+ im,Rt^RIHt^RIHt^RIHt^RIHt^RI H t H t H t H t Ht^RIHt^RIHt^RIHt^R IHt^R IHtR tR tR tRt]R4tR#)z0Tools for constructing domains for expressions. )prod)sympify) pure_complex)ordered)ZZQQZZ_IQQ_IEX) ComplexField) RealField) build_options)parallel_dict_from_basic)publiccRR;p;p;rE.pVPRJdRpMRpVEF1pVP'dVP'gRpK,K.VP'd!V'dR#RpVP V4K`\ V4p V 'dRpV wrV P'd;V P'd)V P'dV P'gRpKRpV P'dVP V 4V P'dVP V 4EKEKV!V4'dV'dR#RpEK1R# V'd\ RV44M^5p V'd\W4wrW3#V'dV'd\V R7p MXV'd\V R7p MCV'gVP'dV'd\M\p MV'd\M\p VUu.uFqPV4NK ppW3#uupi)z?Handle simple domains, e.g.: ZZ, QQ, RR and algebraic domains. FTcBVP;'d VP#N is_number is_algebraiccoeffs&w/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/sympy/polys/constructor.py#_construct_simple..sU__%K%K9K9K%KcR#)Frs&rrrsUrNc38"TFqPxK R#5ir_prec.0cs& r $_construct_simple..>2Mq77Mprec) extension is_Rational is_Integeris_Floatappendrmax_construct_algebraicr r fieldr rrr from_sympy)coeffsopt rationalsfloats complexes algebraics float_numbersrr is_complexxymax_precdomainresults&& r_construct_simpler@s277I77M }}K *     ### $ ^^^$$U+%e,J !===Q]]]LLLQ\\\$( !Fzzz%,,Q/zzz%,,Q/"e$$ ! CJ7Ds2M22H-f: > i!x0F H-F #)))&TBF&TBF8>?u##E*? >@sH$ca a a aaa^RIHp\4oV V3Rlo S !V4p\\ S44oV!SRRR7worE\ R\ VS444p\P!SV34SPP4uo oVUu.uF$pS PPVS\4NK& pp\\ SV44oV V VV3Rlo VU u.uF p S !V 4NK p p S V 3#uupiuup i)zDWe know that coefficients are algebraic so construct the extension. )primitive_elementc\<.pVFpVP'dR\P!V43pMcVP'dRS!VP43pM.build_treesWsA}}}R]]1-.[01[01Qx LL  rT)expolysc36"TFwrW,xK R#5irr)r"sexts& rr$'_construct_algebraic..js3?quu?sc<VwrVR8Xd#SPPV.S\4#VR8Xd!\V3RlV4SP4#VR8Xd\ V3RlV44#VR8Xd SV,#\ h)rDrEc34<"TF pS!V4xK R#5irrr"rM convert_trees& rr$=_construct_algebraic..convert_tree..v6A QrFc34<"TF pS!V4xK R#5irrrZs& rr$r\xr]r^rG)dtype from_listrsumzeror RuntimeError)rNoprIr[r>exts_mapgs& rr[*_construct_algebraic..convert_treeqsy 9<<))4&!R8 8 3Y66 D D 3Y666 6 3YD> ! r)sympy.polys.numberfieldsrBsetlistrrbzipralgebraic_fieldrepto_listr`radict)r3r4rBrLspanHroothexts_domrNr?rOr[r>rPrfrgs&& @@@@@@rr0r0Qs: 5D   E  D"4D=JAt 33tT?3 3D""At9-quu}}IFA:;%= 4s *D)Dc` ..r2VF7pVP4wrVVPV4VPV4K9 \W#,4wrxV'gR#VPfu\;QJdRV4F 'gK RM RM !RV44'dR#\ 4p VF(p V P p W,'dR#W,p K* \V4p \V4^,p VRV pW}RpVP'dRpM-RRV ,rVFp\V4^8g W9gKRpM \ 4pV'gV\W#4FEwrVVX,pVP4F#wppWF,pVPV4WEV&K% KG Md\W#4FUwrVVP\VP444VP\VP444KW R;p;pp.pVEFpVP'dVP 'gRpK,K.VP"'dRpVPV4KU\%V4pVfKfRpVwppVP'd=VP'd+VP 'dVP 'gRpKKRpVP"'dVPV4VP"'gKVPV4EK V'd\'RV44M^5pV'dV'd\)VR7pMHV'd\+VR7pM3V'dV'd\,pM\.pMV'd\0pM\2p.pV'gcVP4!V!pVFHpVP4FwppVP7V4VV&K VPV!V44KJ VV3#VP8!V!p\W#4FywrVVP4FwppVP7V4VV&K VP4FwppVP7V4VV&K VPV!WV344K{ VV3#)z.s#BTc}}11!1!11Ts..TFc38"TFqPxK R#5irrr!s& rr$ryr&r'r())as_numer_denomr.r compositeanyrj free_symbolslenr1rlitemsrKupdaterkvaluesr+r,r-rr/r r r rrr poly_ringr2 frac_field)r3r4numersdenomsrnumerdenomrSgens all_symbolsrxsymbolsnk fractionszerosmonomr5r6r7r9r:r;r<r=groundr?r>s&& r_construct_compositersF++-  e e  +6?;KE  }} 3BTB333BTB B Be C&&G$$&  D A E A A 2AYF 2YF yyy  $q&5E5zA~!3  UF /LE%LE % u 5!$e !.0 /LE MM$u||~. / MM$u||~. /0&+*I*M    ### $ ^^^F   '%e,J% !1===Q]]]LLLQ\\\$( .:"Fzzz%,,Q/zzz%,,Q/),7Ds2M22H )8, )  FF  F !!4(E % u%007e !. MM&- ( " 6>""D)/LE % u%007e !.!& u%007e !. MM&%0 10 6>rch\.r2VF#pVPVPV44K% W#3#)z6The last resort case, i.e. use the expression domain. )r r.r2)r3r4r>r?rs&& r_construct_expressionrs4F f''./ >rc x\V4p\VR4'dR\V\4'd9V'g..rCM2\ \ \ VP 44!4wr4MTpMV.p\ \\V44p\WB4pVeVRJdVwrdMB\WB4wrdM4VPRJdRpM \WB4pVeVwrdM \WB4wrd\VR4'd:\V\4'd!V\\ \ XV4443#Wd3#Wd^,3#)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__NF) r hasattr isinstancerprkrlrmaprr@rr}r)objrIr4monomsr3r?r>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.domainsrrrr r sympy.polys.domains.complexfieldr sympy.polys.domains.realfieldr sympy.polys.polyoptionsr sympy.polys.polyutilsrsympy.utilitiesrr@r0rrrrrrrsW6)&66931:"?D/dzzx!x!r