Sj/ddlmZddlZddlmZddlmZddlmZddl m Z ddl m Z ddl mZmZGdd e e Zej Zd efd ZGd de e Zy)N)Expr) _sympifyit) AtomicExpr)Number)global_parameters)S SingletoncheZdZdZdZdZdZdZdZdZ dZ dZ dZ dZ defdZd Z ed ed ZeZed ed Zed ed Zed edZeZed edZdZdZdZdZfdZdZdZ dZ!dZ"dZ#dZ$ed edZ%e%Z&dZ'dZ(xZ)S) IntInfinityahPositive integer infinite quantity. Integer infinity is a value in an extended integers which is greater than all other integers. We distinguish it from sympy's existing notion of infinity in that it reports that it is_integer. Infinity is a singleton, and can be accessed by ``S.IntInfinity``, or can be imported as ``int_oo``. TFY@c,tj|SNr__new__clss Y/var/www/html/ia-enhanced/venv/lib/python3.12/site-packages/torch/utils/_sympy/numbers.pyrzIntInfinity.__new__*!!#&&returncy)Nint_oor selfprinters r _sympystrzIntInfinity._sympystr-src||k(r|Syrr roldnews r _eval_subszIntInfinity._eval_subs0 3;J rotherct|trhtjrX|tj tj fvr|S|tjtjfvrtjS|Stj||Sr) isinstancerrevaluaterInfinityNegativeInfinityNegativeIntInfinityNaN__add__rr$s rr,zIntInfinity.__add__=sg eV $):)C)CQ%7%788 ..66uu K~~dE**rc^t|trtjrx|tj urtj S|tj urtj S|tjtjfvrtjS|Stj||Sr) r&rrr'rr(r)r r+__sub__r-s rr/zIntInfinity.__sub__Isy eV $):)C)C ")))***zz!..uu K~~dE**rc&| j|Srr,r-s r__rsub__zIntInfinity.__rsub__Uu%%rct|tr\tjrL|js|t j urt j S|jr|St jStj||Sr) r&rrr'is_zerorr+is_extended_positiver*__mul__r-s rr7zIntInfinity.__mul__YsZ eV $):)C)C}}uu )) (( (~~dE**rct|trtjr|tj tj tjtjtjfvrtjS|jrtj StjStj||Sr r&rrr'rr(r r)r*r+is_extended_nonnegative __truediv__r-s rr;zIntInfinity.__truediv__es eV $):)C)C  ""%% uu ,,zz!%% %!!$..rc"tjSrrr rs r__abs__zIntInfinity.__abs__u }}rc"tjSrrr*r>s r__neg__zIntInfinity.__neg__xs$$$rc|jrtjS|jrtjS|tj urtj S|tj urtj S|jdur|jruddl m }||}|jrtj S|jrtjS|jrtj S||jzSyy)NFr)re)r6rr is_extended_negativeZeror+ComplexInfinityis_extended_real is_number$sympy.functions.elementary.complexesrE is_positive is_negativer5evalf)rexptrE expt_reals r _eval_powerzIntInfinity._eval_power{s  $ $==  $ $66M 155=55L 1$$ $55L  E )dnn ?4I$$((($$vv   uu 4::<' '/= )rc"tjSr)mlibfinfrprecs r _as_mpf_valzIntInfinity._as_mpf_vals yyrc t|Srsuper__hash__r __class__s rr[zIntInfinity.__hash__w!!rc&|tjuSrr=r-s r__eq__zIntInfinity.__eq__s %%rc&|tjuSrr=r-s r__ne__zIntInfinity.__ne__sAMM))rc|tjurtjS|tjurtjStj Srrr(sympyfalser truer-s r__gt__zIntInfinity.__gt__s8 AJJ ;;  amm #;; :: rc|tjurtjS|tjurtj Stj Srrdr-s r__ge__zIntInfinity.__ge__s8 AJJ ;;  amm #:: :: rc|tjurtjS|tjurtj Stj Srrr(rergr rfr-s r__lt__zIntInfinity.__lt__s8 AJJ ::  amm #;; ;; rc|tjurtjS|tjurtjStj Srrlr-s r__le__zIntInfinity.