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FractionalPart




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/04.05.27.0031.01









  


  








Input Form





FractionalPart[x] == x - Quotient[x, 1] - 1 + Sign[UnitStep[x] + CharacteristicFunction[x, Integers]] /; Element[x, Reals]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["FractionalPart", "[", "x", "]"]], "\[Equal]", RowBox[List["x", "-", RowBox[List["Quotient", "[", RowBox[List["x", ",", "1"]], "]"]], "-", "1", "+", RowBox[List["Sign", "[", RowBox[List[RowBox[List["UnitStep", "[", "x", "]"]], "+", RowBox[List["CharacteristicFunction", "[", RowBox[List["x", ",", "Integers"]], "]"]]]], "]"]]]]]], "/;", 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> <mi> frac </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> x </mi> <mo> - </mo> <mrow> <mi> quotient </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> x </mi> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 1 </mn> <mo> + </mo> <mrow> <mi> sgn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msub> <mi> &#967; </mi> <mi> &#8484; </mi> </msub> <mo> ( </mo> <mtext> </mtext> <mi> x </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <semantics> <mi> &#952; </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mi> x </mi> <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'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> FractionalPart </ci> <ci> x </ci> </apply> <apply> <plus /> <ci> x </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> quotient </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> <apply> <ci> Sign </ci> <apply> <plus /> <apply> <apply> <ci> Subscript </ci> <ci> &#967; </ci> <ci> &#8484; </ci> </apply> <ci> x </ci> </apply> <apply> <ci> UnitStep </ci> <ci> x </ci> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> x </ci> <reals /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["FractionalPart", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["x", "-", RowBox[List["Quotient", "[", RowBox[List["x", ",", "1"]], "]"]], "-", "1", "+", RowBox[List["Sign", "[", RowBox[List[RowBox[List["UnitStep", "[", "x", "]"]], "+", RowBox[List["CharacteristicFunction", "[", RowBox[List["x", ",", "Integers"]], "]"]]]], "]"]]]], "/;", RowBox[List["x", "\[Element]", "Reals"]]]]]]]]


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





2007-05-02