\hm,SrSSKJr SSKJr SSKJr SSKJr SSK J r J r J r J r Jr SSKJr SSKJr SS KJr SS KJr SS KJr S rS rSrSr\S5rg)z0Tools for constructing domains for expressions. )prod)sympify) pure_complex)ordered)ZZQQZZ_IQQ_IEX) ComplexField) RealField) build_options)parallel_dict_from_basic)publiccS=n=n=pE/nURSLaSnOSnUGH!nUR(aUR(dSnM*M,UR(aU(a gSnUR U5 M[[ U5n U (aSnU upU R(a7U R(a&U R(aU R(dSnMSnU R(aUR U 5 U R(aUR U 5 GMGMU"U5(aU(a gSnGM" g U(a[ SU55OSn U(a[X5upX4$U(aU(a [U S9n OPU(a [U S9n O?U(dUR(aU(a[O[n OU(a[O[n UVs/sHoRU5PM nnX4$s snf) z?Handle simple domains, e.g.: ZZ, QQ, RR and algebraic domains. 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M? Od[X#5HUupVUR[UR555 UR[UR555 MW S=n=nn/nUHnUR(aUR (dSnM)M+UR"(aSnURU5 MQ[%U5nUcMaSnUunnUR(a9UR(a(UR (aUR (dSnMMSnUR"(aURU5 UR"(dMURU5 M U(a['SU55OS nU(aU(a [)US 9nOAU(a [+US 9nO0U(aU(a[,nO[.nOU(a[0nO[2n/nU(daUR4"U6nUHHnUR5HunnUR7U5UU'M URU"U55 MJ UU4$UR8"U6n[X#5HyupVUR5HunnUR7U5UU'M UR5HunnUR7U5UU'M URU"XV455 M{ UU4$) z.s BTc}}1!1!11Ts+-TF)rc38# UHoRv M g7frr r"s rr%r{r'r(r)r*)as_numer_denomr0r compositeanyrl free_symbolslenr3rnitemsrMupdatermvaluesr-r.r/rr1r r r r rr poly_ringr4 frac_field)r5r6numersdenomsrnumerdenomrUgens all_symbolsrzsymbolsnk fractionszerosmonomr7r8r9r;r<r=r>r?groundrAr@s r_construct_compositersF++-  e e  +6?;KE  }} BTB B Be C&&G$&  D A E A A 2AYF 2YF yy  $q&5E5zA~!3  UF /LE%LE % u 5!$e !.0 /LE MM$u||~. / MM$u||~. /0&+*I*M   ## $ ^^F   '%e,J% !1==Q]]LLQ\\$( .:"Fzz%,,Q/zzz%,,Q/),7Ds2M22H )8, )  FF  F !!4(E % u%007e !. MM&- ( " 6>""D)/LE % u%007e !.!& u%007e !. MM&%0 10 6>rch[/p2UH#nURURU55 M% X#4$)z6The last resort case, i.e. use the expression domain. )r r0r4)r5r6r@rArs r_construct_expressionrs4F f''./ >rc \[U5n[US5(aN[U[5(a6U(d//pCO1[ [ [ UR 5565up4OUnOU/n[ [[U55n[XB5nUbUSLaUupdO@[XB5updO2URSLaSnO [XB5nUbUupdO [XB5upd[US5(a8[U[5(a U[[ [ WU5554$Xd4$XdS4$)adConstruct 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 isinstancerrrmrnrmaprrBrrr)objrKr6monomsr5rAr@s rconstruct_domainr sf  CsJ c4 !#R!%c4 +<&=!>F #gv& 'F v +F   #NFF26?NFF ==E !F)&6F  #NFF26?NFsJ c4 4S%8 9:: :> !ay  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.utilitiesrrBr2rrrrrrrsW6)&66931:"?D/dzzx!x!r