__le__s8 AJJ ::  amm #:: ;; rcNt|tstStjSrr&rNotImplementedrr+r-s r__mod__zIntInfinity.__mod__%&! !uu 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 sJ JNIMHLI'C (+)+H( +) +(&)&(+)+H( /) /%(,"&*() Hrr ) metaclassrc|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_infiniters6       rcneZdZdZdZdZdZdZdZdZ dZ dZ dZ dZ dZdefd Z ed ed ZeZed ed Zed ed Zed edZeZed edZdZdZdZdZfdZdZdZ dZ!dZ"dZ#dZ$ed edZ%e%Z&dZ'dZ(dZ)xZ*S)r*zNegative integer infinite quantity. NegativeInfinity is a singleton, and can be accessed by ``S.NegativeInfinity``. See Also ======== IntInfinity r TFr c,tj|Srrrs rrzNegativeIntInfinity.__new__rrc||k(r|Syrr rs rr"zNegativeIntInfinity._eval_subsr#rrcy)Nz-int_oor rs rrzNegativeIntInfinity._sympystrsrr$ct|trftjrV|tj urtj S|tj tjfvrtjS|Stj||Sr) r&rrr'rr(r r+r,r-s rr,zNegativeIntInfinity.__add__ s_ eV $):)C)C "zz!..uu K~~dE**rct|trftjrV|tj urtj S|tjtjfvrtjS|Stj||Sr) r&rrr'rr)r(r*r+r/r-s rr/zNegativeIntInfinity.__sub__sc eV $):)C)C***zz!..66uu K~~dE**rc&| j|Srr1r-s rr2zNegativeIntInfinity.__rsub__#r3rct|tr\tjrL|js|t j urt j S|jr|St jStj||Sr) r&rrr'r5rr+r6r r7r-s rr7zNegativeIntInfinity.__mul__'sX eV $):)C)C}}uu )) == ~~dE**rcht|trtjr}|tj tj tjtjtjfvrtjS|jr|Stj Stj||Srr9r-s rr;zNegativeIntInfinity.__truediv__3s eV $):)C)C  ""%% uu ,, :: !!$..rc"tjSrr=r>s rr?zNegativeIntInfinity.__abs__Cr@rc"tjSrr=r>s rrCzNegativeIntInfinity.__neg__Fr@rcp|jr)|tjtjtjtj tj fvrtjSt|tjr8|jr,|jrtj Stj Stj |z}tj|z}|dk(r|jr|S|tjur(|jr|jstjS||zSy)Nr)rJrr+r(r)r r*r&reIntegerr6is_odd NegativeOne is_finiterHr5)rrOinf_parts_parts rrQzNegativeIntInfinity._eval_powerIs >> "" %% uu $ .43L3L;;000==(}}d*H]]D(F1}!1!1A---$$(((H$ $5 rc"tjSr)rSfninfrUs rrWzNegativeIntInfinity._as_mpf_valfs zzrc t|SrrYr\s rr[zNegativeIntInfinity.__hash__ir^rc&|tjuSrrBr-s rr`zNegativeIntInfinity.__eq__ls----rc&|tjuSrrBr-s rrbzNegativeIntInfinity.__ne__osA1111rc|tjurtjS|tjurtj Stj Srrr)rergr*rfr-s rrhzNegativeIntInfinity.__gt__rs< A&& &::  a++ +;; ;; rc|tjurtjS|tjurtjStj Srrr-s rrjzNegativeIntInfinity.__ge__zs< A&& &::  a++ +:: ;; rc|tjurtjS|tjurtjStj Srrr)rerfr*rgr-s rrmzNegativeIntInfinity.__lt__s< A&& &;;  a++ +;; :: rc|tjurtjS|tjurtj Stj Srrr-s rrozNegativeIntInfinity.__le__s< A&& &;;  a++ +:: :: rcNt|tstStjSrrqr-s rrszNegativeIntInfinity.__mod__rtrc|Srr r>s rrvzNegativeIntInfinity.floorrwrc|Srr r>s rryzNegativeIntInfinity.ceilingrwrcFtjdtjdiS)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*sM LJNMIHI'C(+)+H(+)+(&)&(+)+H( /) /%:".2() H4rr*) mpmath.libmplibmprSrersympy.core.decoratorsrsympy.core.exprrsympy.core.numbersrsympy.core.parametersrsympy.core.singletonrr r rboolrr*r rrrsU ,&%3-|&I|~ &4&I4r