OtjUdZddlmZddlmZddlZddlmZddlm Z ddl m Z ddl m Z dd lmZe Gd d ee ZiZd ed <dZdS)z1Implementation of :class:`ModularInteger` class. ) annotations)AnyN)PicklableWithSlots)CoercionFailed) DomainElement)public)sympy_deprecation_warningc eZdZdZd\ZZZZdZdZ dZ dZ dZ dZ d Zd Zd Zd Zd ZedZdZdZdZdZdZdZdZdZdZdZdZdZ dZ!dZ"dZ#dZ$dZ%d Z&d!Z'd"Z(ed#Z)d$Z*d%S)&ModularIntegerz(A class representing a modular integer. )NNNN)valc|jSN)_parentselfs `/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/sympy/polys/domains/modularinteger.pyparentzModularInteger.parents |ct||jr|j|jz|_dS|j||jz|_dSr) isinstance __class__r moddomconvert)rr s r__init__zModularInteger.__init__sL c4> * * 8w)DHHHx'',,tx7DHHHrc|jSr)rrs rmoduluszModularInteger.modulus s xrc8t|j|jfSr)hashr rrs r__hash__zModularInteger.__hash__#sTXtx()))rc0|jjd|jdS)N())r__name__r rs r__repr__zModularInteger.__repr__&s>222DHHH==rc$|jd|jS)Nz mod )r rrs r__str__zModularInteger.__str__)s"hhh11rc*t|jSr)intr rs r__int__zModularInteger.__int__,s48}}rctddd|jr)|j|jdzkr|jS|j|jz S|jS)NzModularInteger.to_int() is deprecated. Use int(a) or K = GF(p) and K.to_int(a) instead of a.to_int(). 1.13zmodularinteger-to-int)deprecated_since_versionactive_deprecations_target)r symr rrs rto_intzModularInteger.to_int/sb! &,'>      8 x48q=((xx$(**8Orc|Srrs r__pos__zModularInteger.__pos__Bs rc8||j Sr)rr rs r__neg__zModularInteger.__neg__Es~~txi(((rct||r|jS |j|S#t$rYdSwxYwr)rr rrr)clsothers r_get_valzModularInteger._get_valHsW eS ! ! 9  wu---!   tt s3 AAcx||}|||j|zStSrr:rr NotImplementedrr9r s r__add__zModularInteger.__add__R6mmE"" ?>>$(S.11 1! !rc,||Srr?rr9s r__radd__zModularInteger.__radd__Z||E"""rcx||}|||j|z StSrr<r>s r__sub__zModularInteger.__sub__]r@rc.| |SrrBrCs r__rsub__zModularInteger.__rsub__esu%%%rcx||}|||j|zStSrr<r>s r__mul__zModularInteger.__mul__hr@rc,||Sr)rKrCs r__rmul__zModularInteger.__rmul__prErc||}|0||j||zStSr)r:rr _invertr=r>s r __truediv__zModularInteger.__truediv__ssCmmE"" ?>>$(T\\#->->">?? ?! !rcP||Sr)invertrKrCs r __rtruediv__zModularInteger.__rtruediv__{s{{}}$$U+++rcx||}|||j|zStSrr<r>s r__mod__zModularInteger.__mod__~r@rcx||}||||jzStSrr<r>s r__rmod__zModularInteger.__rmod__s6mmE"" ?>>#.11 1! !rc|s||jjS|dkr|j| }}n|j}|t |t ||jS)Nr)rronerRr powr)r)rexpr s r__pow__zModularInteger.__pow__sn 0>>$(,// / 77{{}}(3$CC(C~~c#s3xx::;;;rcp||}|tS||j||jzSr)r:r=r rrr9opr s r_comparezModularInteger._compares8mmE"" ;! !r$(C$(N+++rc||}|tStdddd||j||jzS)Nz~Ordered comparisons with modular integers are deprecated. Use e.g. int(a) < int(b) instead of a < b. r,zmodularinteger-compare)r-r. stacklevel)r:r=r r rr^s r_compare_deprecatedz"ModularInteger._compare_deprecatedsammE"" ;! !! &,'?    r$(C$(N+++rcB||tjSr)r`operatoreqrCs r__eq__zModularInteger.__eq__}}UHK000rcB||tjSr)r`rfnerCs r__ne__zModularInteger.__ne__rircB||tjSr)rdrfltrCs r__lt__zModularInteger.__lt__''x{;;;rcB||tjSr)rdrflerCs r__le__zModularInteger.__le__rprcB||tjSr)rdrfgtrCs r__gt__zModularInteger.__gt__rprcB||tjSr)rdrfgerCs r__ge__zModularInteger.__ge__rprc*t|jSr)boolr rs r__bool__zModularInteger.__bool__sDH~~rcB|j||jSr)rrRr)r8values rrOzModularInteger._invertsw~~eSW---rc\|||jSr)rrOr rs rrRzModularInteger.inverts"~~dll4844555rN)+r$ __module__ __qualname____doc__rrr0r __slots__rrrr r%r'r*r1r4r6 classmethodr:r?rDrGrIrKrMrPrSrUrWr\r`rdrhrlrorsrvryr|rOrRr3rrr r s4223Cc7I888 ***>>>222&)))["""###"""&&&"""###""",,,"""""" < < <,,,,,,$111111<<<<<<<<<<<<..[.66666rr z0dict[tuple[Any, Any, Any], type[ModularInteger]]_modular_integer_cachecR d}n#t$rd}YnwxYw|rdkrtdzf} t|}nI#t$r<Gfddt }r dz|_n dz|_|t|<YnwxYw|S) z1Create custom class for specific integer modulus.TFz*modulus must be a positive integer, got %sc"eZdZcZZZZdS)"ModularIntegerFactory..clsN)r$rrrrr0r)_dom_mod_symrsrr8rs# $MCcGGGrr8zSymmetricModularIntegerMod%szModularIntegerMod%s)rr ValueErrorrKeyErrorr r$)rrrrokkeyr8s```` rModularIntegerFactoryrs)||D!!   NELMMM d C *$S)  * * *          .     89D@CLL047CL&)s### * Js -- AAB$#B$)r __future__rtypingrrfsympy.polys.polyutilsrsympy.polys.polyerrorsr!sympy.polys.domains.domainelementrsympy.utilitiesrsympy.utilities.exceptionsr r r__annotations__rr3rrrs777""""""444444111111;;;;;;""""""@@@@@@}6}6}6}6}6'}6}6}6~LNMMMMr