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FractionalPart




Mathematica Notation

Traditional Notation









Integer Functions > FractionalPart[z] > Complex characteristics > Absolute value





http://functions.wolfram.com/04.05.19.0008.01









  


  








Input Form





Abs[FractionalPart[z]] == Sqrt[FractionalPart[Re[z]]^2 + FractionalPart[Im[z]]^2]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Abs", "[", RowBox[List["FractionalPart", "[", "z", "]"]], "]"]], "\[Equal]", RowBox[List["\[Sqrt]", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["FractionalPart", "[", RowBox[List["Re", "[", "z", "]"]], "]"]], "2"], "+", SuperscriptBox[RowBox[List["FractionalPart", "[", RowBox[List["Im", "[", "z", "]"]], "]"]], "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> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mrow> <mi> frac </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> &#10869; </mo> <msqrt> <mrow> <msup> <mrow> <mi> frac </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mrow> <mi> frac </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <abs /> <apply> <ci> FractionalPart </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <ci> FractionalPart </ci> <apply> <imaginary /> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> FractionalPart </ci> <apply> <real /> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Abs", "[", RowBox[List["FractionalPart", "[", "z_", "]"]], "]"]], "]"]], "\[RuleDelayed]", SqrtBox[RowBox[List[SuperscriptBox[RowBox[List["FractionalPart", "[", RowBox[List["Re", "[", "z", "]"]], "]"]], "2"], "+", SuperscriptBox[RowBox[List["FractionalPart", "[", RowBox[List["Im", "[", "z", "]"]], "]"]], "2"]]]]]]]]


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





2007-05-02