ó ¡¼™\c@ s…dZddlmZmZddlmZddlmZddlm Z m Z ddl m Z e deefd„ƒYƒZ d S( s1Implementation of :class:`PolynomialRing` class. iÿÿÿÿ(tprint_functiontdivision(tRing(tCompositeDomain(tCoercionFailedtGeneratorsError(tpublictPolynomialRingcB s/eZdZeZZeZeZddd„Z d„Z e d„ƒZ e d„ƒZ e d„ƒZd„Zd„Zd„Zd „Zd „Zd „Zd „Zd „Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Z d„Z!d„Z"d„Z#d„Z$RS(s8A class for representing multivariate polynomial rings. cC sæddlm}t||ƒr@|dkr@|dkr@|}n||||ƒ}||_|j|_|j|_|j|_|j|_|j |_ |rÖ|j j rÖ|j j rÖt |ƒdkrÖt |_qÖn|j |_dS(Niÿÿÿÿ(tPolyRingi(tsympy.polys.ringsRt isinstancetNonetringtdtypetgenstngenstsymbolstdomaintis_Fieldtis_ExacttlentTruetis_PIDtdom(tselftdomain_or_ringRtorderRR ((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pyt__init__s'       *cC s|jj|ƒS(N(R tring_new(Rtelement((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pytnew,scC s |jjS(N(R tzero(R((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pyR/scC s |jjS(N(R tone(R((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pyR 3scC s |jjS(N(R R(R((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pyR7scC s.t|jƒddjtt|jƒƒdS(Nt[t,t](tstrRtjointmapR(R((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pyt__str__;scC s(t|jj|jj|j|jfƒS(N(thasht __class__t__name__R R RR(R((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pyt__hash__>scC sCt|tƒoB|jj|j|jf|jj|j|jfkS(s.Returns `True` if two domains are equivalent. (R RR R RR(Rtother((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pyt__eq__AscC s |jƒS(sConvert `a` to a SymPy object. (tas_expr(Rta((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pytto_sympyGscC s|jj|ƒS(s'Convert SymPy's expression to `dtype`. (R t from_expr(RR/((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pyt from_sympyKscC s||jj||ƒƒS(s*Convert a Python `int` object to `dtype`. (Rtconvert(tK1R/tK0((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pytfrom_ZZ_pythonOscC s||jj||ƒƒS(s/Convert a Python `Fraction` object to `dtype`. (RR3(R4R/R5((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pytfrom_QQ_pythonSscC s||jj||ƒƒS(s(Convert a GMPY `mpz` object to `dtype`. (RR3(R4R/R5((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pyt from_ZZ_gmpyWscC s||jj||ƒƒS(s(Convert a GMPY `mpq` object to `dtype`. (RR3(R4R/R5((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pyt from_QQ_gmpy[scC s||jj||ƒƒS(s*Convert a mpmath `mpf` object to `dtype`. (RR3(R4R/R5((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pytfrom_RealField_scC s |j|kr|j|ƒSdS(s*Convert an algebraic number to ``dtype``. N(RR(R4R/R5((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pytfrom_AlgebraicFieldcscC s3y|j|jƒSWnttfk r.dSXdS(s#Convert a polynomial to ``dtype``. N(tset_ringR RRR (R4R/R5((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pytfrom_PolynomialRinghscC sT|j|ƒj|j|ƒƒ\}}|jrL|j||jjjƒƒSdSdS(s*Convert a rational function to ``dtype``. N( tnumertdivtdenomtis_zeroR=tfieldR t to_domainR (R4R/R5tqtr((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pytfrom_FractionFieldos' cC s|jjƒjƒS(s(Returns a field associated with `self`. (R tto_fieldRC(R((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pyt get_fieldxscC s|jj|jƒS(s%Returns True if `LC(a)` is positive. (Rt is_positivetLC(RR/((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pyRI|scC s|jj|jƒS(s%Returns True if `LC(a)` is negative. (Rt is_negativeRJ(RR/((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pyRK€scC s|jj|jƒS(s)Returns True if `LC(a)` is non-positive. (Rtis_nonpositiveRJ(RR/((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pyRL„scC s|jj|jƒS(s)Returns True if `LC(a)` is non-negative. (Rtis_nonnegativeRJ(RR/((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pyRMˆscC s |j|ƒS(sExtended GCD of `a` and `b`. (tgcdex(RR/tb((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pyRNŒscC s |j|ƒS(sReturns GCD of `a` and `b`. (tgcd(RR/RO((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pyRPscC s |j|ƒS(sReturns LCM of `a` and `b`. (tlcm(RR/RO((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pyRQ”scC s|j|jj|ƒƒS(sReturns factorial of `a`. (R Rt factorial(RR/((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pyRR˜sN(%R*t __module__t__doc__Rtis_PolynomialRingtis_Polythas_assoc_Ringthas_assoc_FieldR RRtpropertyRR RR'R+R-R0R2R6R7R8R9R:R;R=RFRHRIRKRLRMRNRPRQRR(((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pyR s>                      N(RTt __future__RRtsympy.polys.domains.ringRt#sympy.polys.domains.compositedomainRtsympy.polys.polyerrorsRRtsympy.utilitiesRR(((sAlib/python2.7/site-packages/sympy/polys/domains/polynomialring.pyts