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Round




Mathematica Notation

Traditional Notation









Integer Functions > Round[z] > Representations through equivalent functions > With related functions > With IntegerPart > For complex arguments





http://functions.wolfram.com/04.03.27.0003.01









  


  








Input Form





Round[z] == IntegerPart[z + (1 + I)/2] - 1 - I - I CharacteristicFunction[(1/4) (-1 + 2 Im[z]), Integers] - CharacteristicFunction[(1/4) (-1 + 2 Re[z]), Integers] + I Sign[CharacteristicFunction[1/2 + Im[z], Integers] + UnitStep[1/2 + Im[z]]] + Sign[CharacteristicFunction[1/2 + Re[z], Integers] + UnitStep[1/2 + Re[z]]]








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Round", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["IntegerPart", "[", RowBox[List["z", "+", FractionBox[RowBox[List["1", "+", "\[ImaginaryI]"]], "2"]]], "]"]], "-", "1", "-", "\[ImaginaryI]", "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["CharacteristicFunction", "[", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", RowBox[List["Im", "[", "z", "]"]]]]]], ")"]]]], ",", "Integers"]], "]"]]]], "-", RowBox[List["CharacteristicFunction", "[", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", RowBox[List["Re", "[", "z", "]"]]]]]], ")"]]]], ",", "Integers"]], "]"]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Sign", "[", RowBox[List[RowBox[List["CharacteristicFunction", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", RowBox[List["Im", "[", "z", "]"]]]], ",", "Integers"]], "]"]], "+", RowBox[List["UnitStep", "[", RowBox[List[FractionBox["1", "2"], "+", RowBox[List["Im", "[", "z", "]"]]]], "]"]]]], "]"]]]], "+", RowBox[List["Sign", "[", RowBox[List[RowBox[List["CharacteristicFunction", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", RowBox[List["Re", "[", "z", "]"]]]], ",", "Integers"]], "]"]], "+", RowBox[List["UnitStep", "[", RowBox[List[FractionBox["1", "2"], "+", RowBox[List["Re", "[", "z", "]"]]]], "]"]]]], "]"]]]]]]]]


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





2001-10-29