o ki/@sddlmZddlZddlmZddlmZddlmZddl m Z ddl m Z ddl mZmZGdd d e ed ZejZd efd d ZGddde ed ZdS)N)Expr) _sympifyit) AtomicExpr)Number)global_parameters)S Singletoncs<eZdZdZdZdZdZdZdZdZ dZ dZ dZ ddZ defd d Zd d Z ed eddZeZed eddZed eddZed eddZeZed eddZddZddZddZddZfd d!Zd"d#Zd$d%Z d&d'Z!d(d)Z"d*d+Z#d,d-Z$ed ed.d/Z%e%Z&d0d1Z'd2d3Z(Z)S)4 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@cC t|SNr__new__clsr r d/var/www/addictedbytheproject.nl/epg/venv/lib/python3.10/site-packages/torch/utils/_sympy/numbers.pyr* zIntInfinity.__new__returncCdS)Nint_oor selfprinterr r r _sympystr-zIntInfinity._sympystrcC||kr|SdSr r roldnewr r r _eval_subs0zIntInfinity._eval_subsothercCsJt|trtjr|tjtjfvr|S|tjtjfvrtjS|St ||Sr ) isinstancerrevaluaterInfinityNegativeInfinityNegativeIntInfinityNaN__add__rr"r r rr)=s zIntInfinity.__add__cCsVt|tr%tjr%|tjurtjS|tjurtjS|tjtjfvr#tjS|St ||Sr ) r#rrr$rr%r&r r(__sub__r*r r rr+Is   zIntInfinity.__sub__cC | |Sr r)r*r r r__rsub__U zIntInfinity.__rsub__cCBt|trtjr|js|tjurtjS|jr|StjSt ||Sr ) r#rrr$is_zerorr(is_extended_positiver'__mul__r*r r rr3Y zIntInfinity.__mul__cCsPt|tr"tjr"|tjtjtjtjtj fvrtj S|j rtjStjSt ||Sr r#rrr$rr%r r&r'r(is_extended_nonnegative __truediv__r*r r rr7es zIntInfinity.__truediv__cCtjSr rr rr r r__abs__uzIntInfinity.__abs__cCr8r rr'r:r r r__neg__xr<zIntInfinity.__neg__cCs|jrtjS|jr tjS|tjurtjS|tjurtjS|jdurF|jrHddl m }||}|j r4tjS|j r:tjS|j r@tjS||SdSdS)NFr)re)r2rr is_extended_negativeZeror(ComplexInfinityis_extended_real is_number$sympy.functions.elementary.complexesr? is_positive is_negativer1evalf)rexptr? expt_realr r r _eval_power{s&    zIntInfinity._eval_powercCr8r )mlibfinfrprecr r r _as_mpf_valr<zIntInfinity._as_mpf_valc tSr super__hash__r: __class__r rrTrzIntInfinity.__hash__cC |tjuSr r9r*r r r__eq__rzIntInfinity.__eq__cC |tjuSr r9r*r r r__ne__rzIntInfinity.__ne__cC&|tjurtjS|tjurtjStjSr rr%sympyfalser truer*r r r__gt__  zIntInfinity.__gt__cC&|tjurtjS|tjurtjStjSr r\r*r r r__ge__razIntInfinity.__ge__cCrbr rr%r]r_r r^r*r r r__lt__razIntInfinity.__lt__cCr[r rdr*r r r__le__razIntInfinity.__le__cCt|tstStjSr r#rNotImplementedrr(r*r r r__mod__ zIntInfinity.__mod__cC|Sr r r:r r rfloorrzIntInfinity.floorcCrlr r r:r r rceilingrzIntInfinity.ceiling)*__name__ __module__ __qualname____doc__ is_integeris_commutativerDrC is_comparabler2is_prime _op_priority __slots__rstrrr rrir)__radd__r+r.r3__rmul__r7r;r>rKrPrTrXrZr`rcrerfrj__rmod__rmrn __classcell__r r rUrr sV         r ) metaclassrcCs|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')exprr r r is_infinites  rcsDeZdZdZdZdZdZdZdZdZ dZ dZ dZ ddZ dd Zd efd d Z ed eddZeZed eddZed eddZed eddZeZed eddZddZddZddZddZfd d!Zd"d#Zd$d%Z d&d'Z!d(d)Z"d*d+Z#d,d-Z$ed ed.d/Z%e%Z&d0d1Z'd2d3Z(d4d5Z)Z*S)6r'zNegative integer infinite quantity. NegativeInfinity is a singleton, and can be accessed by ``S.NegativeInfinity``. See Also ======== IntInfinity r TFr cCr r rrr r rrrzNegativeIntInfinity.__new__cCrr r rr r rr r!zNegativeIntInfinity._eval_subsrcCr)Nz-int_oor rr r rrrzNegativeIntInfinity._sympystrr"cCsFt|trtjr|tjurtjS|tjtjfvrtjS|St||Sr ) r#rrr$rr%r r(r)r*r r rr)   zNegativeIntInfinity.__add__cCsFt|trtjr|tjurtjS|tjtjfvrtjS|St ||Sr ) r#rrr$rr&r%r'r(r+r*r r rr+rzNegativeIntInfinity.__sub__cCr,r r-r*r r rr.#r/zNegativeIntInfinity.__rsub__cCr0r ) r#rrr$r1rr(r2r r3r*r r rr3'r4zNegativeIntInfinity.__mul__cCsNt|tr!tjr!|tjtjtjtjtj fvrtj S|j r|StjSt ||Sr r5r*r r rr73s zNegativeIntInfinity.__truediv__cCr8r r9r:r r rr;Cr<zNegativeIntInfinity.__abs__cCr8r r9r:r r rr>Fr<zNegativeIntInfinity.__neg__cCs|jrK|tjtjtjtjtjfvrtjSt|tj r&|j r&|j r#tjStjStj|}tj |}|dkr9|j r9|S|tjurG|j rG|jsGtjS||SdS)Nr)rDrr(r%r&r r'r#r]Integerr2is_odd NegativeOne is_finiterBr1)rrIinf_parts_partr r rrKIs2   zNegativeIntInfinity._eval_powercCr8r )rLfninfrNr r rrPfr<zNegativeIntInfinity._as_mpf_valcrQr rRr:rUr rrTirzNegativeIntInfinity.__hash__cCrWr r=r*r r rrXlrzNegativeIntInfinity.__eq__cCrYr r=r*r r rrZorzNegativeIntInfinity.__ne__cCrbr rr&r]r_r'r^r*r r rr`rrazNegativeIntInfinity.__gt__cCr[r rr*r r rrczrazNegativeIntInfinity.__ge__cCr[r rr&r]r^r'r_r*r r rrerazNegativeIntInfinity.__lt__cCrbr rr*r r rrfrazNegativeIntInfinity.__le__cCrgr rhr*r r rrjrkzNegativeIntInfinity.__mod__cCrlr r r:r r rrmrzNegativeIntInfinity.floorcCrlr r r:r r rrnrzNegativeIntInfinity.ceilingcCstjdtjdiS)N)rrr r:r r ras_powers_dictsz"NegativeIntInfinity.as_powers_dict)+rorprqrrrwrsrCrtrur@rDrvrxrr ryrrrir)rzr+r.r3r{r7r;r>rKrPrTrXrZr`rcrerfrjr|rmrnrr}r r rUrr'sX          r') mpmath.libmplibmprLr]rsympy.core.decoratorsrsympy.core.exprrsympy.core.numbersrsympy.core.parametersrsympy.core.singletonrrr rboolrr'r r r rs      @