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Round




Mathematica Notation

Traditional Notation









Integer Functions > Round[z] > Zeros





http://functions.wolfram.com/04.03.30.0001.01









  


  








Input Form





Round[z] == 0 /; -(1/2) <= Re[z] <= 1/2 && -(1/2) <= Im[z] <= 1/2








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Round", "[", "z", "]"]], "\[Equal]", "0"]], "/;", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "\[LessEqual]", RowBox[List["Re", "[", "z", "]"]], "\[LessEqual]", FractionBox["1", "2"]]], "\[And]", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "\[LessEqual]", RowBox[List["Im", "[", "z", "]"]], "\[LessEqual]", FractionBox["1", "2"]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mo> &#8970; </mo> <mi> z </mi> <mo> &#8969; </mo> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> &#8804; </mo> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8804; </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> &#8804; </mo> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8804; </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <mo> &#8970; </mo> <mi> z </mi> <mo> &#8969; </mo> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> &#8804; </mo> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8804; </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> &#8804; </mo> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8804; </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Round", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "\[LessEqual]", RowBox[List["Re", "[", "z", "]"]], "\[LessEqual]", FractionBox["1", "2"]]], "&&", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "\[LessEqual]", RowBox[List["Im", "[", "z", "]"]], "\[LessEqual]", FractionBox["1", "2"]]]]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29