o jg ã@sDdZddlmZddlmZmZddlmZeGdd„deƒƒZdS)z(Implementation of :class:`Field` class. é)ÚRing)Ú NotReversibleÚ DomainError)Úpublicc@sheZdZdZdZdZdd„Zdd„Zdd„Zd d „Z d d „Z d d„Z dd„Z dd„Z dd„Zdd„ZdS)ÚFieldzRepresents a field domain. TcCs td|ƒ‚)z)Returns a ring associated with ``self``. z#there is no ring associated with %s)r©Úself©r úQ/var/www/html/zoom/venv/lib/python3.10/site-packages/sympy/polys/domains/field.pyÚget_rings zField.get_ringcCs|S)z*Returns a field associated with ``self``. r rr r r Ú get_fieldszField.get_fieldcCó||S)z=Exact quotient of ``a`` and ``b``, implies ``__truediv__``. r ©rÚaÚbr r r Úexquoóz Field.exquocCr )z6Quotient of ``a`` and ``b``, implies ``__truediv__``. r rr r r Úquorz Field.quocCs|jS)z0Remainder of ``a`` and ``b``, implies nothing. ©Úzerorr r r Úremsz Field.remcCs|||jfS)z6Division of ``a`` and ``b``, implies ``__truediv__``. rrr r r Údiv#sz Field.divcCsfz| ¡}Wn ty|jYSw| | |¡| |¡¡}| | |¡| |¡¡}| ||¡|S)aÙ Returns GCD of ``a`` and ``b``. This definition of GCD over fields allows to clear denominators in `primitive()`. Examples ======== >>> from sympy.polys.domains import QQ >>> from sympy import S, gcd, primitive >>> from sympy.abc import x >>> QQ.gcd(QQ(2, 3), QQ(4, 9)) 2/9 >>> gcd(S(2)/3, S(4)/9) 2/9 >>> primitive(2*x/3 + S(4)/9) (2/9, 3*x + 2) )r rÚoneÚgcdÚnumerÚlcmÚdenomÚconvert©rrrÚringÚpÚqr r r r's   ÿz Field.gcdcCshz| ¡}Wn ty||YSw| | |¡| |¡¡}| | |¡| |¡¡}| ||¡|S)zç Returns LCM of ``a`` and ``b``. >>> from sympy.polys.domains import QQ >>> from sympy import S, lcm >>> QQ.lcm(QQ(2, 3), QQ(4, 9)) 4/3 >>> lcm(S(2)/3, S(4)/9) 4/3 )r rrrrrrrr r r rGs   ÿz Field.lcmcCs|rd|Stdƒ‚)z!Returns ``a**(-1)`` if possible. ézzero is not reversible)r©rrr r r Úrevert_sz Field.revertcCst|ƒS)z$Return true if ``a`` is a invertible)Úboolr#r r r Úis_unitfrz Field.is_unitN)Ú__name__Ú __module__Ú __qualname__Ú__doc__Úis_FieldÚis_PIDr r rrrrrrr$r&r r r r rs  rN) r*Úsympy.polys.domains.ringrÚsympy.polys.polyerrorsrrÚsympy.utilitiesrrr r r r Ús