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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 isinstancerer`rarrmaprr<rrnr)objrCr1monomsr0r;r&rrrconstruct_domain s2S           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<r.rrrrrrrs"         B2}