DomainAndRange[Function[{Subscript[a, 0], Subscript[a, 1], \[Ellipsis], Subscript[a, n]}, Root[Function[z, Sum[Subscript[a, j] z^j, {j, 0, n}]], k]]] == PowerSet[Complexes, n + 1] \[LongRightArrow] Complexes

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 0 </mn> </msub> <mo> &#8902; </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> &#8902; </mo> <mo> &#8230; </mo> <mo> &#8902; </mo> <msub> <mi> a </mi> <mi> n </mi> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#10230; </mo> <msubsup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <msub> <mi> a </mi> <mi> j </mi> </msub> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> j </mi> </msup> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> </mrow> <mo> &#8759; </mo> <mrow> <msup> <mi> &#8450; </mi> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#10230; </mo> <mi> &#8450; </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportion </ci> <apply> <ci> LongRightArrow </ci> <apply> <ci> Star </ci> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 0 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> n </ci> </apply> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <apply> <ci> CompoundExpression </ci> <ci> z </ci> <apply> <sum /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> j </ci> </apply> <apply> <power /> <ci> z </ci> <ci> j </ci> </apply> </apply> </apply> </apply> <ci> k </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> LongRightArrow </ci> <apply> <power /> <ci> &#8450; </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> <ci> &#8450; </ci> </apply> </apply> </annotation-xml> </semantics> </math>

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2001-10-29