U L?h @sDdZddlmZddlmZmZddlmZeGdddeZdS)z(Implementation of :class:`Field` class. )Ring) NotReversible DomainError)publicc@sheZdZdZdZdZddZddZddZd d Z d d Z d dZ ddZ ddZ ddZddZdS)FieldzRepresents a field domain. TcCstd|dS)z)Returns a ring associated with ``self``. z#there is no ring associated with %sN)rselfr K/var/www/html/venv/lib/python3.8/site-packages/sympy/polys/domains/field.pyget_ringszField.get_ringcCs|S)z*Returns a field associated with ``self``. r rr r r get_fieldszField.get_fieldcCs||S)z=Exact quotient of ``a`` and ``b``, implies ``__truediv__``. r rabr r r exquosz Field.exquocCs||S)z6Quotient of ``a`` and ``b``, implies ``__truediv__``. r r r r r quosz Field.quocCs|jS)z0Remainder of ``a`` and ``b``, implies nothing. zeror r r r remsz Field.remcCs|||jfS)z6Division of ``a`` and ``b``, implies ``__truediv__``. rr r r r div#sz Field.divcCshz |}Wntk r&|jYSX|||||}|||||}||||S)a 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 ronegcdnumerlcmdenomconvertrrrringpqr r r r's  z Field.gcdcCsjz |}Wntk r(||YSX|||||}|||||}||||S)z 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 z Field.lcmcCs|r d|StddS)z!Returns ``a**(-1)`` if possible. zzero is not reversibleN)rrrr r r revert_sz Field.revertcCst|S)z$Return true if ``a`` is a invertible)boolr!r r r is_unitfsz Field.is_unitN)__name__ __module__ __qualname____doc__Zis_FieldZis_PIDr r rrrrrrr"r$r r r r rs rN) r(Zsympy.polys.domains.ringrZsympy.polys.polyerrorsrrZsympy.utilitiesrrr r r r s