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Abs




Mathematica Notation

Traditional Notation









Complex Components > Abs[z] > Transformations > Addition formulas





http://functions.wolfram.com/12.01.16.0008.01









  


  








Input Form





Abs[Subscript[z, 1] + Subscript[z, 2]] == Abs[Subscript[z, 1]] + Abs[Subscript[z, 2]] + Abs[Abs[Subscript[z, 1]] - Abs[Subscript[z, 2]]] - Abs[Subscript[z, 1] - Subscript[z, 2]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Abs", "[", RowBox[List[SubscriptBox["z", RowBox[List[" ", "1"]]], "+", SubscriptBox["z", RowBox[List[" ", "2"]]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["Abs", "[", SubscriptBox["z", RowBox[List[" ", "1"]]], "]"]], "+", RowBox[List["Abs", "[", SubscriptBox["z", RowBox[List[" ", "2"]]], "]"]], "+", RowBox[List["Abs", "[", RowBox[List[RowBox[List["Abs", "[", SubscriptBox["z", RowBox[List[" ", "1"]]], "]"]], "-", RowBox[List["Abs", "[", SubscriptBox["z", RowBox[List[" ", "2"]]], "]"]]]], "]"]], "-", RowBox[List["Abs", "[", RowBox[List[SubscriptBox["z", RowBox[List[" ", "1"]]], "-", SubscriptBox["z", RowBox[List[" ", "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> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> - </mo> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> </mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> - </mo> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <abs /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <abs /> <apply> <plus /> <apply> <abs /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <abs /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <abs /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <abs /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <abs /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Abs", "[", RowBox[List[SubscriptBox["z_", "1"], "+", SubscriptBox["z_", "2"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Abs", "[", SubscriptBox["zz", "1"], "]"]], "+", RowBox[List["Abs", "[", SubscriptBox["zz", "2"], "]"]], "+", RowBox[List["Abs", "[", RowBox[List[RowBox[List["Abs", "[", SubscriptBox["zz", "1"], "]"]], "-", RowBox[List["Abs", "[", SubscriptBox["zz", "2"], "]"]]]], "]"]], "-", RowBox[List["Abs", "[", RowBox[List[SubscriptBox["zz", "1"], "-", SubscriptBox["zz", "2"]]], "]"]]]]]]]]


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





2001-10-29