth Table:

    +---+---+---+--------+
    |   |   |   |        |
    |   | B | U |   ?    |
    |   |   |   |        |
    +---+---+---+---+----+
    |   |   |   |   |    |
    |   |   |   | s | /s |
    |   |   |   |   |    |
    +---+---+---+---+----+
    |   |   |   |        |
    | B | B | U |   ?    |
    |   |   |   |        |
    +---+---+---+---+----+
    |   |   |   |   |    |
    | U |   | U | U | ?  |
    |   |   |   |   |    |
    +---+---+---+---+----+
    |   |   |   |        |
    | ? |   |   |   ?    |
    |   |   |   |        |
    +---+---+---+---+----+

        * B = Bounded

        * U = Unbounded

        * ? = unknown boundedness

        * s = signed (hence nonzero)

        * /s = not signed
    TFN)r(   r   r   r    ÚzeroÚextended_nonzero)r"   r#   r*   Úpossible_zeror+   r,   r$   r$   r%   r&   r   s,   '
€€c                 C   s<  | j tkrtt | j¡|ƒS tt | j ¡|ƒ}tt | j¡|ƒ}|du r*|du r*dS |du r9tt | j¡|ƒr9dS |re|rett | j ¡|ƒ}tt | j¡|ƒ}|du rY|du rYdS |durc|durcdS dS t	| j ƒdkdkrytt 
| j¡|ƒrydS t	| j ƒdkdkrtt | j¡|ƒrdS t	| j ƒdkdkrœ|du rœdS dS )z¹
    * Unbounded ** NonZero -> Unbounded

    * Bounded ** Bounded -> Bounded

    * Abs()<=1 ** Positive -> Bounded

    * Abs()>=1 ** Negative -> Bounded

    * Otherwise unknown
    NFTé   )Úbaser   r   r   r    r   r/   r.   ÚnegativeÚabsr)   Úextended_negative)r"   r#   Úbase_boundedÚexp_boundedÚis_base_zeroÚis_exp_negativer$   r$   r%   r&   ¯   s.   
$$c                 C   s   t t | j¡|ƒS ©N)r   r   r    r   r!   r$   r$   r%   r&   Õ   s   c                 C   s2   t t | jd ¡|ƒrdS t t | jd ¡ |ƒS )Nr   F)r   r   Úinfiniter(   r.   r!   r$   r$   r%   r&   Ù   s   c                 C   ó   dS ©NTr$   r!   r$   r$   r%   r&   á   s   c                 C   r<   ©NFr$   r!   r$   r$   r%   r&   æ   ó   c                 C   s   d S r:   r$   r!   r$   r$   r%   r&   ê   r?   c                 C   s"   t  | ¡ |¡}|d u rd S | S r:   )r   r    Ú	_eval_ask)r"   r#   r   r$   r$   r%   r&   ò   s   c                 C   r<   r=   r$   r!   r$   r$   r%   r&   ý   r?   c                 C   r<   r>   r$   r!   r$   r$   r%   r&     r?   c                 C   r<   r=   r$   r!   r$   r$   r%   r&   
  r?   c                 C   r<   r>   r$   r!   r$   r$   r%   r&     r?   N)&Ú__doc__Úsympy.assumptionsr   r   Ú
sympy.corer   r   r   r   r   Úsympy.core.numbersr	   r
   r   r   r   r   r   r   r   r   r   Úsympy.functionsr   r   r   r   r   Úsympy.logic.boolalgr   Úpredicates.calculusr   r   r   r   Úregisterr&   Úregister_manyr$   r$   r$   r%   Ú<module>   sJ    4


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