Otjm,dZddlmZddlmZddlmZddlmZddl m Z m Z m Z m Z mZddlmZddlmZdd lmZdd lmZdd lmZd Zd ZdZdZedZdS)z0Tools for constructing domains for expressions. )prod)sympify) pure_complex)ordered)ZZQQZZ_IQQ_IEX) ComplexField) RealField) build_options)parallel_dict_from_basic)publiccdx}x}x}}g}|jdurd}nd}|D]}|jr |jsd}|jr|rdSd}||7t |} | rad}| \} } | jr| jr| jr| jsd}nd}| jr|| | jr|| ||r|rdSd}dS|rt d|Dnd} |rt||\} n`|r|rt| n=|rt| n*|s|j r|rtntn|rtntfd |D} | fS) z?Handle simple domains, e.g.: ZZ, QQ, RR and algebraic domains. FTc|jo|jSN is_number is_algebraiccoeffs U/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/sympy/polys/constructor.pyz#_construct_simple..sU_%K9KcdS)NFrs rrz#_construct_simple..sUrNc3$K|] }|jV dSr_prec.0cs r z$_construct_simple..>$22q17222222r5precc:g|]}|Sr) from_sympy)r"rdomains r z%_construct_simple..Ls'???u&##E**???r) extension is_Rational is_Integeris_Floatappendrmax_construct_algebraicr r fieldr rr r)coeffsopt rationalsfloats complexes algebraics float_numbersrr is_complexxymax_precresultr+s @r_construct_simplerAs3277I77ZM }KK ** !!   # ! ^  ,uu$$U++++%e,,J  !1= 0Q] 0L)Q\)$( !Fz0%,,Q///z0%,,Q///e$$ ! 55! tt7DKs22M222222H @-fc::  /i /!x000FF  /H---FF  /#) /&.TTBFF&.TTBF??????? 6>rc ddlm}t fd  |}tt  | dd\}}t dt | D}tj|fj c  fd|D}tt | fd fd |D} |fS) zDWe know that coefficients are algebraic so construct the extension. r)primitive_elementcg}|D]}|jrdtj|f}nM|jrd|jf}n3|jrd|jf}nd|f}||||S)NQ+*e)r.rr*is_Addargsis_Muladdr1)rJtreesatree build_treesextss rrPz)_construct_algebraic..build_treesWs  A} R]1--. [[001 [[001Qx LL     rT)expolysc3&K|] \}}||zV dSrr)r"sexts rr$z'_construct_algebraic..js*33Cqu333333rcRg|]#}j|t$Sr)dtype from_listr)r"hr+gs rr,z(_construct_algebraic..ns-<<.convert_tree..v+66A Q666666rrGc3.K|]}|VdSrrr^s rr$z=_construct_algebraic..convert_tree..xr`rrH)rXrYrsumzeror RuntimeError)rOoprJr_r+exts_mapr[s rr_z*_construct_algebraic..convert_treeqsD 99<))4&!R88 8 3YY6666666 DD D 3YY666666666 6 3YYD> ! rc&g|] }|Srr)r"rOr_s rr,z(_construct_algebraic..~s# 3 3 3Tll4  3 3 3r) sympy.polys.numberfieldsrCsetlistrrbzipralgebraic_fieldrepto_listdict)r5r6rCrMspanHrootexts_domr@rPr_r+rQrfr[s @@@@@@rr3r3QsJ:::::: 55D       K  E   D""4D===JAtQ 333tT??333 3 3D"At9--qu}}IFA<<<<rc:gg}}|D]C}|\}}||||Dt||z\}}|sdS|jBt d|DrdSt } |D]} | j} | | zrdS| | z} t|} t|dz} |d| }|| d}|jrd}n'dd| z}}|D]}t|dks||vrd}nt }|sXt||D]F\}}||}| D]$\}}||z}| ||||<%Gn~t||D]m\}}| t|| t|ndx}x}}g}|D]}|jr |jsd}|jrd}||2t%|}|`d}|\}}|jr|jr|jr|jsd}id}|jr|||jr|||rt'd|Dnd }|r|rt)| }n8|rt+| }n%|r|rt,}nt.}n|rt0}nt2}g}|s`|j|}|D]R}| D]\}}||||<|||Sn|j|}t||D]\}}| D]\}}||||<| D]\}}||||<||||f||fS) z.s,BBcs}1!1BBBBBBrTF)rc3$K|] }|jV dSrrr!s rr$z'_construct_composite..r%rr&r')as_numer_denomr1r compositeanyri free_symbolslenr4rkitemsrLupdaterjvaluesr.r/r0rr2r r r r rr poly_ringr* frac_field)r5r6numersdenomsrnumerdenomrSgens all_symbolsrvsymbolsnk fractionszerosmonomr7r8r9r;r<r=r>r?groundr@r+s r_construct_compositers"FF++-- u e e*6F?;;KE4 t } BBTBBB B B 4ee  ' 'C&GW$ 'ttw&  D A E A A 2A2YF 122YF y  $q&5   E5zzA~~e!3!3 "4UUF  0// % %LE5%LE %  % % u 5!!!