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Ceiling




Mathematica Notation

Traditional Notation









Integer Functions > Ceiling[z] > Specific values > Specialized values





http://functions.wolfram.com/04.02.03.0003.01









  


  








Input Form





Ceiling[x + I y] == Ceiling[x] + I Ceiling[y] /; Element[x, Reals] && Element[y, Reals]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Ceiling", "[", RowBox[List["x", "+", RowBox[List["\[ImaginaryI]", " ", "y"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["Ceiling", "[", "x", "]"]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Ceiling", "[", "y", "]"]]]]]]]], "/;", RowBox[List[RowBox[List["Element", "[", RowBox[List["x", ",", "Reals"]], "]"]], "\[And]", " ", RowBox[List["Element", "[", RowBox[List["y", ",", "Reals"]], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <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> &#10869; </mo> <mrow> <mrow> <mo> &#8968; </mo> <mi> x </mi> <mo> &#8969; </mo> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> &#8968; </mo> <mi> y </mi> <mo> &#8969; </mo> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> x </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> y </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ceiling /> <apply> <plus /> <ci> x </ci> <apply> <times /> <imaginaryi /> <ci> y </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <ceiling /> <ci> x </ci> </apply> <apply> <times /> <imaginaryi /> <apply> <ceiling /> <ci> y </ci> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> x </ci> <reals /> </apply> <apply> <in /> <ci> y </ci> <reals /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Ceiling", "[", RowBox[List["x_", "+", RowBox[List["\[ImaginaryI]", " ", "y_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Ceiling", "[", "x", "]"]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Ceiling", "[", "y", "]"]]]]]], "/;", RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "&&", RowBox[List["y", "\[Element]", "Reals"]]]]]]]]]]


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





2001-10-29