ó ¡¼™\c@ s8dZddlmZmZddlmZmZmZmZm Z m Z m Z ddl m Z ddlmZmZddlmZmZddlmZddlZid d 6d d 6d d6dd6dd6dd6dd6dd6dd6dd6dd6dd 6d!d"6d#d$6d%d&6d'd(6d)d*6d+d,6d-d.6d/d06d1d26d3d46d5d66d7d86d9d:6d;d<6Zd=Zejd>ƒZed?„Zd@„ZdA„ZdB„ZdC„Z dD„Z!dE„Z"dF„Z#dG„Z$dH„Z%dI„Z&dJ„Z'dK„Z(dL„Z)dM„Z*e&Z+e(Z,e*Z-dN„Z.dOe/fdP„ƒYZ0dS(Qs6Useful utilities for higher level polynomial classes. iÿÿÿÿ(tprint_functiontdivision(tStAddtMultPowtExprt expand_multexpand_multinomial(trange(tdecompose_powertdecompose_power_rat(tPolynomialErrortGeneratorsError(t build_optionsNi-tai.tbi/tci0tdi1tei2tfi3tgi4thi5tii6tji7tki8tli9tmi:tni;toiØtpiÙtqiÚtriÛtsiÜttiÝtuiÞtvißtwi|txi}tyi~tziès ^(.+?)(\d*)$cC sMtd„|Dƒƒst‚ng|D]8}g|jƒD]}|jdƒjƒd^q9^q&}td„|Dƒƒr‰tdƒ‚ng|D]'\}}|r¨dnd||f^q}tt||ƒƒ}|r1g}g}x@|D]8\\}}}}|r|j|ƒqë|j|ƒqëW||fSt|Œ\}}t|ƒS(s¼Sort the numerical roots putting the real roots first, then sorting according to real and imaginary parts. If ``separated`` is True, then the real and imaginary roots will be returned in two lists, respectively. This routine tries to avoid issue 6137 by separating the roots into real and imaginary parts before evaluation. In addition, the sorting will raise an error if any computation cannot be done with precision. cs s|]}|jVqdS(N(t is_number(t.0R ((s4lib/python2.7/site-packages/sympy/polys/polyutils.pys &siics s+|]!}|D]}|jdkVq qdS(iN(t_prec(R*RR((s4lib/python2.7/site-packages/sympy/polys/polyutils.pys ,ss%could not compute root with precisioni( talltNotImplementedErrort as_real_imagRtanytsortedtziptappendtlist(trootst separatedR Rtkeytimt_R$((s4lib/python2.7/site-packages/sympy/polys/polyutils.pyt_nsorts"  E4 c s¬t|ƒ}id‰‰|dk rfi|j‰‰x.t|jƒD]\}}|dˆ|| t| tj ƒ}} q>nt| ƒ\} }|| ||    !   c sÖˆjdk r!‡fd†}n?ˆjtkr<d„}n$ˆjtk rWd„}n d„}tgƒg}}xJ|D]B}g}|jr¢|j|j }nx t j |ƒD]ù}gi}} xÐt j |ƒD]¿} t | ƒ r | jsý|| ƒr |j| ƒqÕˆjtkr[t| ƒ\} } | dkrm| t| tj ƒ} } qmnt| ƒ\} } | j| dƒ| | | <|j| ƒqÕW|j|| fƒq²W|j|ƒqzWt|dˆƒ}t|ƒi} }x$t|ƒD]\}}|||Dss-non-commutative expressions are not supportedRO(texpandRoR/R ROR|R‰tclone(RsRQRgRRO((s4lib/python2.7/site-packages/sympy/polys/polyutils.pyRŒ?s" cK s(t|t|ƒƒ\}}||jfS(s1Transform an expression into a multinomial form. (t_dict_from_exprRRO(RgRPtrepRQ((s4lib/python2.7/site-packages/sympy/polys/polyutils.pytdict_from_exprOsc s|jtkrtdƒ‚nd„‰|jtk rÍt|tƒsTtdƒ‚n|jƒ}x5t‡fd†tj|ƒDƒƒr—t |ƒ}qcWx2td„tj|ƒDƒƒrÉt |ƒ}q›Wn|j rît ||ƒ\}}nt ||ƒ\}}||ji|d6ƒfS(s1Transform an expression into a multinomial form. s-non-commutative expressions are not supportedcS s+|jo*|jjo*|jjo*|jjS(N(tis_PowR{t is_positivet is_IntegerRztis_Add(Rg((s4lib/python2.7/site-packages/sympy/polys/polyutils.pyt_is_expandable_powZs!sexpression must be of type Exprc3 sC|]9}ˆ|ƒp:|jo:t‡fd†|jDƒƒVqdS(c3 s|]}ˆ|ƒVqdS(N((R*R(R™(s4lib/python2.7/site-packages/sympy/polys/polyutils.pys dsN(tis_MulR/RP(R*R(R™(s4lib/python2.7/site-packages/sympy/polys/polyutils.pys cscs s1|]'}|jo(td„|jDƒƒVqdS(cs s|]}|jVqdS(N(R˜(R*R((s4lib/python2.7/site-packages/sympy/polys/polyutils.pys hsN(RšR/RP(R*R((s4lib/python2.7/site-packages/sympy/polys/polyutils.pys hsRO(RRoR Rt isinstanceRR/RRlRRRORŠR‹R‘(RgRQR“RO((R™s4lib/python2.7/site-packages/sympy/polys/polyutils.pyR’Us   " cG sˆg}xu|jƒD]g\}}|g}x<t||ƒD]+\}}|r8|jt||ƒƒq8q8W|jt|ŒƒqWt|ŒS(s/Convert a multinomial form into an expression. (R…R1R2RRR(R“ROtresultRyRxRwRR((s4lib/python2.7/site-packages/sympy/polys/polyutils.pytexpr_from_dictss cC sOt|ƒ}|jƒ}|jƒ}gtt|ƒƒD] }g^q7}tƒ}x‘|D]‰}yQ|j|ƒ} |j| ƒx.t||ƒD]\} } | j | | ƒqŽWWqYt k ráx|D]} | j dƒqÇWqYXqYWxSt |ƒD]E\} }| |króx*|D]} | | rt dƒ‚qqWqóqóWt t|ƒ|fS(s*Reorder levels using dict representation. isunable to drop generators(R3tkeystvaluesR R<R‚R=R„R1R2R>RKR tmapRN(R“ROtnew_genstmonomstcoeffsR8t new_monomst used_indicesRFRtMtnew_MRRy((s4lib/python2.7/site-packages/sympy/polys/polyutils.pyt _dict_reorder†s(   %        tPicklableWithSlotscB s)eZdZgZdd„Zd„ZRS(sâ Mixin class that allows to pickle objects with ``__slots__``. Examples ======== First define a class that mixes :class:`PicklableWithSlots` in:: >>> from sympy.polys.polyutils import PicklableWithSlots >>> class Some(PicklableWithSlots): ... __slots__ = ['foo', 'bar'] ... ... def __init__(self, foo, bar): ... self.foo = foo ... self.bar = bar To make :mod:`pickle` happy in doctest we have to use these hacks:: >>> from sympy.core.compatibility import builtins >>> builtins.Some = Some >>> from sympy.polys import polyutils >>> polyutils.Some = Some Next lets see if we can create an instance, pickle it and unpickle:: >>> some = Some('abc', 10) >>> some.foo, some.bar ('abc', 10) >>> from pickle import dumps, loads >>> some2 = loads(dumps(some)) >>> some2.foo, some2.bar ('abc', 10) cC sš|dkr|j}ni}x<|jD]1}t|dƒr(|j|j||ƒƒq(q(Wx6|jD]+}t||ƒrgt||ƒ||sJ4  " 0 %    3 J