tj/ddlmZddlZddlmZddlmZddlmZddl m Z ddl m Z ddl mZmZGdd e e ZejZd efd ZGd de e ZdS)N)Expr) _sympifyit) AtomicExpr)Number)global_parameters)S SingletonceZdZdZdZdZdZdZdZdZ dZ dZ dZ dZ defdZd Z ed ed ZeZed ed Zed ed Zed edZeZed edZdZdZdZdZfdZdZdZ dZ!dZ"dZ#dZ$ed edZ%e%Z&dZ'dZ(xZ)S) IntInfinityahPositive integer infinite quantity. Integer infinity is a value in an extended integers which is greater than all other integers. We distinguish it from sympy's existing notion of infinity in that it reports that it is_integer. Infinity is a singleton, and can be accessed by ``S.IntInfinity``, or can be imported as ``int_oo``. TFY@c*tj|SNr__new__clss X/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/torch/utils/_sympy/numbers.pyrzIntInfinity.__new__*!#&&&returncdS)Nint_oor selfprinters r _sympystrzIntInfinity._sympystr-sxrc||kr|SdSrr roldnews r _eval_subszIntInfinity._eval_subs0 3;;J ;rotherct|trPtjrD|tjtjfvr|S|tjtjfvr tjS|Stj ||Sr) isinstancerrevaluaterInfinityNegativeInfinityNegativeIntInfinityNaN__add__rr$s rr,zIntInfinity.__add__=sl eV $ $ ):)C Q%7888 .666u K~dE***rc&t|trhtjr\|tjur tjS|tjur tjS|tjtjfvr tjS|Stj ||Sr) r&rrr'rr(r)r r+__sub__r-s rr/zIntInfinity.__sub__Is} eV $ $ ):)C  ""))***z!...u K~dE***rc.| |Srr,r-s r__rsub__zIntInfinity.__rsub__Uu%%%rct|trBtjr6|js|t jur t jS|jr|St jStj ||Sr) r&rrr'is_zerorr+is_extended_positiver*__mul__r-s rr7zIntInfinity.__mul__Yse eV $ $ )):)C )} u )  ( (~dE***rc:t|trrtjrf|tjtjtjtjtj fvr tj S|j r tjStjStj ||Sr r&rrr'rr(r r)r*r+is_extended_nonnegative __truediv__r-s rr;zIntInfinity.__truediv__es eV $ $ &):)C &  "% u , "z!% %!$...rctjSrrr rs r__abs__zIntInfinity.__abs__u }rctjSrrr*r>s r__neg__zIntInfinity.__neg__xs $$rc|jr tjS|jr tjS|tjur tjS|tjur tjS|jdurh|jrcddl m }||}|j r tjS|j r tjS|j r tjS||zSdSdS)NFr)re)r6rr is_extended_negativeZeror+ComplexInfinityis_extended_real is_number$sympy.functions.elementary.complexesrE is_positive is_negativer5evalf)rexptrE expt_reals r _eval_powerzIntInfinity._eval_power{s  $ !=  $ 6M 15==5L 1$ $ $5L  E ) )dn ) ? ? ? ? ? ?4I$ )(($ v   u 4::<<' ' * ) ) )rctjSr)mlibfinfrprecs r _as_mpf_valzIntInfinity._as_mpf_vals yrcDtSrsuper__hash__r __class__s rr[zIntInfinity.__hash__ww!!!rc|tjuSrr=r-s r__eq__zIntInfinity.__eq__s %%rc|tjuSrr=r-s r__ne__zIntInfinity.__ne__sAM))rc|tjur tjS|tjur tjStjSrrr(sympyfalser truer-s r__gt__zIntInfinity.__gt__s4 AJ  ;  am # #; : rc|tjur tjS|tjur tjStjSrrdr-s r__ge__zIntInfinity.__ge__s4 AJ  ;  am # #: : rc|tjur tjS|tjur tjStjSrrr(rergr rfr-s r__lt__zIntInfinity.__lt__s4 AJ  :  am # #; ; rc|tjur tjS|tjur tjStjSrrlr-s r__le__zIntInfinity.__le__s4 AJ  :  am # #: ; rcRt|tstStjSrr&rNotImplementedrr+r-s r__mod__zIntInfinity.__mod__!