B ˜‘[» ã@sTdZddlmZmZddlmZddlmZmZddl m Z e Gdd„deƒƒZ dS) z(Implementation of :class:`Field` class. é)Úprint_functionÚdivision)ÚRing)Ú NotReversibleÚ DomainError)Úpublicc@s`eZdZdZdZdZdd„Zdd„Zdd„Zd d „Z d d „Z d d„Z dd„Z dd„Z dd„ZdS)ÚFieldzRepresents a field domain. TcCstd|ƒ‚dS)z)Returns a ring associated with ``self``. z#there is no ring associated with %sN)r)Úself©r ú8lib/python3.7/site-packages/sympy/polys/domains/field.pyÚget_ringszField.get_ringcCs|S)z*Returns a field associated with ``self``. r )r r r r Ú get_fieldszField.get_fieldcCs||S)z9Exact quotient of ``a`` and ``b``, implies ``__div__``. r )r ÚaÚbr r r Úexquosz Field.exquocCs||S)z2Quotient of ``a`` and ``b``, implies ``__div__``. r )r rrr r r Úquosz Field.quocCs|jS)z0Remainder of ``a`` and ``b``, implies nothing. )Úzero)r rrr r r Úrem sz Field.remcCs|||jfS)z2Division of ``a`` and ``b``, implies ``__div__``. )r)r rrr r r Údiv$sz Field.divcCsdy | ¡}Wntk r"|jSX| | |¡| |¡¡}| | |¡| |¡¡}| ||¡|S)a¶ Returns GCD of ``a`` and ``b``. This definition of GCD over fields allows to clear denominators in `primitive()`. >>> from sympy.polys.domains import QQ >>> from sympy import S, gcd, primitive >>> from sympy.abc import x >>> QQ.gcd(QQ(2, 3), QQ(4, 9)) 2/9 >>> gcd(S(2)/3, S(4)/9) 2/9 >>> primitive(2*x/3 + S(4)/9) (2/9, 3*x + 2) )r rZoneÚgcdÚnumerÚlcmÚdenomÚconvert)r rrÚringÚpÚqr r r r(s z Field.gcdcCsfy | ¡}Wntk r$||SX| | |¡| |¡¡}| | |¡| |¡¡}| ||¡|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 rrrrrr)r rrrrrr r r rEs  z Field.lcmcCs|r d|Stdƒ‚dS)z!Returns ``a**(-1)`` if possible. ézzero is not reversibleN)r)r rr r r Úrevert]sz Field.revertN)Ú__name__Ú __module__Ú __qualname__Ú__doc__Zis_FieldZis_PIDr r rrrrrrrr r r r r srN) r"Z __future__rrZsympy.polys.domains.ringrZsympy.polys.polyerrorsrrZsympy.utilitiesrrr r r r Ús