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Round




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/04.03.27.0019.01









  


  








Input Form





Round[x] == x - FractionalPart[x + 1/2] - 1/2 - CharacteristicFunction[ (2 x - 1)/4, Integers] + Sign[CharacteristicFunction[1/2 + x, Integers] + UnitStep[1/2 + x]] /; Element[x, Reals]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Round", "[", "x", "]"]], "\[Equal]", RowBox[List["x", "-", RowBox[List["FractionalPart", "[", RowBox[List["x", "+", FractionBox["1", "2"]]], "]"]], "-", FractionBox["1", "2"], "-", RowBox[List["CharacteristicFunction", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["2", "x"]], "-", "1"]], "4"], ",", "Integers"]], "]"]], "+", RowBox[List["Sign", "[", RowBox[List[RowBox[List["CharacteristicFunction", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", "x"]], ",", "Integers"]], "]"]], "+", RowBox[List["UnitStep", "[", RowBox[List[FractionBox["1", "2"], "+", "x"]], "]"]]]], "]"]]]]]], "/;", RowBox[List["x", "\[Element]", "Reals"]]]]]]








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> x </mi> <mo> &#8969; </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> x </mi> <mo> - </mo> <mrow> <mi> frac </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> x </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> - </mo> <mrow> <msub> <mi> &#967; </mi> <mi> &#8484; </mi> </msub> <mo> ( </mo> <mfrac> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> x </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 4 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> sgn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msub> <mi> &#967; </mi> <mi> &#8484; </mi> </msub> <mo> ( </mo> <mrow> <mi> x </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> &#952; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> x </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> x </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <mo> &#8970; </mo> <mi> x </mi> <mo> &#8969; </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> x </mi> <mo> - </mo> <mrow> <mi> frac </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> x </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> - </mo> <mrow> <msub> <mi> &#967; </mi> <mi> &#8484; </mi> </msub> <mo> ( </mo> <mfrac> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> x </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 4 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> sgn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msub> <mi> &#967; </mi> <mi> &#8484; </mi> </msub> <mo> ( </mo> <mrow> <mi> x </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> &#952; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> x </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> x </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Round", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["x", "-", RowBox[List["FractionalPart", "[", RowBox[List["x", "+", FractionBox["1", "2"]]], "]"]], "-", FractionBox["1", "2"], "-", RowBox[List["CharacteristicFunction", "[", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "x"]], "-", "1"]], ")"]]]], ",", "Integers"]], "]"]], "+", RowBox[List["Sign", "[", RowBox[List[RowBox[List["CharacteristicFunction", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", "x"]], ",", "Integers"]], "]"]], "+", RowBox[List["UnitStep", "[", RowBox[List[FractionBox["1", "2"], "+", "x"]], "]"]]]], "]"]]]], "/;", RowBox[List["x", "\[Element]", "Reals"]]]]]]]]


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





2007-05-02