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FTcSs |jo |jSNZ is_number is_algebraiccoeffrV/var/www/html/bwave/python/venv/lib/python3.8/site-packages/sympy/polys/constructor.pyz#_construct_simple..cSsdS)NFrrrrrrrNcss|] }|jVqdSrZ_prec.0crrr >sz$_construct_simple..5preccsg|]}|qSr) from_sympy)rrdomainrr Lsz%_construct_simple..) extension is_Rational is_Integeris_Floatappendrmax_construct_algebraicr r fieldr rrr)coeffsopt rationalsfloats complexesZ algebraics float_numbersrr is_complexxymax_precresultrr"r_construct_simplesX          r8c sddlm}tfdd|}tt|ddd\}}tddt|D}t|fj fd d |D}t t|fd d fd d |D}|fS)zDWe know that coefficients are algebraic so construct the extension. r)primitive_elementcspg}|D]b}|jr"dt|f}n>|jr8d|jf}n(|jrNd|jf}nd|f}|||q|S)NQ+*e)r&rr!Zis_AddargsZis_Muladdr))r>treesatree) build_treesextsrrrCWs  z)_construct_algebraic..build_treesT)expolyscss|]\}}||VqdSrr)rsextrrrrjsz'_construct_algebraic..csg|]}j|tqSr)dtype from_listr)rh)r#grrr$nsz(_construct_algebraic..csz|\}}|dkr"j|gtS|dkrDtfdd|DjS|dkrbtfdd|DS|dkrr|StdS)Nr:r;c3s|]}|VqdSrrrrA convert_treerrrvsz=_construct_algebraic..convert_tree..r<c3s|]}|VqdSrrrMrNrrrxsr=)rIrJrsumzeror RuntimeError)rBopr>)rOr#exts_maprLrrrOqsz*_construct_algebraic..convert_treecsg|] }|qSrr)rrBrNrrr$~s) Zsympy.polys.numberfieldsr9setlistrrPziprZalgebraic_fieldrepZto_listdict) r-r.r9r@spanHrootZexts_domr7r)rCrOr#rDrTrLrr+Qs   r+cCsgg}}|D]$}|\}}||||qt||\}}|sLdS|jdkrtdd|DrldSt} |D] } | j} | | @rdS| | O} qvt|} t|d} |d| }|| d}|jrd}n8dd| }}|D]$}t|dks||krd}qqt}|sbt ||D]@\}}||}| D]$\}}||}| ||||<q6qn:t ||D].\}}| t || t |qld}}}g}|D]}|jr|jsNd}n|jrd}||nlt|}|dk rd}|\}}|jr&|jr&|jr |jsNd}n(d}|jr<|||jr||q|rjtd d|Dnd }|r|rt|d }n:|rt|d }n(|r|rt}nt}n|rt}nt}g}|s|j|}|D]6}| D]\}}||||<q|||qnv|j|}t ||D]`\}}| D]\}}||||<q6| D]\}}||||<qX||||fq&||fS) z.TF)rcss|] }|jVqdSrrrrrrrsrr)Zas_numer_denomr)r compositeanyrUZ free_symbolslenr,rWitemsr?updaterVvaluesr&r'r(rr*r r r rrrZ poly_ringr!Z frac_field)r-r.ZnumersZdenomsrZnumerdenomrFZgensZ all_symbolsr]symbolsnk fractionsZzerosZmonomr/r0r1r2r3r4r5r6Zgroundr7r#rrr_construct_composites                   rkcCs,tg}}|D]}|||q||fS)z6The last resort case, i.e. use the expression domain. )r r)r!)r-r.r#r7rrrr_construct_expressions rlcKst|}t|drLt|trF|s,gg}}qJttt|\}}qR|}n|g}ttt|}t ||}|dk r|dk r|\}}qt ||\}}n:|j dkrd}n t ||}|dk r|\}}nt ||\}}t|drt|tr|ttt||fS||fSn ||dfSdS)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) r hasattr isinstancerYrVrWrcmaprr8rlr`rk)objr>r.Zmonomsr-r7r#rrrconstruct_domain s2S           rrN)__doc__mathrZ sympy.corerZsympy.core.evalfrZsympy.core.sortingrZsympy.polys.domainsrrrr r Z sympy.polys.domains.complexfieldr Zsympy.polys.domains.realfieldr Zsympy.polys.polyoptionsr Zsympy.polys.polyutilsrZsympy.utilitiesrr8r+rkrlrrrrrrs          B2}