%&& "! !u rc|Srr r>s rfloorzIntInfinity.floor rc|Srr r>s rceilingzIntInfinity.ceilingrwr)*__name__ __module__ __qualname____doc__ is_integeris_commutativerJrI is_comparabler6is_prime _op_priority __slots__rstrrr"rrrr,__radd__r/r2r7__rmul__r;r?rCrQrWr[r`rbrhrjrmrors__rmod__rvry __classcell__r]s@rr r sh  JNIMHLI'''C Z((++)(+HZ(( + +)( +Z((&&)(&Z((++)(+HZ(( / /)( /%%%(((,"""""&&&***Z(()( Hrr ) metaclassrcb|tjtjtjtjfvS)a}Check if an expression is any type of infinity (positive or negative). This handles both sympy's built-in infinities (oo, -oo) and PyTorch's integer infinities (int_oo, -int_oo). Note: We cannot rely on sympy's is_finite property because IntInfinity and NegativeIntInfinity have is_integer=True, which implies is_finite=True in sympy's assumption system. )rr(r)r r*)exprs r is_infiniters,       rceZdZdZdZdZdZdZdZdZ dZ dZ dZ dZ dZdefd Z ed ed ZeZed ed Zed ed Zed edZeZed edZdZdZdZdZfdZdZdZ dZ!dZ"dZ#dZ$ed edZ%e%Z&dZ'dZ(dZ)xZ*S)r*zNegative integer infinite quantity. NegativeInfinity is a singleton, and can be accessed by ``S.NegativeInfinity``. See Also ======== IntInfinity r TFr c*tj|Srrrs rrzNegativeIntInfinity.__new__rrc||kr|SdSrr rs rr"zNegativeIntInfinity._eval_subsr#rrcdS)Nz-int_oor rs rrzNegativeIntInfinity._sympystrsyrr$ct|trNtjrB|tjur tjS|tjtjfvr tjS|Stj||Sr) r&rrr'rr(r r+r,r-s rr,zNegativeIntInfinity.__add__ sf eV $ $ ):)C  ""z!...u K~dE***rct|trNtjrB|tjur tjS|tjtjfvr tjS|Stj ||Sr) r&rrr'rr)r(r*r+r/r-s rr/zNegativeIntInfinity.__sub__sh eV $ $ ):)C ***z!.666u K~dE***rc.| |Srr1r-s rr2zNegativeIntInfinity.__rsub__#r3rct|trBtjr6|js|t jur t jS|jr|St jStj ||Sr) r&rrr'r5rr+r6r r7r-s rr7zNegativeIntInfinity.__mul__'sd eV $ $ !):)C !} u )  = ~dE***rc&t|trhtjr\|tjtjtjtjtj fvr tj S|j r|StjStj ||Srr9r-s rr;zNegativeIntInfinity.__truediv__3s eV $ $ ):)C   "% u ,  : !$...rctjSrr=r>s rr?zNegativeIntInfinity.__abs__Cr@rctjSrr=r>s rrCzNegativeIntInfinity.__neg__Fr@rc|jr|tjtjtjtjtjfvr tjSt|tj r&|j r|j r tjStjStj|z}tj |z}|dkr |j r|S|tjur|j r|js tjS||zSdS)Nr)rJrr+r(r)r r*r&reIntegerr6is_odd NegativeOne is_finiterHr5)rrOinf_parts_parts rrQzNegativeIntInfinity._eval_powerIs > % " % u $ .. )43L );)00=(}d*H]D(F1}}!1}A---$..((H$ $5 % %rctjSr)rSfninfrUs rrWzNegativeIntInfinity._as_mpf_valfs zrcDtSrrYr\s rr[zNegativeIntInfinity.__hash__ir^rc|tjuSrrBr-s rr`zNegativeIntInfinity.__eq__ls---rc|tjuSrrBr-s rrbzNegativeIntInfinity.__ne__osA111rc|tjur tjS|tjur tjStjSrrr)rergr*rfr-s rrhzNegativeIntInfinity.__gt__rs6 A& & &:  a+ + +; ; rc|tjur tjS|tjur tjStjSrrr-s rrjzNegativeIntInfinity.__ge__zs6 A& & &:  a+ + +: ; rc|tjur tjS|tjur tjStjSrrr)rerfr*rgr-s rrmzNegativeIntInfinity.__lt__s6 A& & &;  a+ + +; : rc|tjur tjS|tjur tjStjSrrr-s rrozNegativeIntInfinity.__le__s6 A& & &;  a+ + +: : rcRt|tstStjSrrqr-s rrszNegativeIntInfinity.__mod__rtrc|Srr r>s rrvzNegativeIntInfinity.floorrwrc|Srr r>s rryzNegativeIntInfinity.ceilingrwrc6tjdtjdiS)N)rrr r>s ras_powers_dictz"NegativeIntInfinity.as_powers_dicts q!-33r)+rzr{r|r}rr~rIrrrFrJrrrr"rrrrrr,rr/r2r7rr;r?rCrQrWr[r`rbrhrjrmrorsrrvryrrrs@rr*r*su  LJNMIHI'''CZ((++)(+HZ((++)(+Z((&&)(&Z((++)(+HZ(( / /)( /%%%:"""""...222Z(()( H4444444rr*) mpmath.libmplibmprSrersympy.core.decoratorsrsympy.core.exprrsympy.core.numbersrsympy.core.parametersrsympy.core.singletonrr r rboolrr*r rrrs7 ,,,,,,&&&&&&%%%%%%333333--------|||||&I||||~ &44444&I444444r