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Ceiling




Mathematica Notation

Traditional Notation









Integer Functions > Ceiling[z] > Transformations > Transformations and argument simplifications > Argument involving basic arithmetic operations





http://functions.wolfram.com/04.02.16.0005.01









  


  








Input Form





Ceiling[I z] == -Floor[Im[z]] + I Ceiling[Re[z]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Ceiling", "[", RowBox[List["\[ImaginaryI]", " ", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", RowBox[List["Floor", "[", RowBox[List["Im", "[", "z", "]"]], "]"]]]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Ceiling", "[", RowBox[List["Re", "[", "z", "]"]], "]"]]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> &#8968; </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> &#8969; </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mrow> <mo> &#8970; </mo> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8971; </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> &#8968; </mo> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8969; </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ceiling /> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <floor /> <apply> <imaginary /> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <ceiling /> <apply> <real /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Ceiling", "[", RowBox[List["\[ImaginaryI]", " ", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", RowBox[List["Floor", "[", RowBox[List["Im", "[", "z", "]"]], "]"]]]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Ceiling", "[", RowBox[List["Re", "[", "z", "]"]], "]"]]]]]]]]]]


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





2001-10-29