$e  % % // 0 0LE5 MM$u||~~.. / / / MM$u||~~.. / / / /%**I*M00   0# ! ^ 0F   ' ' ' '%e,,J% !1=0Q]0L)Q\)$( !Fz0%,,Q///z0%,,Q///6CKs22M222222H ) 8,,,  )))   FFFF  F 2!!4( ) )E %  8 8 u%0077e MM&&-- ( ( ( (  ) #"D)// 2 2LE5 %  8 8 u%0077e %  8 8 u%0077e MM&&%00 1 1 1 1 6>rcvtg}}|D]*}|||+||fS)z6The last resort case, i.e. use the expression domain. )r r1r*)r5r6r+r@rs r_construct_expressionrsGFF00 f''..//// 6>rc t|}t|drXt|tr@|sgg}}n?t t t |\}}n|}n|g}t tt|}t||}||dur|\}}nKt||\}}n7|j durd}nt||}||\}}nt||\}}t|drEt|tr,|tt t ||fS||fS||dfS)aT Construct a minimal domain for a list of expressions. Explanation =========== Given a list of normal SymPy expressions (of type :py:class:`~.Expr`) ``construct_domain`` will find a minimal :py:class:`~.Domain` that can represent those expressions. The expressions will be converted to elements of the domain and both the domain and the domain elements are returned. Parameters ========== obj: list or dict The expressions to build a domain for. **args: keyword arguments Options that affect the choice of domain. Returns ======= (K, elements): Domain and list of domain elements The domain K that can represent the expressions and the list or dict of domain elements representing the same expressions as elements of K. Examples ======== Given a list of :py:class:`~.Integer` ``construct_domain`` will return the domain :ref:`ZZ` and a list of integers as elements of :ref:`ZZ`. >>> from sympy import construct_domain, S >>> expressions = [S(2), S(3), S(4)] >>> K, elements = construct_domain(expressions) >>> K ZZ >>> elements [2, 3, 4] >>> type(elements[0]) # doctest: +SKIP >>> type(expressions[0]) If there are any :py:class:`~.Rational` then :ref:`QQ` is returned instead. >>> construct_domain([S(1)/2, S(3)/4]) (QQ, [1/2, 3/4]) If there are symbols then a polynomial ring :ref:`K[x]` is returned. >>> from sympy import symbols >>> x, y = symbols('x, y') >>> construct_domain([2*x + 1, S(3)/4]) (QQ[x], [2*x + 1, 3/4]) >>> construct_domain([2*x + 1, y]) (ZZ[x,y], [2*x + 1, y]) If any symbols appear with negative powers then a rational function field :ref:`K(x)` will be returned. >>> construct_domain([y/x, x/(1 - y)]) (ZZ(x,y), [y/x, -x/(y - 1)]) Irrational algebraic numbers will result in the :ref:`EX` domain by default. The keyword argument ``extension=True`` leads to the construction of an algebraic number field :ref:`QQ(a)`. >>> from sympy import sqrt >>> construct_domain([sqrt(2)]) (EX, [EX(sqrt(2))]) >>> construct_domain([sqrt(2)], extension=True) # doctest: +SKIP (QQ, [ANP([1, 0], [1, 0, -2], QQ)]) See also ======== Domain Expr __iter__NFr) rhasattr isinstancerorjrkrmaprrArr{r)objrJr6monomsr5r@r+s rconstruct_domainr sf   CsJ  c4   ?!#R!%c4 +<+<&=!>!>FF #gv&& ' 'F vs + +F    #NFFF263??NFFF =E ! !FF)&#66F  #NFFF263??NFFsJ! c4  "4S%8%8 9 9::: :6> !vay  rN)__doc__mathr sympy.corersympy.core.evalfrsympy.core.sortingrsympy.polys.domainsrrr r r sympy.polys.domains.complexfieldr sympy.polys.domains.realfieldr sympy.polys.polyoptionsrsympy.polys.polyutilsrsympy.utilitiesrrAr3rrrrrrrsC66))))))&&&&&&66666666666666999999333333111111::::::""""""???D///dzzzzx!x!x!x!x!r