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Round




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/04.03.19.0011.01









  


  








Input Form





Sign[Round[x + I y]] == (Round[x] + I Round[y])/Sqrt[Round[x]^2 + Round[y]^2]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Sign", "[", RowBox[List["Round", "[", RowBox[List["x", "+", RowBox[List["\[ImaginaryI]", " ", "y"]]]], "]"]], "]"]], "\[Equal]", FractionBox[RowBox[List[RowBox[List["Round", "[", "x", "]"]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Round", "[", "y", "]"]]]]]], SqrtBox[RowBox[List[SuperscriptBox[RowBox[List["Round", "[", "x", "]"]], "2"], "+", SuperscriptBox[RowBox[List["Round", "[", "y", "]"]], "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> <mi> sgn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mo> &#8968; </mo> <mrow> <mi> x </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> y </mi> </mrow> </mrow> <mo> &#8969; </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <mtext> </mtext> <mrow> <mrow> <mo> &#8970; </mo> <mi> x </mi> <mo> &#8969; </mo> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mtext> </mtext> <mrow> <mo> &#8970; </mo> <mi> y </mi> <mo> &#8969; </mo> </mrow> </mrow> </mrow> </mrow> <msqrt> <mrow> <mtext> </mtext> <mrow> <msup> <mrow> <mo> &#8970; </mo> <mi> x </mi> <mo> &#8969; </mo> </mrow> <mn> 2 </mn> </msup> <mo> + </mo> <mtext> </mtext> <msup> <mrow> <mo> &#8970; </mo> <mi> y </mi> <mo> &#8969; </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mrow> </msqrt> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mi> sgn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mo> &#8968; </mo> <mrow> <mi> x </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> y </mi> </mrow> </mrow> <mo> &#8969; </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <mtext> </mtext> <mrow> <mrow> <mo> &#8970; </mo> <mi> x </mi> <mo> &#8969; </mo> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mtext> </mtext> <mrow> <mo> &#8970; </mo> <mi> y </mi> <mo> &#8969; </mo> </mrow> </mrow> </mrow> </mrow> <msqrt> <mrow> <mtext> </mtext> <mrow> <msup> <mrow> <mo> &#8970; </mo> <mi> x </mi> <mo> &#8969; </mo> </mrow> <mn> 2 </mn> </msup> <mo> + </mo> <mtext> </mtext> <msup> <mrow> <mo> &#8970; </mo> <mi> y </mi> <mo> &#8969; </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mrow> </msqrt> </mfrac> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Sign", "[", RowBox[List["Round", "[", RowBox[List["x_", "+", RowBox[List["\[ImaginaryI]", " ", "y_"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["Round", "[", "x", "]"]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Round", "[", "y", "]"]]]]]], SqrtBox[RowBox[List[SuperscriptBox[RowBox[List["Round", "[", "x", "]"]], "2"], "+", SuperscriptBox[RowBox[List["Round", "[", "y", "]"]], "2"]]]]]]]]]


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





2007-05-02