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FractionalPart




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/04.05.27.0003.01









  


  








Input Form





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








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["FractionalPart", "[", "z", "]"]], "\[Equal]", RowBox[List["z", "-", RowBox[List["Round", "[", RowBox[List["z", "-", FractionBox[RowBox[List["1", "+", "\[ImaginaryI]"]], "2"]]], "]"]], "-", "1", "-", "\[ImaginaryI]", "-", RowBox[List["CharacteristicFunction", "[", RowBox[List[FractionBox[RowBox[List[" ", RowBox[List[RowBox[List["Re", "[", "z", "]"]], "+", "1"]]]], "2"], ",", "Integers"]], "]"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["CharacteristicFunction", "[", RowBox[List[FractionBox[RowBox[List[" ", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "+", "1"]]]], "2"], ",", "Integers"]], "]"]]]], "+", RowBox[List["Sign", "[", RowBox[List[RowBox[List["UnitStep", "[", RowBox[List["Re", "[", "z", "]"]], "]"]], "+", RowBox[List["CharacteristicFunction", "[", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ",", "Integers"]], "]"]]]], "]"]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Sign", "[", RowBox[List[RowBox[List["UnitStep", "[", RowBox[List["Im", "[", "z", "]"]], "]"]], "+", RowBox[List["CharacteristicFunction", "[", RowBox[List[RowBox[List["Im", "[", "z", "]"]], ",", "Integers"]], "]"]]]], "]"]]]]]]]]]]








MathML Form







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Rule Form





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


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





2001-10-29