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Floor




Mathematica Notation

Traditional Notation









Integer Functions > Floor[z] > Complex characteristics > Signum value





http://functions.wolfram.com/04.01.19.0011.01









  


  








Input Form





Sign[Floor[x + I y]] == Floor[x + I y]/Abs[Floor[x + I y]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Sign", "[", RowBox[List["Floor", "[", RowBox[List["x", "+", RowBox[List["\[ImaginaryI]", " ", "y"]]]], "]"]], "]"]], "\[Equal]", FractionBox[RowBox[List["Floor", "[", RowBox[List["x", "+", RowBox[List["\[ImaginaryI]", " ", "y"]]]], "]"]], RowBox[List["Abs", "[", RowBox[List["Floor", "[", RowBox[List["x", "+", RowBox[List["\[ImaginaryI]", " ", "y"]]]], "]"]], "]"]]]]]]]








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> sgn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mo> &#8970; </mo> <mrow> <mi> x </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> y </mi> </mrow> </mrow> <mo> &#8971; </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <mo> &#8970; </mo> <mrow> <mi> x </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> y </mi> </mrow> </mrow> <mo> &#8971; </mo> </mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mrow> <mo> &#8970; </mo> <mrow> <mi> x </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> y </mi> </mrow> </mrow> <mo> &#8971; </mo> </mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Sign </ci> <apply> <floor /> <apply> <plus /> <ci> x </ci> <apply> <times /> <imaginaryi /> <ci> y </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <floor /> <apply> <plus /> <ci> x </ci> <apply> <times /> <imaginaryi /> <ci> y </ci> </apply> </apply> </apply> <apply> <power /> <apply> <abs /> <apply> <floor /> <apply> <plus /> <ci> x </ci> <apply> <times /> <imaginaryi /> <ci> y </ci> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Sign", "[", RowBox[List["Floor", "[", RowBox[List["x_", "+", RowBox[List["\[ImaginaryI]", " ", "y_"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["Floor", "[", RowBox[List["x", "+", RowBox[List["\[ImaginaryI]", " ", "y"]]]], "]"]], RowBox[List["Abs", "[", RowBox[List["Floor", "[", RowBox[List["x", "+", RowBox[List["\[ImaginaryI]", " ", "y"]]]], "]"]], "]"]]]]]]]


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





2007-05-02