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Max






Mathematica Notation

Traditional Notation









Elementary Functions > Max[x1 ,x2,...] > Representations through equivalent functions





http://functions.wolfram.com/01.34.27.0002.01









  


  










Input Form





Max[Subscript[x, 1], Subscript[x, 2], Subscript[x, 3]] == Subscript[x, 2] + (Subscript[x, 1] - Subscript[x, 2]) UnitStep[Subscript[x, 1] - Subscript[x, 2]] + UnitStep[Subscript[x, 3] - Subscript[x, 2]] (Subscript[x, 3] - Subscript[x, 2] - (Subscript[x, 1] - Subscript[x, 2]) UnitStep[Subscript[x, 1] - Subscript[x, 2]]) (UnitStep[Subscript[x, 2] - Subscript[x, 1]] + UnitStep[Subscript[x, 1] - Subscript[x, 2]] UnitStep[Subscript[x, 3] - Subscript[x, 1]])










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Max", "[", RowBox[List[SubscriptBox["x", "1"], ",", SubscriptBox["x", "2"], ",", SubscriptBox["x", "3"]]], "]"]], "\[Equal]", RowBox[List[SubscriptBox["x", "2"], "+", RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["x", "1"], "-", SubscriptBox["x", "2"]]], ")"]], " ", RowBox[List["UnitStep", "[", RowBox[List[SubscriptBox["x", "1"], "-", SubscriptBox["x", "2"]]], "]"]]]], "+", " ", RowBox[List[RowBox[List["UnitStep", "[", RowBox[List[SubscriptBox["x", "3"], "-", SubscriptBox["x", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["x", "3"], "-", SubscriptBox["x", "2"], "-", RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["x", "1"], "-", SubscriptBox["x", "2"]]], ")"]], " ", RowBox[List["UnitStep", "[", RowBox[List[SubscriptBox["x", "1"], "-", SubscriptBox["x", "2"]]], "]"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["UnitStep", "[", RowBox[List[SubscriptBox["x", "2"], "-", SubscriptBox["x", "1"]]], "]"]], "+", RowBox[List[RowBox[List["UnitStep", "[", RowBox[List[SubscriptBox["x", "1"], "-", SubscriptBox["x", "2"]]], "]"]], " ", RowBox[List["UnitStep", "[", RowBox[List[SubscriptBox["x", "3"], "-", SubscriptBox["x", "1"]]], "]"]]]]]], ")"]]]]]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> max </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> x </mi> <mn> 2 </mn> </msub> <mo> , </mo> <msub> <mi> x </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <msub> <mi> x </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> x </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <semantics> <mi> &#952; </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> x </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <semantics> <mi> &#952; </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <msub> <mi> x </mi> <mn> 3 </mn> </msub> <mo> - </mo> <msub> <mi> x </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <semantics> <mi> &#952; </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <msub> <mi> x </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> x </mi> <mn> 1 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mrow> <semantics> <mi> &#952; </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <msub> <mi> x </mi> <mn> 3 </mn> </msub> <mo> - </mo> <msub> <mi> x </mi> <mn> 1 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <semantics> <mi> &#952; </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> x </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> x </mi> <mn> 3 </mn> </msub> <mo> - </mo> <msub> <mi> x </mi> <mn> 2 </mn> </msub> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> x </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <semantics> <mi> &#952; </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> x </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mtext> </mtext> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <max /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <ci> UnitStep </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <ci> UnitStep </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <ci> UnitStep </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <ci> UnitStep </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> UnitStep </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <ci> UnitStep </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Max", "[", RowBox[List[SubscriptBox["x_", "1"], ",", SubscriptBox["x_", "2"], ",", SubscriptBox["x_", "3"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SubscriptBox["xx", "2"], "+", RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["xx", "1"], "-", SubscriptBox["xx", "2"]]], ")"]], " ", RowBox[List["UnitStep", "[", RowBox[List[SubscriptBox["xx", "1"], "-", SubscriptBox["xx", "2"]]], "]"]]]], "+", RowBox[List[RowBox[List["UnitStep", "[", RowBox[List[SubscriptBox["xx", "3"], "-", SubscriptBox["xx", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["xx", "3"], "-", SubscriptBox["xx", "2"], "-", RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["xx", "1"], "-", SubscriptBox["xx", "2"]]], ")"]], " ", RowBox[List["UnitStep", "[", RowBox[List[SubscriptBox["xx", "1"], "-", SubscriptBox["xx", "2"]]], "]"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["UnitStep", "[", RowBox[List[SubscriptBox["xx", "2"], "-", SubscriptBox["xx", "1"]]], "]"]], "+", RowBox[List[RowBox[List["UnitStep", "[", RowBox[List[SubscriptBox["xx", "1"], "-", SubscriptBox["xx", "2"]]], "]"]], " ", RowBox[List["UnitStep", "[", RowBox[List[SubscriptBox["xx", "3"], "-", SubscriptBox["xx", "1"]]], "]"]]]]]], ")"]]]]]]]]]]










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





2001-10-29





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